Review Article
1) Article Reference
Pan TC, Kao JJ (2009) GA-QP Model to Optimize Sewer System Design, JOURNAL OF ENVIRONMENTAL ENGINEERING, 135(1) 17-24
2) Summary
This paper presents an application of genetic algorithms to optimize the design of a sewer system. A case study is presented to illustrate the methodology using system composed of 79 links, 56 nodes and a drainage area of 260 ha.
The author’s presents a discussion of the complexity of designing a sewer system targeting the minimum cost, maintaining the system hydraulic and construction constraints. A description of the concepts of genetic algorithm is also presented including all its elements and behavior. For this problem the decision variable of the sewer are coded as genes and each chromosome represents one design. The first constraint assures that the pipe has enough flow capacity, the second constraint takes care of ensuring the downstream pipe has diameter equal or greater then the upstream neighbor. It is also considered the possibility of installing a pump in each node. The fitness function is used considering the construction cost of the network. A description of the selection, crossover and mutation methods is provided. For this particular study, the author used also a quadratic programming (QP) model, to improve efficiency, the nonlinear cost fitness function was approximated to a QP. The design parameters for this case study were the maximum velocity, minimum velocity, minimum slope, maximum proportional water depth and minimum cover depth. To avoid finding a solution which was not the true best, due to simplifications or factors that are hard to formulate into the model, it was also used a MGA function.
Different results for the case study were presented achieving a minimum cost of approximate 1.7 million dollars. According to the author the GA and quadratic model approach were satisfactory to find a good solution for the problem.
3) Discussion
It really surprised me to see that this paper was published in 2009 and nobody had ever tried such approach for solving sewer systems network. After all our classes, I felt quite confident in understating all the terminology and the methodology for solving the GA presented in this paper. Actually I think the paper had even too much of GA theory instead of new contributions for science. The best part, I think, is that I feel very encouraged to apply GA optimization methods for my research area.
Tuesday, April 28, 2009
Assignment #10a - Optimization in public sector
Review Article
1) Article Reference
BRILL ED (1979) USE OF OPTIMIZATION MODELS IN PUBLIC-SECTOR PLANNING, MANAGEMENT SCIENCE, 25
2) Summary
This paper dates from the seventies and deals with the use of optimization models applied to public sector problem solving. According to the authors, many optimization models were concentrated in finding the best economic solution, but failure to consider equity and have empirical shortcoming in estimating benefits and costs. The author also suggests that multi objective programming can examine tradeoffs between different objectives and mention the use of goal programming as well. Many limitations to the use of optimization techniques are pointed, specially related to complete and incomplete multi objective programming, with some examples as the planning of a lakeside park with solutions favoring boaters or swimmers and the location of regional facilities.
An important issue, as pointed by the author, is that usually optimization models have been used to find the “answer” for the public sector, considering the economic efficiency and social optimality. As empirical problems arise, new approaches had to be developed. Among many reasons pointed by the author, the fact that many of the problems are wicked, demonstrated the difficulty to find one best approach for solving this problems.
A general flow chart on how to use optimization techniques for the planning process is presented and some alternatives discussed in more detail such as the join use of models: optimization and simulation; analytical and optimization; and using a toolbox of models. Several examples are presented, including one study developed in the Netherlands to analyze the implementation of an estuary dam, considering several factors such as flood protection, ecological aspects, costs and social impacts providing elements for the parliament ultimate decision.
Two main advantages by that time are pointed by the author as the capability of generating alternatives and facilitating evaluations and generating alternative solutions that are different from each other.
The author finally concludes that although multiojective planning in the way it was developed by his time, “as the second generation of optimization techniques”, had improved the way of solving optimization problems, but was still limited to the wicked organization of public sector problems. He also argues that such techniques should be used to gain insights about the problem itself, develop alternative scenarios and support human creativity to find the best solutions of a problem.
3) Discussion
I personally think it is great to have a historical overview on how the author, and scientific community, is approaching optimization problems. Besides the historical importance, I think an important issue that puts his discussion a little out of date is the considerable advance of computer potential and capacity to solve mathematical problems nowadays.
1) Article Reference
BRILL ED (1979) USE OF OPTIMIZATION MODELS IN PUBLIC-SECTOR PLANNING, MANAGEMENT SCIENCE, 25
2) Summary
This paper dates from the seventies and deals with the use of optimization models applied to public sector problem solving. According to the authors, many optimization models were concentrated in finding the best economic solution, but failure to consider equity and have empirical shortcoming in estimating benefits and costs. The author also suggests that multi objective programming can examine tradeoffs between different objectives and mention the use of goal programming as well. Many limitations to the use of optimization techniques are pointed, specially related to complete and incomplete multi objective programming, with some examples as the planning of a lakeside park with solutions favoring boaters or swimmers and the location of regional facilities.
An important issue, as pointed by the author, is that usually optimization models have been used to find the “answer” for the public sector, considering the economic efficiency and social optimality. As empirical problems arise, new approaches had to be developed. Among many reasons pointed by the author, the fact that many of the problems are wicked, demonstrated the difficulty to find one best approach for solving this problems.
A general flow chart on how to use optimization techniques for the planning process is presented and some alternatives discussed in more detail such as the join use of models: optimization and simulation; analytical and optimization; and using a toolbox of models. Several examples are presented, including one study developed in the Netherlands to analyze the implementation of an estuary dam, considering several factors such as flood protection, ecological aspects, costs and social impacts providing elements for the parliament ultimate decision.
Two main advantages by that time are pointed by the author as the capability of generating alternatives and facilitating evaluations and generating alternative solutions that are different from each other.
The author finally concludes that although multiojective planning in the way it was developed by his time, “as the second generation of optimization techniques”, had improved the way of solving optimization problems, but was still limited to the wicked organization of public sector problems. He also argues that such techniques should be used to gain insights about the problem itself, develop alternative scenarios and support human creativity to find the best solutions of a problem.
3) Discussion
I personally think it is great to have a historical overview on how the author, and scientific community, is approaching optimization problems. Besides the historical importance, I think an important issue that puts his discussion a little out of date is the considerable advance of computer potential and capacity to solve mathematical problems nowadays.
