SMSEMOA

SMSEMOA, short for S-metric Selection Evolutionary Multi-Objective Algorithm, is a population-based evolutionary algorithm designed for solving multiobjective optimization problems. It uses the hypervolume indicator, also known as the S-metric, as the central measure of solution quality. The algorithm maintains a fixed-size population of candidate solutions, each characterized by a vector of objective values.

At each generation, SMSEMOA generates offspring through standard evolutionary operators such as selection, crossover and mutation. The parent and offspring populations are merged, and a survival selection step is performed to form the next generation. The survival step works by calculating the hypervolume contribution of each individual to the hypervolume of the current population; the individual with the smallest contribution is removed. This removal criterion aims to maximize the hypervolume of the remaining set, thereby promoting convergence toward the Pareto front and maintaining diversity along it. The process repeats until a termination condition is met (for example, a maximum number of evaluations).

Hypervolume-based selection provides a direct measure of the combined quality of the Pareto-optimal front approximation but has high computational cost, especially for many objectives or large populations. Various implementations use exact or approximate HV computations and may include normalization or reference points to stabilize measurements.

SMSEMOA has been shown to produce well-distributed and converged fronts on a range of benchmark problems and real-world design problems. It is often compared with NSGA-II, SPEA2, and MOEA/D; its strength lies in directly optimizing the hypervolume indicator rather than relying on dominance rank and crowding distance alone. Introduced by Beume, Naujoks and Emmerich in 2007.