A tradeoff-based interactive multi-objective optimization method driven by evolutionary algorithms

Multi-objective optimization problems involve two or more conflicting objectives, and they have a set of Pareto optimal solutions instead of a single optimal solution. In order to support the decision maker (DM) to find his/her most preferred solution, we propose an interactive multi-objective optimization method based on the DM's preferences in the form of indifference tradeoffs. The method combines evolutionary algorithms with the gradient-based interactive step tradeoff (GRIST) method. An evolutionary algorithm is used to generate an approximate Pareto optimal solution at each iteration. The DM is asked to provide indifference tradeoffs whose projection onto the tangent hyperplane of the Pareto front provides a tradeoff direction. An approach for approximating the normal vector of the tangent hyperplane is proposed which is used to calculate the projection. A water quality management problem is used to demonstrate the interaction process of the interactive method. In addition, three benchmark problems are used to test the accuracy of the normal vector approximation approach and compare the proposed method with GRIST.