Assignment #9 - Compromise programming - instream flow - multiobjective
1) Article Reference
Shiau JT, Wu FC (2006) Compromise programming methodology for determining instream flow under multiobjective water allocation criteria, JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, 42(5), pp. 1179-1191
2) Summary
This paper presents a multiobjective approach for evaluating instream flow water allocation considering increasing water uses within the basin. This approach uses the concept of Range of Variability (RVA) Approach and the Indicators of Hydrologic Alterations (IHAs).
A case study is presented for the Kaoping creek in southwestern Taiwan. Extensive description of the hydrologic and water use characteristics of the basin is provided. Special concerns are related to endangered and endemic species. By date, instream flows are been provide to support the ecological health of the systems, but is believed that those releases are incapable of guarantying sufficient flow variation required for the sustainability of the aquatic biota. Tables presented monthly average inflow and water uses for agricultural and municipal uses within the basin.
For the optimization analyses of the water allocation schemes, a description of the methodology used is provide, including a short review of the Range of Variability Approach concepts and the overall degree of hydrologic alteration. A detailed table is provided to describe the IHAs used in the RVA. The IHAs are grouped in 5 different specifications which represent different hydrologic parameters.
A description of the weir (main diversion point) operation model is also provided. Within this description the operation of the weir and the different water uses are described.
The main goal of the weir is to supply the registered agricultural demand , the projected municipal water supply and the instream flow conditions. Considering the municipal water supply and the agricultural use, the objective is to minimize the shortages periods, represented by a shortage ratio.
To solve the minimization function, the authors used a Multiobjective compromise programming approach. The results evaluated the current schedule operation impacts on water shortages and hydrologic alterations, the effects of different instream flow releases ,the effects of weighting factors and the Ecological Effects of proposed instream flow release
The main conclusions of the paper were that the inclusion of the individual degrees of alteration associated with the 32 IHAs made possible to optimize the weir operation scheme through compromise programming and showed that the current instream releases do not meet minimum requirements for guarantee ecological health downstream.
3) Discussion
I enjoyed reading this paper as it gave me a better sense on the practical application of multi objective problem solving. I think this kind of optimization is very useful, as it really approaches real life problems. Usually there are more than one objective that almost always differ from each other. Although, I think the evaluation of the intream flow necessities could have been better evaluated.
Shiau JT, Wu FC (2006) Compromise programming methodology for determining instream flow under multiobjective water allocation criteria, JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, 42(5), pp. 1179-1191
2) Summary
This paper presents a multiobjective approach for evaluating instream flow water allocation considering increasing water uses within the basin. This approach uses the concept of Range of Variability (RVA) Approach and the Indicators of Hydrologic Alterations (IHAs).
A case study is presented for the Kaoping creek in southwestern Taiwan. Extensive description of the hydrologic and water use characteristics of the basin is provided. Special concerns are related to endangered and endemic species. By date, instream flows are been provide to support the ecological health of the systems, but is believed that those releases are incapable of guarantying sufficient flow variation required for the sustainability of the aquatic biota. Tables presented monthly average inflow and water uses for agricultural and municipal uses within the basin.
For the optimization analyses of the water allocation schemes, a description of the methodology used is provide, including a short review of the Range of Variability Approach concepts and the overall degree of hydrologic alteration. A detailed table is provided to describe the IHAs used in the RVA. The IHAs are grouped in 5 different specifications which represent different hydrologic parameters.
A description of the weir (main diversion point) operation model is also provided. Within this description the operation of the weir and the different water uses are described.
The main goal of the weir is to supply the registered agricultural demand , the projected municipal water supply and the instream flow conditions. Considering the municipal water supply and the agricultural use, the objective is to minimize the shortages periods, represented by a shortage ratio.
To solve the minimization function, the authors used a Multiobjective compromise programming approach. The results evaluated the current schedule operation impacts on water shortages and hydrologic alterations, the effects of different instream flow releases ,the effects of weighting factors and the Ecological Effects of proposed instream flow release
The main conclusions of the paper were that the inclusion of the individual degrees of alteration associated with the 32 IHAs made possible to optimize the weir operation scheme through compromise programming and showed that the current instream releases do not meet minimum requirements for guarantee ecological health downstream.
3) Discussion
I enjoyed reading this paper as it gave me a better sense on the practical application of multi objective problem solving. I think this kind of optimization is very useful, as it really approaches real life problems. Usually there are more than one objective that almost always differ from each other. Although, I think the evaluation of the intream flow necessities could have been better evaluated.
Wednesday, April 1, 2009
Assignment #8 - Neural Network / Reservoir Optimization
Review Article
1) Article Reference
Neelakantan TR, Pundarikanthan NV (2000) “Neural network-based simulation-optimization model for reservoir operation,” JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT, 126(2) pp. 57-64
2) Summary
This paper presents an application of neural network-based simulation optimization model for reservoir operation. A case study is presented for Chennai city, in India. The general framework of the study presented by the author follows: 1) Develop a conventional simulation model to obtain results from different operation policies; 2) Train a back propagation neural network model using those results; 3) Link the neural network model as a sub model with direct search non-linear programming optimization models; 4)Find the optimal policy and near optimal policies using neural network –optimization model; 5)Refine the optimal policies obtained using conventional simulation optimization model and determine the optimal policy.
The optimization is done using the Hookes and Jeeves direct search method. For this case it was considered better to have small water supply restrictions along the time from having one big drought. Then the optimization goal was to minimize the minimum sum of the deficits. For that a deficit index was defined. The optimization procedure started at an initial point and progress using Hookes and Jeeves method until an optimal solution. Several initial points were used as this algorithm can get stacked in local minimums.
A neural network simulation model was used in order to enhance the speed of the process. For this case the authors used a back propagation approach. The network was trained using pairs of input and output vectors.
The decision set was composed of 18 decision variables. Based in inflow pattern the year was divided into six time periods. Four out of five supply levels were considered at each time. The results are presented in two different scenarios. For each scenario, the authors presents the results for 4 different policies including the storage for each time period, the release and the deficit. The inclusion of two additional reservoirs is also analyzed.
As the major result, the authors concluded that the neural network based simulation-optimization model performed satisfactory. Also the authors mention that reservoir operation problems considering several and more complicated networks could be handled by this method.
3) Discussion
The paper presents a very interesting approach to solve a very common reservoir operation problem. I believe several attempts have been made to find methodologies for optimal operation rules for reservoir. I think this is an emerging issue as water demand is increasing significantly in large metropolitan areas and the reservoirs systems have to be used optimally.
