An extended ε-constraint method for a multiobjective finite-horizon Markov decision process

A Markov decision process (MDP) is an appropriate mathematical framework for analysis and modeling a large class of sequential decision-making problems. Real-world applications necessitate the evaluation of the value of a decision according to several conflicting objectives. This paper presents an extended epsilon-constraint method for a multiobjective finite-horizon MDP. This study integrates the epsilon-constraint method with the K-best policies algorithm to find the nondominated deterministic Markovian policies on the Pareto-optimal frontier. The proposed algorithm is evaluated on biobjective maintenance scheduling and machine running speed selection problems, and its performance is compared with a classic approach in the literature (weighted-sum, WS, method). Satisfying results show that the proposed algorithm obtains a good-quality Pareto frontier and has advantages over the WS method.