02-05-2014, 02:11 PM
Unified Particle Swarm Optimization for Solving Constrained Engineering Optimization Problems
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Abstract.
We investigate the performance of the recently proposed Uni-
fied Particle Swarm Optimization method on constrained engineering
optimization problems. For this purpose, a penalty function approach
is employed and the algorithm is modified to preserve feasibility of the
encountered solutions. The algorithm is illustrated on four well–known
engineering problems with promising results. Comparisons with the stan-
dard local and global variant of Particle Swarm Optimization are re-
ported and discussed.
Introduction
Many engineering applications, such as structural optimization, engineering de-
sign, VLSI design, economics, allocation and location problems [1], involve diffi-
cult optimization problems that must be solved efficiently and effectively. Due to
the nature of these applications, the solutions usually need to be constrained in
specific parts of the search space that are delimited by linear and/or nonlinear
constraints.
Different deterministic as well as stochastic algorithms have been developed
for tackling such problems. Deterministic approaches such as Feasible Direction
and Generalized Gradient Descent make strong assumptions on the continuity
and differentiability of the objective function [1,2]. Therefore their applicability is
limited since these characteristics are rarely met in problems that arise in real–
life applications.
Unified Particle Swarm Optimization
PSO is a stochastic, population–based algorithm for solving optimization prob-
lems. It was introduced in 1995 by Eberhart and Kennedy for numerical op-
timization tasks and its dynamic is based on principles that govern socially
organized groups of individuals [12].
In PSO’s context, the population is called a swarm and its individuals (search
points) are called particles. Each particle has three main characteristics: an
adaptable velocity with which it moves in the search space, a memory where
it stores the best position it has ever visited in the search space (i.e., the posi-
tion with the lowest function value), and the social sharing of information, i.e.,
the knowledge of the best position ever visited by all particles in its neighbor-
hood. The neighborhoods are usually determined based on the indices of the
particles, giving rise to the two main variants of PSO, namely the global and the
local variant. In the former, the whole swarm is considered as the neighborhood
of each particle, while in the latter strictly smaller neighborhoods are used.
Conclusions
We investigated the performance of the recently proposed Unified Particle Swarm
Optimization method on four well–known constrained engineering optimization
problems, using a penalty function approach and a feasibility preserving mod-
ification of the algorithm. The results were very promising, with UPSO out-
performing the standard PSO algorithm, conforming with previous results for
different unconstrained optimization problems.
Further work will consider the investigation of the effect of the penalty func-
tion on the algorithm’s performance as well as different feasibility preserving
mechanisms.