1) Article Reference
Neelakantan TR, Pundarikanthan NV (2000) “Neural network-based simulation-optimization model for reservoir operation,” JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT, 126(2) pp. 57-64
2) Summary
This paper presents an application of neural network-based simulation optimization model for reservoir operation. A case study is presented for Chennai city, in India. The general framework of the study presented by the author follows: 1) Develop a conventional simulation model to obtain results from different operation policies; 2) Train a back propagation neural network model using those results; 3) Link the neural network model as a sub model with direct search non-linear programming optimization models; 4)Find the optimal policy and near optimal policies using neural network –optimization model; 5)Refine the optimal policies obtained using conventional simulation optimization model and determine the optimal policy.
The optimization is done using the Hookes and Jeeves direct search method. For this case it was considered better to have small water supply restrictions along the time from having one big drought. Then the optimization goal was to minimize the minimum sum of the deficits. For that a deficit index was defined. The optimization procedure started at an initial point and progress using Hookes and Jeeves method until an optimal solution. Several initial points were used as this algorithm can get stacked in local minimums.
A neural network simulation model was used in order to enhance the speed of the process. For this case the authors used a back propagation approach. The network was trained using pairs of input and output vectors.
The decision set was composed of 18 decision variables. Based in inflow pattern the year was divided into six time periods. Four out of five supply levels were considered at each time. The results are presented in two different scenarios. For each scenario, the authors presents the results for 4 different policies including the storage for each time period, the release and the deficit. The inclusion of two additional reservoirs is also analyzed.
As the major result, the authors concluded that the neural network based simulation-optimization model performed satisfactory. Also the authors mention that reservoir operation problems considering several and more complicated networks could be handled by this method.
3) Discussion
The paper presents a very interesting approach to solve a very common reservoir operation problem. I believe several attempts have been made to find methodologies for optimal operation rules for reservoir. I think this is an emerging issue as water demand is increasing significantly in large metropolitan areas and the reservoirs systems have to be used optimally.
Tuesday, March 24, 2009
Assignment #7 - Infiltration Based BMP Optimization
Review Article
1) Article Reference
Perez-Pedini C, Limbrunner JF, Vogel RM (2005) “Optimal location of infiltration-based best management practices for storm water management,” JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT, 131(6) pp. 441-448
2) Summary
This paper presents an approach to optimize the location of infiltration based best management practices to reduce peak flow during storm events. According to the author many optimization applications were previously developed to find optimal location, design and operation of detention ponds in a watershed to reduce peak flow.
The infiltration based best management practices considered are infiltration basins, rain gardens and pervious pavements. The approach to integrate a wide variety of distributed storage and infiltration storm water controls acting in combination have been called as low impact development (LID).
According to the author the major goal of this study is to introduce a methodology to determine the optimal number and location of infiltration based practices to reduce peak flow. It was used a fully distributed model based on the SCS curve number approach. The model was applied to the Aberjona River watershed. This model was programmed in excel and VBA with a system of 4533 square HRUs that have a side length of 120 m. It was used the D8 algorithm for runoff routing. A detailed description of all mathematical formulas used to model the water movement within the distributed model was presented. This model was then calibrated for a storm event using 15 min storm data from two rain gages and compared with a flow gage at the watershed outlet.
The optimization routines were developed using excel and a commercial available Genetic Algorithm optimizer called Evolver. The overall goal of the optimization was to locate the HRUs which if BMPs were applied, would lead to a maximum reduction of peak flow. Some restrictions were applied in order to reduce the feasible space. The author also provided some details of the constraints used in the Genetic Algorithm programming.
As the main results the authors showed a Trade off curve between the reduction of peak flow and the number of best management practices to be implemented. The optimum locations were also presented in maps showing its location within the watershed. The authors concluded that a GA algorithm with a distributed hydrologic model presented satisfactory results for finding the optimal locations and quantity of BMPs to reduce peak flow.
3) Discussion
These papers are getting better and better to read. This one was especially nice as it is easy to understand and I am more familiar with the concepts used throughout the research. I think the authors had a good idea developing this application as it seems a new approach using consolidated methods. This is quite encouraging as I am feeling that the amount of my understanding of the article is increasing significantly.
Tuesday, March 3, 2009
Assignment #6
Review Article
1) Article Reference
Behera, P, Papa, F., Adams, B (1999) “Optimization of Regional Storm-Water Management Systems” Journal of Water Resources Planning and Management, 125(2) pp. 107-114
2) Summary
The paper discusses the application of optimization methods for storm water management systems. As new lands are being occupied, land developers and municipalities have to deal with runoff quantity and quality control. One of the most common solutions adopted are the implementation of detention ponds followed by a number of Best Management Practices available nowadays. In this case, the detention ponds referred as storm water management (SWM) ponds are considered to control both quantity and quality for a given catchment.
To support finding the best alternative for this projects, optimization using dynamic programming is used to find the best design parameters such as storage volume, release rate and pond depth. The objective is to minimize the costs of implementing the SWM ponds in each of the catchments. The authors consider costs related to the value of land, construction, and operation, maintenance and repair. The decision variables are the active storage volume of the pond, controlled release rate of the pond, and pond depth.
The system constraints are based on two major categories: Runoff Control Performance and Pollution Control Performance. The runoff model inputs statistical meteorological data and transform to runoff considering catchment hydrology and control systems hydraulics. The pollution control is modeled considering the average annual fraction of suspended solids removed from the SWM pond.
The constrains and the conceptual models for the optimization of SWM pond design for single catchment are explained as well as the previous work done in the area and the assumptions made. For the multiple parallel catchments the authors also present an specific model, with a optimization function and constrains for pollution control and runoff. Some details about the computations are also provided.
The authors concludes that is possible to optimize SWM ponds using dynamic programming and to achieve optimal design criteria’s considering single catchment and multi-catchment systems with water quantity and quality aspects. They also suggest different uses such as planning activities, preliminary design and scenario analyses.
