Newton’s Law of Gravity-Based Search Algorithms

S Raja Balachandar

doi:10.17485/ijst/2013/v6i2.21

Abstract

Many heuristic optimization methods have been developed in recent years that are derived from Nature. These methods take inspiration from physics, biology, social sciences, and use of repeated trials, randomization, and specific operators to solve NP-hard combinatorial optimization problems. In this paper we try to describe the main characteristics of heuristics derived from Newton's law of gravitation, namely a gravitational emulation local search algorithm and a gravitational search algorithm. We also present the detailed survey of distinguishing properties, parameters and applications of these two algorithms.

Highlights

Heuristic techniques are developed for solving combinatorial optimization problems (COP) with exponential search spaces because exact techniques are not practical for these cases
In the literature various heuristic approachesderived from nature have been developed by researchers, namelyGenetic Algorithms (GA) (Tang et al, 1996), Simulated Annealing(SA)(Kirkpatrick et al, 1983),Ant Search Algorithm(ASA)(Dorigo et al, 1996), Particle Swarm Optimization(PSO)(Kennedy and Eberhart, 1995), Neural Nets(NN)(Hopfield, 1982; Righini,1992),Tabu Search (TS)(Glover,1989; Glover, 1990), etc
Benchmark problems have been taken from the OR-Library (Beasley, 1990) to check the performance of Gravitational Search Algorithm (GSA), and to validate the computational efficiency of GSA comparisons have been made with other recent heuristics that are available in the literature and report the efficiency of their proposed algorithm

Summary

Introduction

Heuristic techniques are developed for solving combinatorial optimization problems (COP) with exponential search spaces because exact techniques are not practical for these cases. From(1) and (2), we conclude that there is an attracting gravity force among all particles of the universe, where the effect becomes greater with increasing mass of the particles and decreasing distance between them.In the literature, two different gravitational algorithms are available and based on equation (1), namely GELS and GSA Researchers have designed these two approaches for solving various COP. In the remaining two versions, the speed could be increased or decreased by more than one unit at a time, depending on the strength of the gravitational influence(relative quality) of a nearby solution In both cases, the algorithm stopped when the speed of its pointer dropped to zero(or after a specified maximum number of iterations, in order to prevent the possibility of a non-terminating execution)

Applications of GELS

RGES Procedure

Procedure GELSAR

Application of GSA

Convergence analysis

Conclusion