A hybrid modified Bat Algorithm with Dynamic Spiral Method for solving mixed integer non-linear programming optimization

Most optimization problems in engineering are nonlinear, with many constraints. Consequently, finding optimal solutions to such nonlinear problems requires efficient optimization methods. Most of the methods used so far are gradient-based methods. In gradient-based methods, the objective function must be differentiable, and the search for the optimum solution usually starts with a guess-point. For multimodal objectives, the search will likely get stuck at a local optimum. Nowadays, new metaheuristic methods are being developed for solving nonlinear optimization problems. Metaheuristic methods neither require a guess-point nor a derivative of the objective function. Metaheuristic methods, called Bat Algorithm and Spiral Dynamic Method, have been developed for solving optimization problems. Each of the methods has the strength to solve the problem. We propose combining Bat Algorithm (BA) and Dynamic Spiral Method (DSM) for solving mixed integer optimization. The bat Algorithm is used for the exploration stage to find some candidate solutions. Meanwhile, the dynamic spiral method is used in local search to find the best optimum solution. The result obtained by Bat Algorithm-Dynamic Spiral Method (BA-DSM) were more effective than the standard Bat Algorithm in solving the problem.