DIFFERENTIAL EVOLUTION AND ITS VARIANTS FOR REAL LIFE OPTIMIZATION MODELS

Abstract

Most of the real life optimization problems arising in various fields of science and engineering can be modelled as global optimization problems. In such problems it is desired and is often necessary to determine a global optimal solution rather than a local optimal solution. Determining the global optimal solution of a nonlinear optimization problem is considered to be more difficult as compared to the problem of determining a local optimal solution. The various approaches available for solving the global optimization problems can be broadly categorized as deterministic and probabilistic approaches. Deterministic approaches extensively use the analytical properties such as continuity, convexity, differentiability etc. of the objective and the constraints to locate a neighbourhood of the global optimum. Most of these techniques are designed to solve a particular class of optimization problem. Consequently, these techniques are not generic in nature. On the other hand, stochastic methods, utilize randomness in an efficient way to explore the set over which the objective function is to be optimized. Stochastic methods performed well in the case of the most of the realistic problems over which these have been applied. Among stochastic approaches, Evolutionary Algorithms (EA) or Nature Inspired Algorithms (NIA) are found to be very promising search techniques for solving global complex optimization problems. Some popular EA/NIA includes Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO) and Differential Evolution (DE) etc. The focus of the present study is on DE, which has emerged as a powerful optimization tool for solving complex global optimization problems. Comparative studies have confirmed that DE outperforms many other optimizers. Practical experiences however show that DE is not completely flawless. It is vulnerable to problems like slow and/ or premature convergence, is sometimes unable to locate global optima or gets stuck in local optima. Also, like most of the other population based EA/NIA, the performance of DE deteriorates with the increase in the size of the problem. These shortcomings of DE become more persistent in case of multimodal or noisy functions.