Abstract
This paper presents a novel method for computing the multi-objective problem in the case of a metric state space using the Manhattan distance. The problem is restricted to a class of ergodic controllable finite Markov chains. This optimization approach is developed for converging to an optimal solution that corresponds to a strong Pareto optimal point in the Pareto front. The method consists of a two-step iterated procedure: (a) the first step consists on an approximation to a strong Pareto optimal point and, (b) the second step is a refinement of the previous approximation. We formulate the problem adding the Tikhonov's regularization method to ensure the convergence of the cost-functions to a unique strong point into the Pareto front. We prove that there exists an optimal solution that is a strong Pareto optimal solution and it is the closest solution to the utopian point of the Pareto front. The proposed solution is validated theoretically and by a numerical example considering the vehicle routing planning problem.
Original language | English |
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Pages (from-to) | 2269-2286 |
Number of pages | 18 |
Journal | International Journal of Computer Mathematics |
Volume | 95 |
Issue number | 11 |
DOIs | |
State | Published - 2 Nov 2018 |
Keywords
- Markov chains
- Multi-objective optimization
- Pareto front
- Pareto optimality
- strong Pareto policies