Article Reference:
Tze Chin Pan, Jehng Jung Kao, GA-QP Model to Optimize Sewer System Design, January 2009, Journal of Environmental Engineering
Summary:
The paper explains the importance of optimizing the sewer network (Pipe diameter, pipe slopes, pipe buried depths etc) in reducing the total cost of establishing the sewer system. Optimizing sewer network is difficult because of few typical constraints associated in the design. Typical constraints are – maintaining minimum velocity (for self cleansing), preventing maximum velocity (which causes scouring), upstream elevation greater than the downstream elevation giving sufficient slope for the flow, designing the depth to accommodate the flow of the design capacity, commercially available pipe diameters, and ensuring the diameter of the downstream pipes to be greater or equal than the upstream pipes thereby letting the downstream pipes to carry cumulative flow. Many approaches have been developed to design sewer network. One such approach was using discrete differential dynamic programming (DDDP), but this approach restricts the search space which reduces the opportunities locate global optimum. Pan and Kao used combined GA and QP as QP is a better way of representing a non linear cost function than LP where you need to convert the nonlinear functions to linear by piecewise linearization. As few of the design factors such as geology, traffic impact, people’s preference, land availability etc are not considered in the study as they are difficult to model. Authors mention that the solution obtained from this model would not be feasible when un-modeled factors are evaluated. This paper explains modeling a different Modeling for Generating Alternative (MGA) function to evaluate the difference between the results obtained from GA-QP and DDDP models.
GA Model components-
Genes: Pipe and pumping station locations in binary code
Chromosomes: Pipe diameters and pumping locations which represent a design layout of the sewer system.
Fitness function: Reciprocal of the cost function (1/Cost of chromosome)
Selection Process: Based on greater the area on the wheel higher the probability being chosen (Simpson et.al. 1994)
Crossover: Random mother chromosomes binary (gene) information is exchanged to generate two child chromosomes.
Mutation: Changes the binary information randomly
The values of the genes are randomly produced. All the unacceptable chromosomes are discarded than repairing as it is too complex, thus producing new set of chromosomes. The two major constraints in deciding the acceptability of the chromosomes are – pipe having required flow capacity (i.e dia of pipe should be capable to carry the flow) and maintain flow continuity (i.e d/s dia is greater than the u/s). Fitness function used in the GA model to evaluate the fitness of the chromosomes generated is defined as the reciprocal of the cost function. Therefore chromosomes with high fitness value are superior to the chromosome with low fitness value. Selection, mutation and crossover are used to create new set of chromosomes. As the cost decreases, the fitness value increases thereby occupying greater area on the wheel which increases the probability of being selected for crossover. The Crossover process exchanges pipe diameters and pumping locations of randomly generated chromosomes to generated new set of chromosomes. Mutation randomly changes the binary information in the chromosomes so that they are not stuck with the local optimum.
Quadratic Programming-
This study has used QP to evaluate the fitness value of the chromosome. The objective function includes – construction cost of pipe based on the diameter, depth and the length, construction cost of manhole and construction cost of pumping station. The authors have constrained the flow velocities and depth by limiting the pipe slope. All the sewer pipes need to be buried at a specific depth from the ground so as to be able to connect the household waste flow. Therefore the decision variables associated in this model are pipe slopes and the buried depths of the downstream end of the pipes.
MGA identifies maximally different solutions which could still be regarded as good and different alternatives.
Discussion:
The authors have explained in detail how each component of GA is taken into consideration. Implementation of GA in the real time practical models is clearer to me after reading this paper. It is true as mentioned by Author about the solution not being feasible without taking into account few factors like land availability, geology etc, which is considered to be of major component in the designing procedure. This paper carries out a practical case explanation of importance of having generating alternative solutions as discussed in the earlier article by Brill.The comparison of different results/solutions DDDP, GA, MGA1, and MGA2 clearly explains the importance of having a feasible alternative which could be considered when all the non considered factors are evaluated into these solutions. Every individual sewer system has specific concern which could not be modeled mathematically into the model, this approach of generating alternatives would be helpful to see and evaluate the feasibility of these factors along with the optimization solution obtained from the GA model. This would be more of a practical approach than just optimizing without considering these factors which are vital in the decisions of these systems.
Sunday, April 26, 2009
Assignment # 10 (1)
Article Reference:
E. Downey Brill, The Use of Optimization Models in Public Sector Planning, May 1979, Management Science
Summary:
The paper discusses about how solutions obtained from optimization model for the public sector problems are not very useful as there is a multitude of local optima and as these models do not formulate essential planning elements. Because of this omitted planning elements the solutions may actually lie in the inferior region than along the non-inferior frontier. Many of the early public sector optimization models concentrated majorly on the economic efficiency objective. Two of the difficulties in these models were that they failed considering equity and empirical shortcomings in estimation of benefits and costs. The author’s mention that even by using multi objective model which is used to capture all the issues pertaining to the problem, it would be impractical to generate complete set of trade off relationships.
