Multimodal scalarized preferences in multi-objective optimization

Scalarization functions represent preferences in multi-objective optimization by mapping the vector of objectives to a single real value. Optimization techniques using scalarized preferences mainly focus on obtaining only a single global preference optimum. Instead, we propose considering all local and global scalarization optima on the global Pareto front. These points represent the best choice in their immediate neighborhood. Additionally, they are usually sufficiently far apart in the objective space to present themselves as true alternatives if the scalarization function cannot capture every detail of the decision maker's true preference. We propose an algorithmic framework for obtaining all scalarization optima of a multi-objective optimization problem. In said framework, an approximation of the global Pareto front is obtained, from which neighborhoods of local optima are identified. Local optimization algorithms are then applied to identify the optimum of every neighborhood. In this way, we have an optima-based approximation of the global Pareto front based on the underlying scalarization function. A computational study reveals that local optimization algorithms must be carefully configured for being able to find all optima.