Approximating multi-objective scheduling problems

Authors:
Said Dabia;El-Ghazali Talbi;Tom Van Woensel;Ton De Kok
Affiliations:
Eyefreight B.V., the Netherlands and Eindhoven University of Technology, School of Industrial Engineering, The Netherlands;University of Lille, INRIA, CNRS, France;Eindhoven University of Technology, School of Industrial Engineering, The Netherlands;Eindhoven University of Technology, School of Industrial Engineering, The Netherlands
Venue:
Computers and Operations Research
Year:
2013

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Abstract

In many practical situations, decisions are multi-objective by nature. In this paper, we propose a generic approach to deal with multi-objective scheduling problems (MOSPs). The aim is to determine the set of Pareto solutions that represent the interactions between the different objectives. Due to the complexity of MOSPs, an efficient approximation based on dynamic programming is developed. The approximation has a provable worst case performance guarantee. Even though the approximate Pareto set consists of fewer solutions, it represents a good coverage of the true set of Pareto solutions. We consider generic cost parameters that depend on the state of the system. Numerical results are presented for the time-dependent multi-objective knapsack problem, showing the value of the approximation in the special case when the state of the system is expressed in terms of time.