Author quotes the recommendation made by Liebman that these optimization models should not be used to resolve the wicked problems instead they should be used to provide understanding and insight of the problem which supplements the decision makers. As explained by Liebman if we consider these components in out planning process than our models needs to be formulated differently and using different computer codes to met the requirements. The paper explains the methods of using the optimization model in combination with other models to include the elements of conventional planning and generating alternative solutions which could be used in the planning process. Authors explain about how the optimization could be used to generate alternative solutions and assisting in evaluating the solutions. To enhance these optimization models to aid creative planning process, the generated solutions should meet the minimum required and the solutions should be different. With the help of these alternative solutions the planners are able to gain better understanding of the objective, constraints and relationships of the problem. These generations of alternative solutions acts as catalyst for human creativity and inventions in making new solutions.
Discussion:
This paper is an extension of Liebman’s article who explained about many public sector problems to be wicked problems and these problems could be tackled by understanding, insight and intuitive of the problem. The solutions obtained by the optimization model are usually not very helpful as these do not consider the vital factors which are involved in the planning process, thereby making those solutions infeasible. This paper extends this discussion based on the usage of optimization models and how these models could incorporate all the omitted components of the planning process to land up at practically feasible solutions. I feel the approach of generating alternative solutions is more a practical approach as many models decisions are majorly dependent on the factors which might not be formulated mathematically. With these alternative solutions it would be an aid for the planner to come up with better practical solutions.
E. Downey Brill, The Use of Optimization Models in Public Sector Planning, May 1979, Management Science
Summary:
The paper discusses about how solutions obtained from optimization model for the public sector problems are not very useful as there is a multitude of local optima and as these models do not formulate essential planning elements. Because of this omitted planning elements the solutions may actually lie in the inferior region than along the non-inferior frontier. Many of the early public sector optimization models concentrated majorly on the economic efficiency objective. Two of the difficulties in these models were that they failed considering equity and empirical shortcomings in estimation of benefits and costs. The author’s mention that even by using multi objective model which is used to capture all the issues pertaining to the problem, it would be impractical to generate complete set of trade off relationships.
Author quotes the recommendation made by Liebman that these optimization models should not be used to resolve the wicked problems instead they should be used to provide understanding and insight of the problem which supplements the decision makers. As explained by Liebman if we consider these components in out planning process than our models needs to be formulated differently and using different computer codes to met the requirements. The paper explains the methods of using the optimization model in combination with other models to include the elements of conventional planning and generating alternative solutions which could be used in the planning process. Authors explain about how the optimization could be used to generate alternative solutions and assisting in evaluating the solutions. To enhance these optimization models to aid creative planning process, the generated solutions should meet the minimum required and the solutions should be different. With the help of these alternative solutions the planners are able to gain better understanding of the objective, constraints and relationships of the problem. These generations of alternative solutions acts as catalyst for human creativity and inventions in making new solutions.
Discussion:
This paper is an extension of Liebman’s article who explained about many public sector problems to be wicked problems and these problems could be tackled by understanding, insight and intuitive of the problem. The solutions obtained by the optimization model are usually not very helpful as these do not consider the vital factors which are involved in the planning process, thereby making those solutions infeasible. This paper extends this discussion based on the usage of optimization models and how these models could incorporate all the omitted components of the planning process to land up at practically feasible solutions. I feel the approach of generating alternative solutions is more a practical approach as many models decisions are majorly dependent on the factors which might not be formulated mathematically. With these alternative solutions it would be an aid for the planner to come up with better practical solutions.
Monday, April 13, 2009
Reading Assignment # 9
Article Reference:
Jenq-Tzong Shiau, Fu Chun Wu, Compromise Programming Methodology for Determining Instream Flow Under Multi-Objective Water Allocation Criteria, 2006, Journal of American Water Resource Association
Summary:
The paper by Jenq Tzong and Fu chun determines a quantitative assessment for determining in-stream flow under multi objective water allocation criteria. They explain the concept of compromise programming which is used to optimize water allocation scheme by minimizing hydrologic alterations and water supply shortages. This methodology was applied to a case study of Kaoping diversion weir in Taiwan. The paper focuses on evaluating the hydrologic alterations of the weir and the optimal operation schemes.