3) Discussion
I personally enjoyed more this paper than the other previous two. Maybe because I am more familiar with the conceptual models of storm water systems and I actually find this area more interesting. One thing that really surprised me was to realize that the first author of the paper is a graduate student of the civil engineering department like us. As this is the first of this kind we are dealing I still haven’t completely understood the paper. I´m hoping to clarify it better on the class discussion on Wednesday. See you guys there…
1) Article Reference
Behera, P, Papa, F., Adams, B (1999) “Optimization of Regional Storm-Water Management Systems” Journal of Water Resources Planning and Management, 125(2) pp. 107-114
2) Summary
The paper discusses the application of optimization methods for storm water management systems. As new lands are being occupied, land developers and municipalities have to deal with runoff quantity and quality control. One of the most common solutions adopted are the implementation of detention ponds followed by a number of Best Management Practices available nowadays. In this case, the detention ponds referred as storm water management (SWM) ponds are considered to control both quantity and quality for a given catchment.
To support finding the best alternative for this projects, optimization using dynamic programming is used to find the best design parameters such as storage volume, release rate and pond depth. The objective is to minimize the costs of implementing the SWM ponds in each of the catchments. The authors consider costs related to the value of land, construction, and operation, maintenance and repair. The decision variables are the active storage volume of the pond, controlled release rate of the pond, and pond depth.
The system constraints are based on two major categories: Runoff Control Performance and Pollution Control Performance. The runoff model inputs statistical meteorological data and transform to runoff considering catchment hydrology and control systems hydraulics. The pollution control is modeled considering the average annual fraction of suspended solids removed from the SWM pond.
The constrains and the conceptual models for the optimization of SWM pond design for single catchment are explained as well as the previous work done in the area and the assumptions made. For the multiple parallel catchments the authors also present an specific model, with a optimization function and constrains for pollution control and runoff. Some details about the computations are also provided.
The authors concludes that is possible to optimize SWM ponds using dynamic programming and to achieve optimal design criteria’s considering single catchment and multi-catchment systems with water quantity and quality aspects. They also suggest different uses such as planning activities, preliminary design and scenario analyses.
3) Discussion
I personally enjoyed more this paper than the other previous two. Maybe because I am more familiar with the conceptual models of storm water systems and I actually find this area more interesting. One thing that really surprised me was to realize that the first author of the paper is a graduate student of the civil engineering department like us. As this is the first of this kind we are dealing I still haven’t completely understood the paper. I´m hoping to clarify it better on the class discussion on Wednesday. See you guys there…
Sunday, February 22, 2009
Assignment #5 - Sensor Placement in Municipal Water Networks
Review Article
1) Article Reference
Berry, J., Fleisher, L, Hart, W. Phillips, C. and Watson, J.-P. (2005) “Sensor Placement in Municipal Water Networks”, Journal of Water Resources Planning and Management, 131(3) pp. 237-243
2) Summary
This paper presents an approach for determining the placement of contaminant sensors within a municipal water network. To increase the protection of water supply systems, the use of real time early warning systems (EWS), have been widely adopted. Usually, utilities wish to place online sensors so deployment cost is minimized and the level protection maximized.
Considering a variety of approaches, the paper assumes that a attack occurs only in a single point; consider the total population exposed; the sensors protect downstream populations; and transitions between time periods are ignored. With this assumptions the authors simplify health impacts, ignore concentration and temporal effects.
The objective of the model was to minimize the expected fraction of the population that is at risk for some attack. The attack is modeled as a release of contaminant at a single point of the network. It is assumed that any point downstream of the attack can be contaminated. The EPANET water network simulator was used to determine water flow in the network. The attack scenarios were defined by a probability distribution over all pairs of population weighted flow and attacks points (from experts and scenario development).
To solve the optimization problem it was used mixed integer programming were the objective was to minimize the expected number of exposed people. The constraint considered that if a node is directly attacked it is directly contaminated. The second relate that a sensor can cover flow in a pipe in both directions. The third propagates the contaminant along the flow. One constraint is used to limit the maximum number of sensors.
To evaluate the model it was used three data sets. Two dataset were develop in EPANET and one is real. As all three dataset have some missing data, synthetic data was used to complete the datasets. The EPANET was used to determine flow patterns during four six-hour period with a 24 hour time period. The dataset 1 was adapted from Example Network provided by EPANET 2.0 with 36 nodes, 40 pipes and 1 pump station. The dataset 2 was adapted from Example Network 3 from EPANET 2.0 with 97 nodes, 117 pipes, two reservoirs and three tanks. The dataset 3 was adapted from a real world data with 470 nodes, 621 pipes, three pumps and four tanks.
The results are presented numerically in three tables. For dataset 1 and 2 the maximum number of sensors was 7 while for dataset 3 the maximum was 300. The authors present a comprehensive discussion about the numerical results and some explanations about the unlikely or unexpected outcomes. The conclusions showed that mixed integer programming can be used effectively to solve large scale sensor placement problems. Some ideas of the model generalization are presented relating the temporal effects, placement locations, sensor costs, and performance objective.
3) Discussion
I found this article useful to better understand optimization problems and it s applications and more specifically the integer programming method. I found it very similar to the previous paper. I couldn’t find any problems with the problem proposed. Further research suggestions would be to apply this methodology to real real life problems.
The objective of the model was to minimize the expected fraction of the population that is at risk for some attack. The attack is modeled as a release of contaminant at a single point of the network. It is assumed that any point downstream of the attack can be contaminated. The EPANET water network simulator was used to determine water flow in the network. The attack scenarios were defined by a probability distribution over all pairs of population weighted flow and attacks points (from experts and scenario development).
To solve the optimization problem it was used mixed integer programming were the objective was to minimize the expected number of exposed people. The constraint considered that if a node is directly attacked it is directly contaminated. The second relate that a sensor can cover flow in a pipe in both directions. The third propagates the contaminant along the flow. One constraint is used to limit the maximum number of sensors.
To evaluate the model it was used three data sets. Two dataset were develop in EPANET and one is real. As all three dataset have some missing data, synthetic data was used to complete the datasets. The EPANET was used to determine flow patterns during four six-hour period with a 24 hour time period. The dataset 1 was adapted from Example Network provided by EPANET 2.0 with 36 nodes, 40 pipes and 1 pump station. The dataset 2 was adapted from Example Network 3 from EPANET 2.0 with 97 nodes, 117 pipes, two reservoirs and three tanks. The dataset 3 was adapted from a real world data with 470 nodes, 621 pipes, three pumps and four tanks.
The results are presented numerically in three tables. For dataset 1 and 2 the maximum number of sensors was 7 while for dataset 3 the maximum was 300. The authors present a comprehensive discussion about the numerical results and some explanations about the unlikely or unexpected outcomes. The conclusions showed that mixed integer programming can be used effectively to solve large scale sensor placement problems. Some ideas of the model generalization are presented relating the temporal effects, placement locations, sensor costs, and performance objective.
