Tapabrata Ray, Hemant Singh, Kamrul Rahi, Tobias Rodemann, Markus Olhofer, "Towards identification of solutions of interest for multi-objective problems considering both objective and variable space information", Applied Soft Computing, vol. 119, 2022.

In practical multi/many-objective optimization problems, a decision maker (DM) is often only interested in a handful of solutions of interest (SOI) instead of a large collection of trade-off solutions spanning the entire Pareto Front (PF). Optimization algorithms capable of searching for SOIs have so far considered selection measures based on objective space only, such as reflex angle, bend angle, expected marginal utility, etc. Depending on the application, a DM may additionally require such solutions to (a) be robust i.e. insensitive to variable perturbations or (b) have a large number of performance clones, i.e., multiple solutions with similar objective values that look significantly different in the variable space. Both of these require design of new measures and search strategies with both objective and variable space considerations. In this paper, we introduce one such approach that can deliver (a) a few SOIs purely based on performance (quantified using easily comprehensible L1 measure and angle of influence) (b) a set of solutions with trade-offs between performance and robustness (quantified using T1 measure) and (c) a set of solutions with trade-offs between performance and the number of clones (quantified using T2 measure). We first define the measures and illustrate the use of such measures for offline selection of different number of SOIs using uniformly sampled solutions of well studied two and three objective test problems (DO2DK, DEB2DK4,DEB3DK1 and DEB3DK4). These serve as benchmarks for performance assessment as they can be visually assessed. Apart from the above unconstrained multi-objective test cases, we establish the credibility of the proposed approach using a multi-objective, constrained welded beam design optimization problem which has long been used for performance and robustness optimization studies. We also illustrate the performance of our approach on a practical wind turbine design optimization problem involving five objectives and twenty-two constraints.