Multi-objective optimization, metaheuristics and visual analytics

Multi-objective optimization, metaheuristics and visual analytics


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Speaker(s): Nicolas Wesner (Mazars Actuariat)

This paper presents a system for interactive multi-objective optimization that makes use of a genetic algorithm and very simple and intuitive interactive visualization techniques. In a first step optimal solutions are selected by the decision maker through direct visualization of a multidimensional Pareto Frontier that is constructed from a limited set of point (the reduced decision space). Genetic algorithms are then used in order to search for alternative optimal solutions in the neighborhood of the user's selection.

The interactive visualization technique used here for multi-objective optimization stands mid-way between the brush and link technique, a visual method used in operational research for exploratory analysis of multidimensional data sets, and interactive multi-criteria decision methods that use the concept of reference point. Multiple views of the potential solutions on scatterplots allow the user to directly search acceptable solutions in bi-objective spaces whereas a Venn diagram displays information about the relative scarcity of potential acceptable solutions under distinct criteria.

In this system interactive visualization techniques allows the user to directly observe and select preferred solutions but also to steer the genetic algorithm and guide it in the search space. The genetic algorithm permits to refine search in creating novelty in the search space and allows to evaluate the robustness of selected solutions. Finally those very intuitive data visualization techniques allow for comprehensive interpretation and permit to communicate the results efficiently.

An application to a strategic asset allocation problem is presented. The problem consist in determining optimal weights for a fixed mix investment strategy with various asset classes when various objective functions are considered (mean, volatility and other statistics of past returns measured over long and short periods, stress tests resilience, transaction cost,…).

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