Studies on some Aspects of Meta-Heuristic Algorithms in Solving Engineering Optimization Problems

Abstract

Optimization is the process of finding the best solution from a set of available solutions of a problem. The optimization problems in the field of mechanical engineering requires to maximize or minimize a mathematical function which represent a physical phenomenon. Traditional methods of solving optimization problems may provide exact solutions but largely fail to obtain good solution in reasonable computational time while solving complex nonlinear optimization problems because of trapping at local minima. Therefore, meta-heuristic techniques can be conveniently adopted to solve large-scale nonlinear problems for which it is difficult to obtain exact solutions by traditional methods. The capability of meta-heuristic approaches is not limited in solving particular type of problem; rather they can be applied to different types of optimization functions like linear, nonlinear, continuous, discrete etc. These algorithms do not guarantee exact solutions but produce solutions with required accuracy in finite time in most of the cases. Since engineers and practitioners need to design and manufacture products of superior quality at low cost in order to obtain competitive edge in the market place, optimization of product or process design and/ or operations of process is highly essential. The problems encountered in real world are mostly nonlinear in nature with restrictions in use of resources. Sometimes multiple conflicting objectives need to be satisfied. To solve such type of problems, meta-heuristic algorithms can be conveniently applied. Before applying the algorithms to solve real world problems, they must be tested with a variety of test problems.
In this thesis, an efficient but simple meta-heuristic algorithm known as simple optimization algorithm (SOPT) is proposed to solve complex engineering problems. An improvement is made in the algorithm so that it should get escaped from the local optima whenever it gets stuck up. It is applied to solve twenty-five unconstrained benchmark functions of different characteristics. The results of optimization are compared with some of the well-known meta-heuristic techniques viz. artificial bee colony algorithm (ABC), particle swarm optimization (PSO), genetic algorithm (GA), shuffled frog leaping algorithm (SFLA), imperialistic competitive algorithm(ICA) and teaching learning based optimization(TLBO). Promising and comparable results are obtained for most of the test problems. Initial results encourage to further develop the SOPT algorithm for getting solution for constrained optimization problems. However, performance of an algorithm in solving constrained optimization problem depends on proper selection of constraint handling method. In this research, a constraint fitness priority based ranking method is used to handle constraints in SOPT algorithm. SOPT algorithm is applied to solve eighteen constrained problems. Some of these problems are continuous, some are restricted to take only integer values and some are of mixed type where some parameter take only integer values and others take any continuous value. These problems include eleven constrained single objective design and manufacturing optimization problems. Results of optimization from SOPT algorithm is compared with other meta-heuristic algorithms like GA, PSO, ABC, TLBO, differential evolution (DE), firefly algorithm (FA), league championship algorithm (LCA), water cycle algorithm (WCA) and mine blast algorithm (MBA) and some of the modified versions of these algorithms. To check stability of algorithm, it is run for thirty times to calculate mean result and standard deviation of results. Promising stable results are obtained in most of the problems. In engineering applications, often situation arises when optimization of multiple objectives, sometimes conflicting in nature, is required. In such cases, a closed form solution is difficult to obtain but a set of non-dominated solutions are generated to provide the decision maker a wide choice of selecting a solution depending on the situation. SOPT algorithm is incorporated with a dynamically weighted aggregation approach where multiple objectives are aggregated into a single objective through dynamically varying weights. To maintain uniformly distributed non-dominated solutions, a crowding distance approach is employed in SOPT algorithm. Multi-objective SOPT algorithm is applied to solve seventeen multi-objective problems from the literature including six engineering optimization problems. Sets of non-dominated solutions are obtained from multi-objective SOPT algorithm and these are compared with the results of non-dominated sorting based genetic algorithm II (NSGA II). To measure the quality of solutions, four metrics are defined - two metrics for finding closeness of obtained solutions from the best possible solutions and two are defined to check the diversity of solutions. Results indicate that SOPT algorithm delivers results comparable to NSGA II results. SOPT algorithm being a simple method to understand, easy to implement and able to solve variety of optimization problems including unconstrained and constrained, single and multi-objective problems, it becomes a good choice for solving real world engineering optimization problems