PSO+: A new particle swarm optimization algorithm for constrained problems

The Particle Swarm Optimization algorithm is a metaheuristic based on populations of individuals in which solution candidates evolve through simulation of a simplified model of social adaptation. By aggregating robustness, efficiency and simplicity, PSO has gained great popularity. Modified PSO algorithms have been proposed to solve optimization problems with domain, linear and nonlinear constraints. Other algorithms that use multi-objective optimization to deal with constrained problems face the problem of not being able to guarantee finding feasible solutions. Current PSO algorithms that deal with constraints only treat domain constraints by controlling the velocity of particle displacement in the swarm, or do so inefficiently by randomly resetting each infeasible particle. This approach may make it infeasible to optimize certain problems, especially real ones. This work presents a new particle swarm optimization algorithm, called PSO+, capable of solving problems with linear and nonlinear constraints in order to solve these deficiencies. The proposed algorithm uses a feasibility repair operator and two swarms to ensure there will always be a swarm whose particles fully respect every constraint. A new particle update method is also proposed to insert diversity into the swarm and improve search-space coverage, allowing the search-space border to be exploited as well, which is particularly convenient when the optimization involves active constraints in global optimum. Two heuristics are proposed to initialize a feasible swarm with the purpose of speeding up the initialization mechanism and ensuring diversity at the starting point of the optimization process. Furthermore, a neighborhood topology is proposed to minimize premature convergence. The proposed algorithm was tested for twenty-four benchmark functions, as well as in a real reservoir drainage plan optimization problem. Results attest that the new algorithm is competitive, since it increases the efficiency of the PSO and the speed of convergence.