3) Discussion
I found this article useful to better understand optimization problems and it s applications and more specifically the integer programming method. I found it very similar to the previous paper. I couldn’t find any problems with the problem proposed. Further research suggestions would be to apply this methodology to real real life problems.
Sunday, February 15, 2009
Assignment #4
1) Article Reference
LEE, B. H. and DEININGER, R. A. (1992) “Optimal Locations of Monitoring Stations in Water Distribution Systems”, Journal of Environmental Engineering, 118(1) pp. 4-16
2) Summary
As a requirement of the Safe Drinking Water Act the water quality in water supply systems has to be monitored. Although the sampling frequency and the water quality parameters are prescribed by law, there are no specifications for representatively sampling within the pipe network. Placing a monitoring point in a demand point represents coverage for that specific demand. However this water might be coming from a series of upstream nodes and going to a series of downstream nodes. The water flow path within the network carries water quality information. The nodes upstream or downstream of a monitored node are likely to be known. The water flow in a pipe network is modeled today with a variety of hydraulic models.
The paper presents a small example to demonstrate its methodology. This network with seven nodes and seven demands is used to illustrate the principles of sampling and coverage nodes. “From this network is derived a matrix called the water fraction matrix. From this matrix several knowledge carrying matrices can be derived based on a decision on which fraction of water is acceptable to call a node covered”. A general form algorithm is presented for generating the coverage matrix. To apply this procedure a demand scenario, the flows and the flow directions for a given water distribution system must be knows. Basically one node is chosen arbitrary and all flows upstream are mapped and if the demand is greater than the threshold value its given value one otherwise zero.
An example of the formulation of an optimization model is provided considering the task of placing two monitoring point in a distribution system. The question is where to places this points to maximize the demand coverage. Two sets of variable are used. They are both 0 and 1 value and one represents the whether there is a sampling station or not and the other represents whether the demand is covered or not. A maximization function and constrains are derived for the simple case example.
A case study is presented at the distribution system for the city of Flint, Michigan. The system had 337 pipes, 211 nodes and 14 monitoring points covering 18% of the demands. An integer programming was formulated with 211 constrains, 422 variables and over 6.000 non zero entries in the tableau. The solution was developed using two different programs, the COVER and the COVTOIP. Respectively they are used to solve the hydraulic flows and determine the coverage matrix. An optimal solution if found with a coverage of 54%, considering only one scenario.
The multiple flow scenarios approach permits the inclusion and consideration of the patterns of variation of the demand, such as daily, monthly or seasonally differences. A general optimization equation is provided and a solution for the small example is also provided using LINDO programming.
A second example is provided, with a case study for the city of Cheshire, Connecticut. To model this system four scenarios were used, where each scenario represents a demand and flow pattern pre established. This problem had 245 variables and 197 constrains and was solved using LINDO integer programming code. There were 4 monitoring stations to be optimally placed. The results showed the best location for the monitoring station according with the number of station to be included.
As a conclusion the author demonstrated the importance of an optimal location of monitoring station within a water distribution system as its location can have a great affect in the coverage of the system.
3) Discussion
I really enjoyed reading this article as it is becoming clearer and easier to read this kind of approach. The authors used simple examples to clarify the methodology and presented two specific case studies to illustrate the point. The optimization functions, constrains and the set up of the matrixes were quite interesting. I think further research in this theme would be to verify different methods of optimization and to also implement water quality decays models between the nodes.
LEE, B. H. and DEININGER, R. A. (1992) “Optimal Locations of Monitoring Stations in Water Distribution Systems”, Journal of Environmental Engineering, 118(1) pp. 4-16
2) Summary
As a requirement of the Safe Drinking Water Act the water quality in water supply systems has to be monitored. Although the sampling frequency and the water quality parameters are prescribed by law, there are no specifications for representatively sampling within the pipe network. Placing a monitoring point in a demand point represents coverage for that specific demand. However this water might be coming from a series of upstream nodes and going to a series of downstream nodes. The water flow path within the network carries water quality information. The nodes upstream or downstream of a monitored node are likely to be known. The water flow in a pipe network is modeled today with a variety of hydraulic models.
The paper presents a small example to demonstrate its methodology. This network with seven nodes and seven demands is used to illustrate the principles of sampling and coverage nodes. “From this network is derived a matrix called the water fraction matrix. From this matrix several knowledge carrying matrices can be derived based on a decision on which fraction of water is acceptable to call a node covered”. A general form algorithm is presented for generating the coverage matrix. To apply this procedure a demand scenario, the flows and the flow directions for a given water distribution system must be knows. Basically one node is chosen arbitrary and all flows upstream are mapped and if the demand is greater than the threshold value its given value one otherwise zero.
An example of the formulation of an optimization model is provided considering the task of placing two monitoring point in a distribution system. The question is where to places this points to maximize the demand coverage. Two sets of variable are used. They are both 0 and 1 value and one represents the whether there is a sampling station or not and the other represents whether the demand is covered or not. A maximization function and constrains are derived for the simple case example.
A case study is presented at the distribution system for the city of Flint, Michigan. The system had 337 pipes, 211 nodes and 14 monitoring points covering 18% of the demands. An integer programming was formulated with 211 constrains, 422 variables and over 6.000 non zero entries in the tableau. The solution was developed using two different programs, the COVER and the COVTOIP. Respectively they are used to solve the hydraulic flows and determine the coverage matrix. An optimal solution if found with a coverage of 54%, considering only one scenario.
The multiple flow scenarios approach permits the inclusion and consideration of the patterns of variation of the demand, such as daily, monthly or seasonally differences. A general optimization equation is provided and a solution for the small example is also provided using LINDO programming.
A second example is provided, with a case study for the city of Cheshire, Connecticut. To model this system four scenarios were used, where each scenario represents a demand and flow pattern pre established. This problem had 245 variables and 197 constrains and was solved using LINDO integer programming code. There were 4 monitoring stations to be optimally placed. The results showed the best location for the monitoring station according with the number of station to be included.
As a conclusion the author demonstrated the importance of an optimal location of monitoring station within a water distribution system as its location can have a great affect in the coverage of the system.
