The Improvement Direction Mapping Method

The Improvement Direction Mapping (IDM) is a novel multi-objective local-search method, that independently steers a solution set towards promising regions by computing improvement directions in the objective space and transform them, into the variable space, as search directions. The IDM algorithm consists of two main sub-tasks 1) the computation of the improvement directions in the objective space 2) the transformation of directions from the objective space to the variable space. The transformation from the objective to the variable space is carried out via a pseudo-inverse of the Jacobian matrix. The goal of this paper is two fold: it introduces the main IDM algorithm and three approaches to determine improvement directions, and then it explores the trade-off of either approach by performing statistical analysis on the experimental results. The approaches are based on: 1) Pareto dominance, 2) aggregation functions, and 3) indicator functions. A set of well-known benchmark problems are used to compare the three proposed improvement directions and the Directed Search method. This paper is devoted to introduce the IDM algorithm for multi-objective optimization, nonetheless, the application of IDM for hybridizing stochastic-global-search algorithms is straight forward.