The Kaoping diversion weir was constructed to meet the increasing municipal water demands. The design diversion capacity for the municipal use is about 35 cumec. However prior to the construction there was long history of agricultural water withdrawals from the downstream of the Kaoping creek. From the data it is observed that there has been no flow diversion during dry season for meeting municipal demand due to insufficient amount of water. The operation model of weir has three components – meeting the reserved agricultural water demand, providing projected municipal water demand and instream flow release. Based on the environmental protection, they have set different priorities, first being instream flow release, second priority being registered agricultural demand and third priority being projection flow for municipal demand.
Range of variability of approach has been used to evaluate the hydrologic alterations caused by the flow diversions of the weir. RVA assesses the hydrologic regime with respect to 32 ecological relevant indicators of hydrologic alteration (IHA). As suggested by Richter et al. (1998) RVA range of variation for each IHA is taken as 25th and 75th percentile pre diversion values. Weir operations are aimed such that pre diversion flow conditions reach the targeted RVA ranges. Overall degree of hydrologic alteration (D) is estimated to measure the deviation between post impact flow regime and pre impact flow regime. Richter et al. (1998) classified the overall degree of alterations as low, medium and high alteration. Therefore value of D for a particular IHA quantifies the effect of flow diversion on the flow regime. For including these overall hydrologic alteration index needs to be estimated. Richter et al. suggested the method of averaging the 32 IHA degrees so as to have an overall impact index. By using this averaged index, high impact alterations would be offset by the low degree alterations. This paper considers the method proposed by Shiau and Wu (2004b) which calculates the single index for hydrologic alteration in categories of high and medium alterations.
A water supply deficit is estimated when the actual demand is greater than the registered or projected demand. In the optimizing model, water supply objective is to minimize the shortage ratio (total deficit / total demand) of agricultural water and municipal demand. Minimizing both hydrologic alterations and supply shortages is the goal of Kaoping diversion weir which is formulated as a multi objective programming.
Min {SRW, SRD, D}
SRW = supply shortage of registered agricultural withdrawals
SRD = supply shortage of projected municipal uses
D = overall degree of hydrologic alteration
All these supply shortages values are the function of the instream flow value (i.e. decision variable). There are many techniques used to deal with the multi objective problems, this study considers using of compromising programming.
Compromising programming estimates the optimal solution which has the least distance from the ideal point (i.e. point where multiple objectives reach the optimal solution). This compromise programming is carried out in two steps –
1. First the best and worst solutions of both the objective functions needs to be found which is within the computation domain (which is found out based on the decision variable- instream flow)
2. Seeking the optimal solution by calculating the shortest distance to the best estimated point
In the current operation of the weir, it releases a minimum of 9.5 cumec instream flow. The overall hydrologic alteration is about 69.3% i.e categorized as highly altered. Though agricultural withdrawals are the highest priority 18% shortage of water exists when compared to 6% of municipal water shortage. With the highest percentage of alteration it is evident that the present instream release is not sufficient to restore the natural flow variability. To evaluate effect of different instream flows, Shiau and Wu studied different flows ranging from o to 100 cumec. Corresponding SRW, SRD, D and value of L were estimated. This study showed that SRW increased rapidly with smaller instream than that of larger instream flow. SRD increased linearly. Value of D decreased with the increase in the instream flow. Two drops were observed – one (26 cumec) to convert from highly altered to medium alteration and the second drop (93 cumec) to convert from medium alteration to low alteration. For a given instream flow the SRW, SRD and D values are fixed, but the value of L changes with respect to the weighing factors. Therefore a study of various weighting factors was considered to see how the instream flow and the Minimum distance L is changed. The proposed optimal instream flow 26 cumec would not be able to restore the altered hydrologic regime to pre diversion condition but then it helps in mitigating the adverse effects of the highly and moderately altered IHA’s.
Discussion:
The paper was very informative about how we can optimize a model considering multi objectives i.e. minimizing water shortages and hydrologic alterations. With the increase of municipal demands, many reservoirs have been affecting the riverine environment by reduced instream flow. By using the quantitative assessment of 32 relevant IHA’s it would be helpful to check the hydrologic alterations caused due to this reduced instream flow. Future research would obviously be considering the biological component into the RVA. It would be interesting to note the changes in the optimized results with the added biological component. Compromising programming is a useful technique which can be used in many models to optimize two conflicting objectives for example flood management vs. downstream eco system,
Jenq-Tzong Shiau, Fu Chun Wu, Compromise Programming Methodology for Determining Instream Flow Under Multi-Objective Water Allocation Criteria, 2006, Journal of American Water Resource Association
Summary:
The paper by Jenq Tzong and Fu chun determines a quantitative assessment for determining in-stream flow under multi objective water allocation criteria. They explain the concept of compromise programming which is used to optimize water allocation scheme by minimizing hydrologic alterations and water supply shortages. This methodology was applied to a case study of Kaoping diversion weir in Taiwan. The paper focuses on evaluating the hydrologic alterations of the weir and the optimal operation schemes.