3) Discussion
I really enjoyed reading this article as it is becoming clearer and easier to read this kind of approach. The authors used simple examples to clarify the methodology and presented two specific case studies to illustrate the point. The optimization functions, constrains and the set up of the matrixes were quite interesting. I think further research in this theme would be to verify different methods of optimization and to also implement water quality decays models between the nodes.
Sunday, February 8, 2009
Assignment #3: The Tragedy of the Commons
Review Article
1) Article Reference
HARDIN, G. (1968) “The Tragedy of the Commons” Science, 162, pp. 1243 – 1248.
2) Summary
The tragedy of the commons is a classical paper that presents an important recognition by society that a finite resources world would not be able to supply the demands of an exponential increasing human population. Although it was written 40 years ago, by that time, nature was already charging its price and pollution problems become more and more apparent in highly populated places. This recognition can easily be seen as the author says: “A finite world can only support a finite population; therefore the population growth must eventually be equal to zero”. The author analyses the possibility of trying to maximize population and maximize goods and find this goal impossible, as he concludes: “the optimum population is then, less than the maximum”.
The classical story behind the tragedy of commons is based on the example of the “commons” as the place where all the herdsman of a small society would, in common, raised their herbs. The principle of the commons is that everyone could raise it´s herbs inside the collective space. The point is that any rational individual would soon realized that if he increased his number of animals, he would increase not only increase his profit but also share the costs of the resources needed to develop the animal with all society. When each individual increases his herbs to a point where the total herb demand is greater than the resources that the commons could offer, the system collapsed and nobody could than rise their herbs anymore.
The author than point some specific examples of the tragedy of the commons that were taking place by his time. He mentions the national parks that were been overused and over developed. The oceans, which are treated by the nations as a huge “commons”, where each tried to get as much as possible out of it to guarantee it´s profit. The pollution problem illustrates very well the relation of the commons and its tragedy collapse. Pollution in small scale can easily be treated by nature within the natural cycle. But when it overpasses the limit of auto depuration, pollution very quickly demonstrates all the magnitude of the tragedy of the commons.
The author points out the controversial of the United Nations Universal Declaration of Human Rights that states that every family has the right to choose its size. The author recognizes that is very hard for the individuals to give up a share of the commons, as he says “It is a mistake to think that we can control the breeding of mankind in the long run by an appeal to conscience”.
Several alternatives are pointed by the author considering that “Not prohibition, but carefully biased options are what we offer him”. A very good example that society have learned to avoid the tragedy of the commons are the taxes system. Nobody enjoys taxes, but everyone agree to use a compulsory system knowing that in a voluntary system would favor the conscienceless. The author is very prismatic and urges the necessity to control the human breeding is becoming vital to guarantee other and more precious freedoms.
3) Discussion
This paper was published almost 40 years ago at the end of the sixties in a rather different social context than we face today. By that time cold war was taking place in a nuclear world. In the fastest growing cities it was becoming more evident that society was reaching a point where nature could not adequately supply all that mankind was ready to charge.
I think this paper represents the beginning of the human awareness of the earth limited resources and that the increasing population would soon face shortage of basic resources. After this paper many more recent concepts related to this theme have evolved such as pollution control, the sustainable development and clean energies alternatives. Although today we have evolved in many aspects of trying to increase the availability of resources I feel humanity still believes it is possible to maximize population and resources, although it was wisely recognized by the author decades ago that this is not possible.
I recognize that future research within this theme would be how to apply modern optimization techniques to find limits and the best alternatives to use wisely the resources available to an increasing population.
1) Article Reference
HARDIN, G. (1968) “The Tragedy of the Commons” Science, 162, pp. 1243 – 1248.
2) Summary
The tragedy of the commons is a classical paper that presents an important recognition by society that a finite resources world would not be able to supply the demands of an exponential increasing human population. Although it was written 40 years ago, by that time, nature was already charging its price and pollution problems become more and more apparent in highly populated places. This recognition can easily be seen as the author says: “A finite world can only support a finite population; therefore the population growth must eventually be equal to zero”. The author analyses the possibility of trying to maximize population and maximize goods and find this goal impossible, as he concludes: “the optimum population is then, less than the maximum”.
The classical story behind the tragedy of commons is based on the example of the “commons” as the place where all the herdsman of a small society would, in common, raised their herbs. The principle of the commons is that everyone could raise it´s herbs inside the collective space. The point is that any rational individual would soon realized that if he increased his number of animals, he would increase not only increase his profit but also share the costs of the resources needed to develop the animal with all society. When each individual increases his herbs to a point where the total herb demand is greater than the resources that the commons could offer, the system collapsed and nobody could than rise their herbs anymore.
The author than point some specific examples of the tragedy of the commons that were taking place by his time. He mentions the national parks that were been overused and over developed. The oceans, which are treated by the nations as a huge “commons”, where each tried to get as much as possible out of it to guarantee it´s profit. The pollution problem illustrates very well the relation of the commons and its tragedy collapse. Pollution in small scale can easily be treated by nature within the natural cycle. But when it overpasses the limit of auto depuration, pollution very quickly demonstrates all the magnitude of the tragedy of the commons.
The author points out the controversial of the United Nations Universal Declaration of Human Rights that states that every family has the right to choose its size. The author recognizes that is very hard for the individuals to give up a share of the commons, as he says “It is a mistake to think that we can control the breeding of mankind in the long run by an appeal to conscience”.
Several alternatives are pointed by the author considering that “Not prohibition, but carefully biased options are what we offer him”. A very good example that society have learned to avoid the tragedy of the commons are the taxes system. Nobody enjoys taxes, but everyone agree to use a compulsory system knowing that in a voluntary system would favor the conscienceless. The author is very prismatic and urges the necessity to control the human breeding is becoming vital to guarantee other and more precious freedoms.
3) Discussion
This paper was published almost 40 years ago at the end of the sixties in a rather different social context than we face today. By that time cold war was taking place in a nuclear world. In the fastest growing cities it was becoming more evident that society was reaching a point where nature could not adequately supply all that mankind was ready to charge.
I think this paper represents the beginning of the human awareness of the earth limited resources and that the increasing population would soon face shortage of basic resources. After this paper many more recent concepts related to this theme have evolved such as pollution control, the sustainable development and clean energies alternatives. Although today we have evolved in many aspects of trying to increase the availability of resources I feel humanity still believes it is possible to maximize population and resources, although it was wisely recognized by the author decades ago that this is not possible.
