Abstract
Problem solving and modelling in traditional substitution methods at large scale for systems using sets of simultaneous equations is time consuming. For such large scale global-optimization problem, Simulated Annealing (SA) algorithm and Genetic Algorithm (GA) as meta-heuristics for random search technique perform faster. Therefore, this study applies the SA to solve the problem of linear equations and evaluates its performances against Genetic Algorithms (GAs), a population-based search meta-heuristic, which are widely used in Travelling Salesman problems (TSP), Noise reduction and many more. This paper presents comparison between performances of the SA and GA for solving real time scientific problems. The significance of this paper is to solve the certain real time systems with a set of simultaneous linear equations containing different unknown variable samples those were simulated in Matlab using two algorithms-SA and GA. In all of the experiments, the generated random initial solution sets and the random population of solution sets were used in the SA and GA respectively. The comparison and performances of the SA and GA were evaluated for the optimization to take place for providing sets of solutions on certain systems. The SA algorithm is superior to GA on the basis of experimentation done on the sets of simultaneous equations, with a lower fitness function evaluation count in MATLAB simulation. Since, complex non-linear systems of equations have not been the primary focus of this research, in future, performances of SA and GA using such equations will be addressed. Even though GA maintained a relatively lower number of average generations than SA, SA still managed to outperform GA with a reasonably lower fitness function evaluation count. Although SA sometimes converges slowly, still it is efficient for solving problems of simultaneous equations in this case. In terms of computational complexity, SA was far more superior to GAs.
Highlights
The Simulated Annealing (SA) algorithm is a well-known meta-heuristic for solving problems that require best or optimal results
The purpose of this research is to study the performances of the SA algorithm while comparing it with Genetic Algorithms (GAs), in solving simultaneous linear equations
In the area of industrial cutting, one study has investigated a problem called multi-objective optimization for irregular objects,[21] in the field of processing aquatic products, and have developed a SA technique for the problem of squid cutting. In this study, both SA and GA have been implemented in MATLAB (Version: R2017a, RRID: SCR_001622) based on the setup of two algorithms stated in Table 1 and Table 2
Summary
The Simulated Annealing (SA) algorithm is a well-known meta-heuristic for solving problems that require best or optimal results. This algorithm can be implemented using some programming language and as such it has gained wide acceptance in the arena of computational and scientific research over the past few decades. The Elimination method can be an easier alternative to solving equations involving three equations with three variables. A numerical method called the Gaussian Elimination method is not always capable of finding good quality solutions for complex systems of equations.[2] to be able to solve simultaneous equations using the SA approach could make the process of finding possible solution sets much easier, faster, and convenient
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