Pareto Landscapes Analyses via Graph-Based Modeling for Interactive Decision-Making

We consider two complementary tasks for consuming optimization results of a given multiobjective problem by decision-makers. The underpinning in both exploratory tasks is analyzing Pareto landscapes, and we propose in both cases discrete graph-based reductions. Firstly, we introduce interactive navigation from a given suboptimal reference solution to Pareto efficient solution-points. The proposed traversal mechanism is based upon landscape improvement-transitions from the reference towards Pareto-dominating solutions in a baby-steps fashion – accepting relatively small variations in the design-space. The Efficient Frontier and the archive of Pareto suboptimal points are to be obtained by population-based multiobjective solvers, such as Evolutionary Multiobjective Algorithms. Secondly, we propose a framework for automatically recommending a preferable subset of points belonging to the Frontier that accounts for the decision-maker’s tendencies. We devise a line of action that activates one of two approaches: either recommending the top offensive team – the gain-prone subset of points, or the top defensive team – the loss-averse subset of points. We describe the entire recommendation process and formulate mixed-integer linear programs for solving its combinatorial graph-based problems.