A Brief Look at Multi-Criteria Problems: Multi-Threshold Optimization versus Pareto-Optimization

What is it about?

Multi-objective optimization problems are important as they arise in many practical circumstances. In such problems, there is no general notion of optimality, as there are different objective criteria which can be contradictory. In practice, often there is no unique optimality criterion for measuring the solution quality. The latter is rather determined by the value of the solution for each objective criterion. In fact, a practitioner seeks for a solution that has an acceptable value of each of the objective functions and, in practice, there may be different tolerances to the quality of the delivered solution for different objective functions: for some objective criteria, solutions that are far away from an optimal one can be acceptable. Traditional Pareto-optimality approach aims to create all non-dominated feasible solutions in respect to all the optimality criteria. This often requires an inadmissible time. Besides, it is not evident how to choose an appropriate solution from the Pareto-optimal set of feasible solutions, which can be very large. Here we propose a new approach and call it multi-threshold optimization setting that takes into account different requirements for different objective criteria and so is more flexible and can often be solved in a more efficient way.

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