Improved understanding of the searching behavior of ant colony optimization algorithms applied to the water distribution design problem

Evolutionary algorithms (EAs) have been applied successfully to many water resource problems, such as system design, management decision formulation, and model calibration. The performance of an EA with respect to a particular problem type is dependent on how effectively its internal operators balance the exploitation/exploration trade-off to iteratively find solutions of an increasing quality. For a given problem, different algorithms are observed to produce a variety of different final performances, but there have been surprisingly few investigations into characterizing how the different internal mechanisms alter the algorithm's searching behavior, in both the objective and decision space, to arrive at this final performance. This paper presents metrics for analyzing the searching behavior of ant colony optimization algorithms, a particular type of EA, for the optimal water distribution system design problem, which is a classical NP-hard problem in civil engineering. Using the proposed metrics, behavior is characterized in terms of three different attributes: (1) the effectiveness of the search in improving its solution quality and entering into optimal or near-optimal regions of the search space, (2) the extent to which the algorithm explores as it converges to solutions, and (3) the searching behavior with respect to the feasible and infeasible regions. A range of case studies is considered, where a number of ant colony optimization variants are applied to a selection of water distribution system optimization problems. The results demonstrate the utility of the proposed metrics to give greater insight into how the internal operators affect each algorithm's searching behavior.