I recognize that future research within this theme would be how to apply modern optimization techniques to find limits and the best alternatives to use wisely the resources available to an increasing population.
Monday, February 2, 2009
Assignment #2
Review Article
1) Article Reference
ATWOOD, D., F. and GORELICK, S., M. (1985) “Hydraulic gradient control for groundwater contaminant removal” Journal of Hydrology 76 pp. 85 - 106
2) Summary
This paper presents a methodology for determining an optimal operation schedule for an aquifer restoration plan. The aquifer restoration plan consists of the use of wells for both cleaning up pollutants from the aquifer as well as stopping the flow of the contaminant plume to spread out.
A case study was developed in the Rocky Mountain Arsenal, which is a military facility design to manufacture and process toxic chemicals. This aquifer is located near Denver, Colorado. The study area was chosen due the high quantity of hydrological and geological data available.
The groundwater management plan for pollutant removal basically is consisted of wells for pollutant removal (those wells have to be located inside the pollutant plume) and hydraulic gradient control wells (which have to be located outside the plume area) that are used to control the flow of the groundwater (pumping on high elevations or recharging in low elevations). An optimization model is used to find the best operation plan for this purpose. Note that a pump can be inside the plume at the beginning of the operation, but after some clean up, become outside of the plume and could them be used for hydraulic gradient control.
The equations used to model this process were the finite difference model developed by Trescott et al. (1976) for the ground water movement and the solute transport combined with groundwater flow simulation in the computer code developed by Konikow and Bredehoeft (1978) for pollutant transport. The methodology is dived in two main stages. First the velocity field is assumed based on initial data. Within this stage the plume boundary is estimated. With this information the Contamination distribution is approximated. On Stage 2, the optimization for the best well selection and operation is developed. Based on the known velocity field the solution is checked and some interactive process back in Stage 1 can be developed.
For the optimization model, the objective is to minimize the sum of pumping and recharge rates. One constrain is to guarantee the flow to go inwards in the direction of the center of the plume. For this gradient control constraint detailed information is provided.
The results showed that a best selection of wells and operation schedule could be achieved. The two stage procedure allowed a single global optimization for all 32 pumping periods. A verification of the results is provided by running the model with the chosen conditions.
3) Discussion
I think this paper is very interesting and shows the utility of optimization procedures solving water resources problems. It seems to me that optimizations procedures are intrinsically related to modeling practices in the modern time. The application of models that represent a reality is followed by an optimization procedure that allows the decision makers to choose from a set of alternatives the one that best fits the desiring goals.
Still this paper is a little too advanced for me, as some of the constrains and the matrix operation were not very clear to me. But the good part is I can feel is getting much more easy to understand them and I hoping by the end of the semester we will be pretty close to develop applications such as this one.
1) Article Reference
ATWOOD, D., F. and GORELICK, S., M. (1985) “Hydraulic gradient control for groundwater contaminant removal” Journal of Hydrology 76 pp. 85 - 106
2) Summary
This paper presents a methodology for determining an optimal operation schedule for an aquifer restoration plan. The aquifer restoration plan consists of the use of wells for both cleaning up pollutants from the aquifer as well as stopping the flow of the contaminant plume to spread out.
A case study was developed in the Rocky Mountain Arsenal, which is a military facility design to manufacture and process toxic chemicals. This aquifer is located near Denver, Colorado. The study area was chosen due the high quantity of hydrological and geological data available.
The groundwater management plan for pollutant removal basically is consisted of wells for pollutant removal (those wells have to be located inside the pollutant plume) and hydraulic gradient control wells (which have to be located outside the plume area) that are used to control the flow of the groundwater (pumping on high elevations or recharging in low elevations). An optimization model is used to find the best operation plan for this purpose. Note that a pump can be inside the plume at the beginning of the operation, but after some clean up, become outside of the plume and could them be used for hydraulic gradient control.
The equations used to model this process were the finite difference model developed by Trescott et al. (1976) for the ground water movement and the solute transport combined with groundwater flow simulation in the computer code developed by Konikow and Bredehoeft (1978) for pollutant transport. The methodology is dived in two main stages. First the velocity field is assumed based on initial data. Within this stage the plume boundary is estimated. With this information the Contamination distribution is approximated. On Stage 2, the optimization for the best well selection and operation is developed. Based on the known velocity field the solution is checked and some interactive process back in Stage 1 can be developed.
For the optimization model, the objective is to minimize the sum of pumping and recharge rates. One constrain is to guarantee the flow to go inwards in the direction of the center of the plume. For this gradient control constraint detailed information is provided.
The results showed that a best selection of wells and operation schedule could be achieved. The two stage procedure allowed a single global optimization for all 32 pumping periods. A verification of the results is provided by running the model with the chosen conditions.
3) Discussion
I think this paper is very interesting and shows the utility of optimization procedures solving water resources problems. It seems to me that optimizations procedures are intrinsically related to modeling practices in the modern time. The application of models that represent a reality is followed by an optimization procedure that allows the decision makers to choose from a set of alternatives the one that best fits the desiring goals.
Still this paper is a little too advanced for me, as some of the constrains and the matrix operation were not very clear to me. But the good part is I can feel is getting much more easy to understand them and I hoping by the end of the semester we will be pretty close to develop applications such as this one.
Monday, January 26, 2009
Assignment #1
Review Article 1
1) Article Reference
Liebman, Jon (1976) “Some simple-minded observations on the role of optimization in public systems decision making” Interfaces 6 (4) pp. 102-108
2) Summary
This paper was written in 1976 and presents a very good overview on the constrains for the application of optimization (in this case could be: modeling, operations research, system analysis) in the public sector. The author provides some definitions of public sector and two specific examples of applications by the NY fire department and for a watershed water quality plan.
The main point of the paper is to present the crucial difference in applying optimization to solve wicked and unwicked problems. To clarify the understanding of wicked problems, I´m considering the wikipedia definition “Wicked problem is a phrase used in social planning to describe a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognize. Moreover, because of complex interdependencies, the effort to solve one aspect of a wicked problem may reveal or create other problems.”
According to the author, usually in the past, optimization procedures could have been solved using linear programming methods such as the Simplex method. By this time the analyst had the simple task of processing many alternatives to find the best solution. The author consider that the decision makers in the private sector organizations have often the some goals and objectives, which makes the role of optimization a lot easier and direct. But in the case of the public sector, considering the existence of many different stake-holders, and even the difference between individuals, there are many goals which can be completely different from each other, characterizing a conflict, resulting often in two groups, the winners and the losers.
