Multimodal Function Optimization Using an Improved Bat Algorithm in Noise-Free and Noisy Environments

Modern optimization problems in economics, medicine, and engineering are becoming more complicated and have a convoluted search space with multiple minima. These problems are multimodal with objective functions exhibiting multiple peaks, valleys, and hyperplanes of varying heights. Furthermore, they are nonlinear, non-smooth, non-quadratic, and can have multiple satisfactory solutions. In order to select a best solution among several possible solutions that can meet the problem objectives, it is desirable to find many such solutions. For these problems, the gradient information is either not available or not computable within reasonable time. Therefore, solving such problems is a challenging task. Recent years have seen a plethora of activities to solve such multimodal problems using non-traditional methods. These methods are nature inspired and are becoming popular due to their general applicability and effective search strategies. In this chapter, we assess the ability of an improved bat algorithm (IBA) to solve multimodal problems in noise-free and additive white Gaussian noise (AWGN) environments. Numerical results are presented to show that the IBA can successfully locate multiple solutions in both noise-free and AWGN environments with a relatively high degree of accuracy.