Using OMOPSO & MMOPSO algorithms on water distribution systems design.
The particle swarm optimization, PSO, was firstly developed by Kennedy & Eberhart (1995) to solve simple single-objective continuous optimization problems. This algorithm depends mainly on imitating the concept of swarm intelligence which is extensively found in birds flocks or fish schools. The algorithm initiates a prespecified number of flying particles that are led by a leader which moves towards the area of the global optimum solution with the most reasonable direction and flying speed. The algorithm keeps iterating while improving the positions and flying speeds for all the particles by following the particles’ leader. Eventually, the algorithm may reach the global optimum or may fall in local optima (if any). Coello Coello & Lechuga (2002) extended the usage of the PSO algorithm to adapt with multi-objective optimization problems by providing an external archive to store the set of non-dominated solutions that may be found during the search. The original multi-objective particle swarm optimization, OMOPSO, algorithm usually suffers from some difficulties when it is applied in the problem of designing water distribution systems (WDSs) since this problem is a combinatorial discrete NP-hard optimization problem (Montalvo et al., 2010; Surco et al., 2017). The algorithm frequently falls in local minima during the search and fails to capture the whole set of non-dominated feasible solutions after the end of search especially in medium to large search space problems. Therefore, a trial is made to improve the performance of the OMOPSO in designing WDSs by developing a modified multi-objective particle swarm optimization, MMOPSO. The modifications include using some strategies to improve the overall convergence and diversity of the final non-dominated feasible set of solutions such as; the self-adaptive PSO parameters strategy, the selection strategy of the external archive members, the regeneration-on-collision strategy, and the adaptive population size strategy. In the subsequent sections, the pseudo-codes of the OMOPSO and MMOPSO are presented, the explanations of using both algorithms are provided, and an example of using both algorithms is illustrated.