Genetic operators and constraint handling for pipe network optimization

Abstract

Evolution Programs (EPs), including Genetic Algorithms and Evolution Strategies, are wellsuited for pipe network optimization problems due to the large number of candidate solutions to be examined, non-linearity of the problem and discrete decision space. However, pipe network problems are highly constrained and random initialization and standard genetic operators often cause infeasibility of generated solutions. The paper describes coding and genetic operators adapted to preserve feasibility of pipe network solutions generated in an EP run. Examples of ‘hard’ and ‘soft’ constraints found in pipe network optimization problems are used to illustrate the coding and genetic operators developed. The ‘hard’ constraints must be satisfied for each candidate solution and the ‘soft’ constraints may be violated but with a penalty associated with the violation. Procedures devised to include different type of constraints into an EP structure are also summarized. Examples of EPs developed include: (1) optimal pipe sizing for water distribution networks (2) layout design of branched hydraulic networks; and (3) pressure regulation in water distribution networks. The first example involves a classical operational-research type constraint of the form f (x) ≥ b. The second example involves a topological (connectivity) constraint which ensures that all nodes are connected (supplied). The last example combines the two constraints in a single problem. The examples provided clearly demonstrate the ability of the EPsdeveloped to find solutions to problems difficult to solve using classical operational research methods.