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.
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