Enhanced superposition determination for weighted superposition attraction algorithm

Abstract

This paper argues the efficiency enhancement study of a recent meta-heuristic algorithm, WSA, by modifying one of its operators, superposition (target point) determination procedure. The original operator is based on the weighted vector summation and has some potential disadvantages with regard to domain of the decision variables such that determining a superposition out of the search space. Such potential disadvantages may cause WSA to behave as a random search and result in an unsatisfactory performance for some problems. In order to eliminate such potential disadvantages, we propose a new superposition determination procedure for the WSA algorithm. Thus, the mWSA algorithm will be able to behave more consistent during its search and its robustness will improve significantly in comparison to its original version. The mWSA algorithm is compared against the WSA algorithm and some other algorithms taken from the existing literature on both the constrained and unconstrained optimization problems. The experimental results clearly indicate that the mWSA algorithm is an improvement for the original WSA algorithm, and also prove that the mWSA algorithm is more robust and consistent search procedure in solving complex optimization problems.

Appendix: Notations and Abbreviations

Notations used throughout the paper and their definitions

Notation	Definition
$Maxiter$	Iteration number (stopping condition)
$Iteration$	Current iteration number
$AA$	Number of artificial agents
$D$	Number of dimensions of the problem
$\tau$	User defined parameter
$\lambda$	User defined parameter
$\varphi$	User defined parameter
$UL$	Upper limit for the dimensions
$LL$	Lower limit for the dimensions
$f\left( i \right)$	Fitness of the current point of agent i
$f\left( {tar} \right)$	Fitness of the target point
$weight$	Weight of the current point of an agent
$\vec{x}$	Current position vector of an agent
$\overrightarrow {tar}$	Position vector of the target point
$\overrightarrow {gap}$	Vector combines an agent to target point
$\overrightarrow {direct}$	Move direction vector of an agent
$sign()$	Signum function
$sl$	Step length

Abbreviations

WSA	Weighted superposition attraction
mWSA	Modified weighted superposition attraction
BPA	Best performance algorithm
IBPA	Iterative best performance algorithm
LADA	Largest absolute difference algorithm
TS	Tabu search
SA	Simulated annealing
PSO	Particle swarm optimization
PSO-w	PSO with inertia weight
PSO-cf	PSO with constriction Factor
FDR-PSO	Fitness-distance-ratio based PSO
FIPS	Fully informed particle swarm
HPSO-TVAC	Hierarchical PSO with time-varying acceleration coefficients
DMS-PSO	Dynamic multi-swarm particle swarm optimizer
GPSO	Gregarious PSO
CLPSO	Comprehensive learning PSO
OPSO	Orthogonal PSO
FPSO	Frankenstein’s PSO
APSO	Adaptive PSO
AIWPSO	PSO with adaptive inertia weight
OLPSO-G	Orthogonal learning PSO with global star neighbourhood
OLPSO-L	Orthogonal learning PSO with local ring neighbourhood
ALC-PSO	PSO with an aging leader and challenger
PSOPB	Co-evolutionary particle swarm optimizer with parasitic behaviour
ITCH	Inverse tangent constraint handling
HEFAG	Human effort for achieving goals
ABC	Artificial bee colony
HS	Harmony search
CSGA	Cuckoo search-gravitational search
BFO-CC	Bacterial foraging based on new conjugation and chemotaxis strategies
GA	Genetic algorithm
TLBO	Teacher-learner-based optimization