Exclusion of regions method for multi-objective optimization

摘要

The Exclusion of Regions Method (TERM) and Concurrent Gradients Method (CGM) for multi-objective optimization of objective functions considered in a multi-dimensional domain are provided. TERM decomposes the domain into a set of non-intersecting sub-regions, and applies a special criterion to each sub-region to determine if it does not contain Pareto-points. Non-prospective sub-regions are filtered out, while prospective ones are used for generating points-candidates, and their improvement by a recursive procedure until pre-assigned accuracy is achieved. CGM works as any gradient-based algorithm. But on each step CGM determines the area of simultaneous objective functions improvement and a direction for the next step in this area. The area is determined in a simple way based on gradients for each objective function calculated on current point. This introduces new a type of numerical analysis in the multi-objective optimization theory, and allows developing extremely efficient optimization algorithms without using the scalarization technique or any kind of heuristic.