A Bee Colony Optimization with Automated Parameter Tuning for Sequential Ordering Problem

Sequential Ordering Problem (SOP) is a type of Combinatorial Optimization Problem (COP). Solving SOP requires finding a feasible Hamiltonian path with minimum cost without violating the precedence constraints. SOP models myriad of real world industrial applications, particularly in the fields of transportation, vehicle routing and production planning. The main objective of this research is to propose an idea of solving SOP using the Bee Colony Optimization (BCO) algorithm. The underlying mechanism of the BCO algorithm is the bee foraging behavior in a typical bee colony. Throughout the research, the SOP benchmark problems from TSPLIB will be chosen as the testbed to evaluate the performance of the BCO algorithm in terms of the solution cost and the computational time needed to obtain an optimum solution. Moreover, efforts are taken to investigate the feasibility of using the Genetic Algorithm to optimally tune the parameters equipped in the existing BCO model. On average, over the selected 40 benchmark problems, the proposed method has successfully solved 9 (22.5%) benchmark problems to optimum, 17 (42.5%) benchmark problems <= 1% of deviation from the known optimum, and 37 (85%) benchmark problems <= 5% of deviation from the known optimum. Overall, the 40 benchmark problems are solved to 2.19% from the known optimum on average.