Optimization procedures have evolved a lot since the limitation of non-linear problems but the increasing perception of the complexity evolved in most of public decision making processes have showed that “optimization can only be useful when the goals are clear and explicit”. Considering that, the author states that instead of “The role of optimization and modeling in nonwicked problems is the selection of a solution among alternatives” is switching to “The role of optimization and modeling in wicked problems is the formulation of alternatives rather than the selection of one of them”. Even though a direct use of optimization models is not appropriate to wicked problems, those models can have a great value for illuminating the conflict, for example: expanding the problem understanding, to formulate alternatives or even to evaluate scenarios.
3) Discussion
a) I think the paper represents a very good overview from the 80´s about the constrains of the application of optimization models to complex or wicked problems. Considering the use of optimization trough history, the author points a moment in time where society is finding that optimization models are as good as the goals provided to them. If the decision makers don’t agree with the some goals, optimization procedures can´t be set to solve them.
b) I don’t see many limitations on this work, as I think is hard to tell what was the reality or the understanding of complex problems by that time.
c) If this where my research I would focus in the point of finding benefits and trying to develop specific applications to improve decision making with optimization models in wicked problems. That would include conflict resolution and processes that try to find the best for all, minimizing the existence of the winner/losers distinction. I find this a very interesting research topic.
______________________________________________________________________________
Review Article 2
1) Article Reference
Karterakis, S., M.; Karatzas, G., P.; NIKOLOS, I., K. and Papadopolou, M., P. (2007) “ Application of linear programming and differential evolutionary optimization methodologies for the solution of coastal subsurface water management problems subject to environmental criteria” Journal
2) Summary
This paper presents an application of optimization methods to solve groundwater management’s problems including environmental criteria. The authors used linear programming and differential evolutionary methods. This study is applied to the coastal region of Hersonissos, Crete.
A comprehensive literature review about optimization applications for environmental issues is presented. To approach the conceptual model and develop the physical model a characterization of the study area is provided among the theoretical concepts used for the simulation of seawater intrusion phenomenon (Sharp interface approach).
The goal of the optimization is to maximize the total extracted water from five selected pumping locations. The constrains are to ensure no further intrusion of the seawater front at ten selected observation well were the calculated hydraulic head should be greater than 102.5m at the end of the 10 year management period.
A brief overview and literature review of linear programming (the simplex method) and heuristic optimization (differential evolution algorithm) is provided. The solutions of the simulations with both methods are compared. A extensive sensitivity analyses is also provided.
The main conclusion for this case study both methods had very similar results, by the exception of one well. The simplex method had much less computer time demand but needs a constantly interaction worth the user and the heuristic methods although requires much more computer time is completely automated.
3) Discussion
I felt really enthusiastic seeing that the Journal of Hydrology is currently publishing applications of optimization procedures for water resources management problems. This is particularly interesting in the sense to show the importance of the subject for my research. I think maybe more management alternatives could have been analyzed. To improve the research I would try different optimization approach and enlarge the alternative scenarios.
A comprehensive literature review about optimization applications for environmental issues is presented. To approach the conceptual model and develop the physical model a characterization of the study area is provided among the theoretical concepts used for the simulation of seawater intrusion phenomenon (Sharp interface approach).
The goal of the optimization is to maximize the total extracted water from five selected pumping locations. The constrains are to ensure no further intrusion of the seawater front at ten selected observation well were the calculated hydraulic head should be greater than 102.5m at the end of the 10 year management period.
A brief overview and literature review of linear programming (the simplex method) and heuristic optimization (differential evolution algorithm) is provided. The solutions of the simulations with both methods are compared. A extensive sensitivity analyses is also provided.
The main conclusion for this case study both methods had very similar results, by the exception of one well. The simplex method had much less computer time demand but needs a constantly interaction worth the user and the heuristic methods although requires much more computer time is completely automated.
3) Discussion
I felt really enthusiastic seeing that the Journal of Hydrology is currently publishing applications of optimization procedures for water resources management problems. This is particularly interesting in the sense to show the importance of the subject for my research. I think maybe more management alternatives could have been analyzed. To improve the research I would try different optimization approach and enlarge the alternative scenarios.
Thursday, January 22, 2009
Assigment # 0 : " What is critical thinking ? "
Hello Everyone!!
I´m currently a 1st year PhD student of Water Resources Engineering in the Civil Engineering Department at Texas A & M University. My back ground is Environmental Engineering (M.Sc.), Hydrology (M.E.) and Civil Engineering (B.S.). My research line is GIS applied to Water Resources under the supervision of Dr. Francisco Olivera.
The main reason why I´m taking this class is to learn more about the mathematical models used for water resources analyses and optimization. My goal this semester within this class is to gain confidence in the selection, application and analyses of different models for water resources systems.
I´m currently a 1st year PhD student of Water Resources Engineering in the Civil Engineering Department at Texas A & M University. My back ground is Environmental Engineering (M.Sc.), Hydrology (M.E.) and Civil Engineering (B.S.). My research line is GIS applied to Water Resources under the supervision of Dr. Francisco Olivera.
The main reason why I´m taking this class is to learn more about the mathematical models used for water resources analyses and optimization. My goal this semester within this class is to gain confidence in the selection, application and analyses of different models for water resources systems.
Now the difficult question: “What is Critical thinking?”
If we look at several definitions for “critical thinking” we will find that each applies better for the context or purpose we want to use it, e.g.: teaching critical thinking, applying critical thinking or developing critical thinking. For example, from Wikipedia: “when using critical thinking one makes a decision or solves the problem of judging what to believe or what to do, but does so in a reflective way”. I think the key here is reflective way. Do whatever is the right thing to do, but always in a reflective way. This means, always think “why”.
I think another key expression that would bring the same meaning would be: “Think outside the box”. Be creative and always try to come up with something new.
Teaching critical thinking within engineering schools is not a direct task. Usually engineers are tough to solve problems using available knowledge. Questioning the available knowledge is not usually part of the recipe. But if we consider that the basis of the engineering work that is done today was developed hundreds years ago, isn’t it inspiring to think: Isn’t there anything new that we can come up with? The advance of science or the development of new knowledge is only going to be possible with critical thinking and people that thinks outside the box…
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