The use of prospect theory framework in constrained multi-objective particle swarm optimisation

Many practical problems in the real world nowadays can be formulated as constraintsingle or multiple objective optimisation problems with constraints. Particle swarmoptimisation (PSO) is a population-based stochastic algorithm has been shown to be aneffective optimisation method for solving these types of problems since it is capable ofgenerating random multi-start points, it is simple to perform and it does not requiregradient continuity. Despite the popularity of this approach, PSO still needs moreadaptation to the guide selection mechanisms in order to improve the search capacity ofthe particles and achieve better convergence. Moreover, PSO lacks an explicitmechanism to handleIn this work, new constrained PSO-based optimisation algorithms are proposed forsolving both single and multi-objective optimisation problems. The proposed methodsintroduce new decision mechanism that inspired from human behaviour under risk intothe guide selection of particles. This human behaviour was formalised by Kahnemanand Tversky in 1979 into mathematical equations represented by prospect theory (PT).Including PT in the proposed methods help to direct the swarm towards the feasibleregion, encourage the swarm to explore a new area in the search space andconsequently, improve the convergence to the optimal solution (or the Pareto- optimalin the case of multi- objective problems).The performance of the proposed methods are tested and evaluated firstly onconstrained nonlinear single-objective optimisation problems (CNOPs) using sixteenwell-known benchmark functions. Moreover, the proposed method are tested andevaluated secondly on constrained multi-objective problems (CMOPs) using fourteenbenchmark problems and two mechanical design-engineering problems. The proposedmethods are validated also by comparing them with the current established state-of-the-artalgorithms in the area. The results showed that the proposed methods arecompetitive when compared to the other approaches and outperforms the otheralgorithms in many cases