An Adaptive Convergence-Trajectory Controlled Ant Colony Optimization Algorithm With Application to Water Distribution System Design Problems

Evolutionary algorithms and other meta-heuristics have been employed widely to solve optimization problems in many different fields over the past few decades. Their performance in finding optimal solutions often depends heavily on the parameterization of the algorithm's search operators, which affect an algorithm's balance between search diversification and intensification. While many parameter-adaptive algorithms have been developed to improve the searching ability of meta-heuristics, their performance is often unsatisfactory when applied to real-world problems. This is, at least in part, because available computational budgets are often constrained in such settings due to the long simulation times associated with objective function and/or constraint evaluation, thereby preventing convergence of existing parameter-adaptive algorithms. To this end, this paper proposes an innovative parameter-adaptive strategy for ant colony optimization (ACO) algorithms based on controlling the convergence trajectory in decision space to follow any prespecified path, aimed at finding the best possible solution within a given, and limited, computational budget. The utility of the proposed convergence trajectory controlled ACO (ACOCTC) algorithm is demonstrated using six water distribution system design problems (WDSDPs, a difficult type of combinatorial problem in water resources) with varying complexity. The results show that the proposed ACOCTCsuccessfully enables the specified convergence trajectories to be followed by automatically adjusting the algorithm's parameter values. Different convergence trajectories significantly affect the algorithm's final performance (solution quality). The trajectory with a slight bias toward diversification in the first half and more emphasis on intensification during the second half of the search exhibits substantially improved performance compared to the best available ACO variant with the best parameterization (no convergence control) for all WDSDPs and computational scenarios considered. For the two large-scale WDSDPs, new best-known solutions are found by the proposed ACOCTC.