Online intensification of search around solutions of interest for multi/many-objective optimization

In practical multi/many-objective optimization problems, a decision maker is often only interested in a handful of solutions of interest (SOI) instead of the entire Pareto Front (PF). It is therefore of significant research interest to design algorithms that can automatically detect SOIs and search around them instead of attempting to find the entire PF. However, this is challenging for a number of reasons. First and foremost, the interpretation of the underlying measures in terms of quantifying trade-off information for SOIs is not straightforward. Scalability is also an issue for most of such existing measures. Additionally, for many-objective algorithms that rely on decomposition, adaptation of reference directions and appropriate means to scale the objectives to maintain solution density around SOIs is not trivial. Lastly, constraints and decision-space are often overlooked in the existing studies but are important for practical applications. In this work, we present a simple approach to identify SOIs, using normalized net gain over nadir point and angle of influence. We illustrate the utility of the measure for offline and online identification of SOIs using a range of unconstrained and constrained benchmarks and practical design problems spanning up to 5 objectives. We also show further analysis in decision-space for an application problem to aid decision-making in practical scenarios.