Weight Minimization of a Speed Reducer Using Prey Predator Algorithm

Weight Minimization of a Speed Reducer Using Prey Predator Algorithm

Surafel Luleseged Tilahun (Department of Mathematical Sciences, University of Zululand, KwaDlangeZwa, South Africa) and Maba B. Matadi (Department of Mathematical Sciences, University of Zululand, KwaDlangeZwa, South Africa)
DOI: 10.4018/IJMMME.2018040102

Abstract

This article describes how a speed reducer is a mechanical device which is very useful to reduce speed in different machineries. The use of gears to adjust a speed is an old practice, however the formulation of the problem as an optimization problem and solving it using different approaches begun in early 1970's. The problem is a constrained, nonlinear and nonconvex problem. That makes it challenging to handle it by deterministic approaches. Hence, different metaheuristic and hybrid methods have been proposed and used. Furthermore, due to the challenging behaviour of the problem, it has been used as a benchmark problem to test and compare new algorithms. In this article, a brief review of the problem, its application and the advances in solving the problem will be presented. A metaheuristic algorithm called prey predator algorithm will then be used to solve the problem. Prey-predator algorithm has been found to be effective with an easy way to control the exploration and exploitation search behaviour. Simulation-based comparison with previous results shows that indeed the algorithm produces a promising result. Hence, this study showed that applying prey predator algorithm for speed reducer production is a reasonable idea.
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1. Introduction

The applications and uses of optimization techniques become very important and crucial for different engineering applications. For a mathematically formulated decision making problem, different methods can be used as a solution approach. These methods can be classified as deterministic and non-deterministic methods. A deterministic method refers to methods which are based on mathematical arguments to obtain an optimal solution, for example simplex algorithm, whereas, non-deterministic methods are methods which try to approximate the optimal solution within a reasonable run time. Metaheuristic algorithms are non-deterministic approaches which become very common in different application from a wide range of disciplines. One of the major reasons for that, is that their effectiveness to deal with complex and also high dimensional problems. Even though these algorithms do not guarantee to produce an optimal solution, they are found to give an acceptable solution within a reasonable time. Generally, there are two class of these algorithms, namely evolutionary computing and swarm intelligence.

Engineering design has been one of the application areas where metaheuristic algorithms become very applicable. Designing a speed reducer is one of the interesting engineering problems, researchers try to address since early 1980's. It is a gear box of a mechanical system, where it is applicable in a wide range of applications where reducing a speed is needed. These includes turbine generators, motor or machine tools, airplanes and the likes. The speed reducer is enclosed in a rigid housing so that it can be lubricated, protected from moisture and dust with an enough space for cooling. The design of a speed reducer with an optimum minimized weight without affecting all the needed functioning has been one of the challenging problem, hence it is taken as a challenging benchmark for optimization methods. In this paper, a detailed discussion on the problem, along with proposing a solution approach based on a swarm intelligence algorithm called prey predator algorithm and possible future works will be discussed.

Prey predator algorithm is a swarm based metaheuristic algorithm inspired by the interaction of a predator and its prey (Hamadneh, Tilahun, Sathasivam, & Ong, 2013; Tilahun, & Ong, 2015). It works by exploring the solution space by categorizing the solutions into three categories as predator, best prey and ordinary prey. By increasing the number of best prey and predators, recent studies suggested that the degree of exploration and exploitation of prey predator algorithm can easily be tuned (Tilahun et al., 2016). In addition, the algorithm has been extended to a new version where adaptive step length is used (Tilahun, & Melesse, 2015; Tilahun, & Ngnotchouye, 2016). It has been found to be promising when compared to other algorithms (Tilahun et al., 2015; Tilahun et al., 2012; Tilahun et al., 2013). The algorithm has been tasted in different application and found to be effective (Hamadneh et al., 2013; Tilahun et al., 2016a, 2016 b; Tilahun, Goshu, & Ngnotchouye, 2017; Tilahun, 2012; Tilahun, 2013; Bahmani-Firouzi, Shari nia, Azizipanah-Abarghooee,& Niknam, 2015; Dai, Liu, & Chai, 2015).

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