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

Bunny, MN

Abstract

Many practical problems in the real world nowadays can be formulated as constraint
single or multiple objective optimisation problems with constraints. Particle swarm
optimisation (PSO) is a population-based stochastic algorithm has been shown to be an
effective optimisation method for solving these types of problems since it is capable of
generating random multi-start points, it is simple to perform and it does not require
gradient continuity. Despite the popularity of this approach, PSO still needs more
adaptation to the guide selection mechanisms in order to improve the search capacity of
the particles and achieve better convergence. Moreover, PSO lacks an explicit
mechanism to handle
In this work, new constrained PSO-based optimisation algorithms are proposed for
solving both single and multi-objective optimisation problems. The proposed methods
introduce new decision mechanism that inspired from human behaviour under risk into
the guide selection of particles. This human behaviour was formalised by Kahneman
and Tversky in 1979 into mathematical equations represented by prospect theory (PT).
Including PT in the proposed methods help to direct the swarm towards the feasible
region, encourage the swarm to explore a new area in the search space and
consequently, improve the convergence to the optimal solution (or the Pareto- optimal
in the case of multi- objective problems).
The performance of the proposed methods are tested and evaluated firstly on
constrained nonlinear single-objective optimisation problems (CNOPs) using sixteen
well-known benchmark functions. Moreover, the proposed method are tested and
evaluated secondly on constrained multi-objective problems (CMOPs) using fourteen
benchmark problems and two mechanical design-engineering problems. The proposed
methods are validated also by comparing them with the current established state-of-the-art
algorithms in the area. The results showed that the proposed methods are
competitive when compared to the other approaches and outperforms the other
algorithms in many cases.

Citation

Bunny, M. The use of prospect theory framework in constrained multi-objective particle swarm optimisation. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Aug 4, 2021
• Award Date: Oct 1, 2012