Ofer Shir

Self-organizing maps for multi-objective pareto frontiers

Decision makers often need to take into account multiple conflicting objectives when selecting a solution for their problem. This can result in a potentially large number of candidate solutions to be considered. Visualizing a Pareto Frontier, the optimal set of solutions to a multi-objective problem, is considered a difficult task when the problem at hand spans more than three objective functions. We introduce a novel visual-interactive approach to facilitate coping with multi-objective problems. We propose a characterization of the Pareto Frontier data and the tasks decision makers face as they reach their decisions. Following a comprehensive analysis of the design alternatives, we show how a semantically-enhanced Self-Organizing Map, can be utilized to meet the identified tasks. We argue that our newly proposed design provides both consistent orientation of the 2D mapping as well as an appropriate visual representation of individual solutions. We then demonstrate its applicability with two real-world multi-objective case studies. We conclude with a preliminary empirical evaluation and a qualitative usefulness assessment.

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.

Pareto optimization and tradeoff analysis applied to meta-learning of multiple simulation criteria

Simulation performance may be evaluated according to multiple quality measures that are in competition and their simultaneous consideration poses a conflict. In the current study we propose a practical framework for investigating such simulation performance criteria, exploring the inherent conflicts amongst them and identifying the best available tradeoffs, based upon multiobjective Pareto optimization. This approach necessitates the rigorous derivation of performance criteria to serve as objective functions and undergo vector optimization. We demonstrate the effectiveness of our proposed approach by applying it to a specific Artificial Neural Networks (ANN) simulation, with multiple stochastic quality measures. We formulate performance criteria of this use-case, pose an optimization problem, and solve it by means of a simulation-based Pareto approach. Upon attainment of the underlying Pareto Frontier, we analyze it and prescribe preference-dependent configurations for the optimal simulation training.