Apply Manta Ray Foraging Optimization to Solve the Continuous-Time Markov Chain Problems

Continuous-time Markov chains problems (CTMCP) are continuous-time, discrete-state stochastic problems that can be modeled by the continuous-time Markov chains. Solving the CTMCP by existing algorithms becomes highly time-consuming when the problem size is increased. Ordinal optimization (OO) theory provides a reliable framework to solve CTMCP. However, the stochastic inequality constraints limit the efficiency and competitiveness of OO theory. In this work, a method combining ordinal optimization (OO) and manta ray foraging optimization (MRFO) is developed for solving the CTMCP in a reasonable time. MRFO is a swarm intelligence metaheuristic technique that arises from the modeling of the hunting mechanism of manta rays in nature. The proposed method is applied for finding the optimal number of agents to minimize the total cost of agents under service level constraints in a multi-skill call center. Experimental results of the proposed approach are compared to three heuristic methods. Simulation results show that the proposed method can obtain an illustrious decision vector with a higher computing performance and solution quality than the three heuristic approaches.