f-MOPSO/Div: an improved extreme-point-based multi-objective PSO algorithm applied to a socio-economic-environmental conjunctive water use problem.

In this paper, a new version of the multi-objective particle swarm optimizer named the Diversity-enhanced fuzzy multi-objective particle swarm optimization (f-MOPSO/Div) algorithm is proposed. This algorithm is an improved version of our recently proposed f-MOPSO. In the proposed algorithm, a new characteristic of the particles in the objective space, which we named the "extremity," is also evaluated, along with the Pareto dominance, to appoint proper guides for the particles in the search space. Three improvements are applied to the f-MOPSO to mitigate its shortcomings, generating f-MOPSO/Div: (1) selecting the global best solution based on the diversity of the extreme solutions, (2) impeding the particles to be trapped in the local optima using a mutation scheme based on the dynamic probability, and (3) removing the pre-optimization process. To validate f-MOPSO/Div, it was compared with some other popular multi-objective algorithms on 14 standard low- and high-dimensional test problem suites. After the comparative results indicated the outperformance of the proposal, the f-MOPSO/Div was applied to solve an optimal conjunctive water use management problem, in a semi-arid study area in west-central Iran, over a 13-year long-term planning period with two main objectives: (1) maximizing the aquifer sustainability as an environmental goal, and (2) maximizing the crop yields as a socio-economic goal. As the results suggest, the cumulative groundwater level drawdown is considerably decreased over the whole planning period to make the aquifer sustainable, while the water productivity is held at a desirable level, demonstrating the superiority of the f-MOPSO/Div when also applied to solve a large-scale real-world optimization problem.