The Kaoping diversion weir was constructed to meet the increasing municipal water demands. The design diversion capacity for the municipal use is about 35 cumec. However prior to the construction there was long history of agricultural water withdrawals from the downstream of the Kaoping creek. From the data it is observed that there has been no flow diversion during dry season for meeting municipal demand due to insufficient amount of water. The operation model of weir has three components – meeting the reserved agricultural water demand, providing projected municipal water demand and instream flow release. Based on the environmental protection, they have set different priorities, first being instream flow release, second priority being registered agricultural demand and third priority being projection flow for municipal demand.
Range of variability of approach has been used to evaluate the hydrologic alterations caused by the flow diversions of the weir. RVA assesses the hydrologic regime with respect to 32 ecological relevant indicators of hydrologic alteration (IHA). As suggested by Richter et al. (1998) RVA range of variation for each IHA is taken as 25th and 75th percentile pre diversion values. Weir operations are aimed such that pre diversion flow conditions reach the targeted RVA ranges. Overall degree of hydrologic alteration (D) is estimated to measure the deviation between post impact flow regime and pre impact flow regime. Richter et al. (1998) classified the overall degree of alterations as low, medium and high alteration. Therefore value of D for a particular IHA quantifies the effect of flow diversion on the flow regime. For including these overall hydrologic alteration index needs to be estimated. Richter et al. suggested the method of averaging the 32 IHA degrees so as to have an overall impact index. By using this averaged index, high impact alterations would be offset by the low degree alterations. This paper considers the method proposed by Shiau and Wu (2004b) which calculates the single index for hydrologic alteration in categories of high and medium alterations.
A water supply deficit is estimated when the actual demand is greater than the registered or projected demand. In the optimizing model, water supply objective is to minimize the shortage ratio (total deficit / total demand) of agricultural water and municipal demand. Minimizing both hydrologic alterations and supply shortages is the goal of Kaoping diversion weir which is formulated as a multi objective programming.
Min {SRW, SRD, D}
SRW = supply shortage of registered agricultural withdrawals
SRD = supply shortage of projected municipal uses
D = overall degree of hydrologic alteration
All these supply shortages values are the function of the instream flow value (i.e. decision variable). There are many techniques used to deal with the multi objective problems, this study considers using of compromising programming.
Compromising programming estimates the optimal solution which has the least distance from the ideal point (i.e. point where multiple objectives reach the optimal solution). This compromise programming is carried out in two steps –
1. First the best and worst solutions of both the objective functions needs to be found which is within the computation domain (which is found out based on the decision variable- instream flow)
2. Seeking the optimal solution by calculating the shortest distance to the best estimated point
In the current operation of the weir, it releases a minimum of 9.5 cumec instream flow. The overall hydrologic alteration is about 69.3% i.e categorized as highly altered. Though agricultural withdrawals are the highest priority 18% shortage of water exists when compared to 6% of municipal water shortage. With the highest percentage of alteration it is evident that the present instream release is not sufficient to restore the natural flow variability. To evaluate effect of different instream flows, Shiau and Wu studied different flows ranging from o to 100 cumec. Corresponding SRW, SRD, D and value of L were estimated. This study showed that SRW increased rapidly with smaller instream than that of larger instream flow. SRD increased linearly. Value of D decreased with the increase in the instream flow. Two drops were observed – one (26 cumec) to convert from highly altered to medium alteration and the second drop (93 cumec) to convert from medium alteration to low alteration. For a given instream flow the SRW, SRD and D values are fixed, but the value of L changes with respect to the weighing factors. Therefore a study of various weighting factors was considered to see how the instream flow and the Minimum distance L is changed. The proposed optimal instream flow 26 cumec would not be able to restore the altered hydrologic regime to pre diversion condition but then it helps in mitigating the adverse effects of the highly and moderately altered IHA’s.
Discussion:
The paper was very informative about how we can optimize a model considering multi objectives i.e. minimizing water shortages and hydrologic alterations. With the increase of municipal demands, many reservoirs have been affecting the riverine environment by reduced instream flow. By using the quantitative assessment of 32 relevant IHA’s it would be helpful to check the hydrologic alterations caused due to this reduced instream flow. Future research would obviously be considering the biological component into the RVA. It would be interesting to note the changes in the optimized results with the added biological component. Compromising programming is a useful technique which can be used in many models to optimize two conflicting objectives for example flood management vs. downstream eco system,
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