In this article, the authors introduce the problem of designing sanitary sewer systems and review the methods other researchers have used to attempt to solve design problems. The authors then describe the motivation for using a GA-QP model. A regular GA might be inappropriate since the solving efficiency can be reduced by many variables, and "many of the randomly produced alternatives are unreasonable or inappropriate." They describe how an LP can help improve a GA, but for their purposes they don't want to reduce their non-linear program into an LP. Instead, they transform their functions into quadratic forms and solve using quadratic programming (QP).
The paper defines the decision variables of the GA genes to be pipe diameters and pumping station locations, and describes the constraints in detail. The fitness function is the inverse of the cost, so the higher the fitness, the better. The two decision variables for the QP include pipe slope and buried depth.
It was a very interesting point that the best design found in the optimization model doesn't even begin to consider many important factors, such as construction, geology, traffic impact, public preferences and land availability. It may be an extremely iterative process to find a solution, determine the real feasibility (based on the above listed factors), have to throw out that solution, and repeat. As powerful as computers are in implementing optimization models, in the end any public sector planning problem requires a large human component in the process.
Monday, April 27, 2009
BRILL ED (1979) USE OF OPTIMIZATION MODELS IN PUBLIC-SECTOR PLANNING, MANAGEMENT SCIENCE, 25
This article written by Brill in 1979 addresses the trend towards using optimization models in solving public policy problems.
Brill argues that optimization models used to help find solutions to public policy problems "have serious shortcomings" which include failture to consider equity or distribution of income, as well as difficulties in estimating benefits/costs of public programs. Brill says public programs' benefits and costs are better kept in their original units rather than trying to translate them into common units to judge amongst completely different types of objectives.
Brill notes that multi-objective programming was increasingly common to try to address these issues, but he makes the point that all objectives need to be clearly identified in order to truly distinguish between inferior and noninferior solutions, as illustrated well in Figure 2.
Brill proposes that a good way to involve optimization models in public sector planning is to: 1, use them to stimulate creativity, and 2. create a man-machine interactive process. This man-machine interactive process is something he briefly describes in this paper, but it sounds like he most likely researched this idea more and published a paper on it soon after this paper. I found Brill's point interesting that optimization models should generate alternatives that meet minimal requirements and are different.
I'd really like to see a case study of these ideas, and how optimization models can assist public planners in generating creative solutions. It seems to me that a human would easily be just as creative as a computer, so I'd like to see an example showing otherwise.
Brill argues that optimization models used to help find solutions to public policy problems "have serious shortcomings" which include failture to consider equity or distribution of income, as well as difficulties in estimating benefits/costs of public programs. Brill says public programs' benefits and costs are better kept in their original units rather than trying to translate them into common units to judge amongst completely different types of objectives.
Brill notes that multi-objective programming was increasingly common to try to address these issues, but he makes the point that all objectives need to be clearly identified in order to truly distinguish between inferior and noninferior solutions, as illustrated well in Figure 2.
Brill proposes that a good way to involve optimization models in public sector planning is to: 1, use them to stimulate creativity, and 2. create a man-machine interactive process. This man-machine interactive process is something he briefly describes in this paper, but it sounds like he most likely researched this idea more and published a paper on it soon after this paper. I found Brill's point interesting that optimization models should generate alternatives that meet minimal requirements and are different.
I'd really like to see a case study of these ideas, and how optimization models can assist public planners in generating creative solutions. It seems to me that a human would easily be just as creative as a computer, so I'd like to see an example showing otherwise.
Tuesday, April 14, 2009
Shiau and Wu (2006)
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
Increasing demand of water for human consumption results in a decreased availability of water for instream flows to sustain the natural ecology of a stream or river. This therefore creates a multiple-objective problem. The authors use the Indicators of Hydrologic Alteration (IHA) method as well as a Range of Variability Approach (RVA) to quantify the effects of a diversion weir on a stream in Taiwan.
The objectives of this problem are to meet demands and not harm the environment according to IHA and RVA. The method the authors use to solve this multi-objective program is called "compromise programming" which identifies the optimal solution as having the shortest distance to a theoretical ideal point.
Their study really seemed to be two part: first, they demonstrate that the current instream flow of 9.5 m3/s is not sufficient, then they found the optimal solution of 26 m3/s better protects the environment while compromising with preventing water shortages.
I had a difficult time understanding this paper since there were so many different variables being thrown around and I didn't have the patience to memorize/lookup each variable as I came across it. I don't know if they could've communicated their work in any easier way, but it definately hindered getting their point across.
It was nice to see an example of compromise programming being used, and I personally liked that the ecological needs were weighted the same as the human needs (since human needs will increase when ecological needs are ignored).
Increasing demand of water for human consumption results in a decreased availability of water for instream flows to sustain the natural ecology of a stream or river. This therefore creates a multiple-objective problem. The authors use the Indicators of Hydrologic Alteration (IHA) method as well as a Range of Variability Approach (RVA) to quantify the effects of a diversion weir on a stream in Taiwan.
The objectives of this problem are to meet demands and not harm the environment according to IHA and RVA. The method the authors use to solve this multi-objective program is called "compromise programming" which identifies the optimal solution as having the shortest distance to a theoretical ideal point.
Their study really seemed to be two part: first, they demonstrate that the current instream flow of 9.5 m3/s is not sufficient, then they found the optimal solution of 26 m3/s better protects the environment while compromising with preventing water shortages.
I had a difficult time understanding this paper since there were so many different variables being thrown around and I didn't have the patience to memorize/lookup each variable as I came across it. I don't know if they could've communicated their work in any easier way, but it definately hindered getting their point across.
It was nice to see an example of compromise programming being used, and I personally liked that the ecological needs were weighted the same as the human needs (since human needs will increase when ecological needs are ignored).
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