Bird Mating Optimizer for Combinatorial Optimization Problems

Abstract

The bird mating optimizer is a new metaheuristic algorithm that was originally proposed to solve continuous optimization problems with a very promising performance. However, the algorithm has not yet been applied for solving combinatorial optimization problems. Thus, the formulation may not be able to generate a discrete feasible solution. Many continuous algorithms used random-key representation to represent the discrete solution using real numbers or a discrete variant of the algorithm is used to deal with the discrete solution of the problem. However, there is no evidence which methodology is better for solving combinatorial optimization problems. Therefore, this work proposes two variants of bird mating optimizer (random-key bird mating optimizer and the discrete bird mating optimizer), to identify which one is more efficient in solving combinatorial optimization problems. In the first one, we use a random-key encoding scheme, whilst, in the later one, we use crossover (multi-parent) and mutation operators to combine the components of the selected parents to generate new broods. The performance of these algorithms is tested on the travelling salesman problem and berth allocation problem, and are compared with the results of two well-known optimization algorithms: Genetic Algorithm and Particle Swarm Optimization. Experimental results show that the discrete bird mating optimizer is more efficient than the others on all tested benchmark instances. Indeed, it is able to attain the best-known results in some of the BAP benchmark instances. These indicate the applicability and the effectiveness of the proposed discrete bird mating optimizer in solving combinatorial optimization problems.

Keywords

• Heuristics
• bird mating optimizer
• berth allocation problem
• travelling salesman problem
• random-key
• combinatorial optimization