Evolutionary multi-objective optimization in water distribution network design

There are many criteria in water systems design that need to be optimized simultaneously. Capital, operational, life cycle, and maintenance costs, system reliability, and quality of water could be mentioned as some of the most obvious among the large number of objectives. Rehabilitation, calibration and operational scheduling of water systems are also tasks which could be viewed as multi-objective problems. Rather than searching for a single solution with the best scalar fitness value, the target in a multi-objective problem is to find a set of diverse solutions which together define the best possible multi-objective trade-off surface, the Pareto optimal front. Evolutionary algorithms (EAs) have demonstrated unique ways of handling multi-objective optimization problems. Since multi-objective evolutionary algorithms use population-based EAs, they offer a means of finding the Pareto optimal front in a single run. Depending on the preference of a decision maker, the remaining task is to choose from the Pareto optimal set a group of solutions for more detailed analysis. The focus of this article is on a comparative study of three common evolutionary multi-objective optimization methods with application to water distribution system design. A brief description of each method is given and the ability of each multi-objective algorithm is examined using two design case studies. A comparison of the results is presented by visualization of the non-dominated fronts achieved by the different methods. In addition, a direct comparison of the multi-objective optimization methods is presented using two performance indicators.