Related papers: Runtime Analyses of NSGA-III on Many-Objective Pro…
NSGA-II and NSGA-III are two of the most popular evolutionary multi-objective algorithms used in practice. While NSGA-II is used for few objectives such as 2 and 3, NSGA-III is designed to deal with a larger number of objectives. In a…
Evolutionary algorithms are widely used for solving multi-objective optimization problems. A prominent example is NSGA-III, which is particularly well suited for solving problems involving more than three objectives, distinguishing it from…
In recent years, a theoretical understanding has rapidly advanced regarding how popular multi-objective evolutionary algorithms (MOEAs) can optimize many-objective problems. However, the benefits of using crossover in many-objective…
The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is the most prominent multi-objective evolutionary algorithm for real-world applications. While it performs evidently well on bi-objective optimization problems, empirical studies…
The non-dominated sorting genetic algorithm~II (NSGA-II) is the most popular multi-objective optimization heuristic. Recent mathematical runtime analyses have detected two shortcomings in discrete search spaces, namely, that the NSGA-II has…
Very recently, the first mathematical runtime analyses of the multi-objective evolutionary optimizer NSGA-II have been conducted. We continue this line of research with a first runtime analysis of this algorithm on a benchmark problem…
Due to the more complicated population dynamics of the NSGA-II, none of the existing runtime guarantees for this algorithm is accompanied by a non-trivial lower bound. Via a first mathematical understanding of the population dynamics of the…
Very recently, the first mathematical runtime analyses for the NSGA-II, the most common multi-objective evolutionary algorithm, have been conducted. Continuing this research direction, we prove that the NSGA-II optimizes the OneJumpZeroJump…
This article addresses theory in evolutionary many-objective optimization and focuses on the role of crossover operators. The advantages of using crossover are hardly understood and rigorous runtime analyses with crossover are lagging far…
The NSGA-II is the most prominent multi-objective evolutionary algorithm (cited more than 50,000 times). Very recently, a mathematical runtime analysis has proven that this algorithm can have enormous difficulties when the number of…
The NSGA-II is one of the most prominent algorithms to solve multi-objective optimization problems. Despite numerous successful applications, several studies have shown that the NSGA-II is less effective for larger numbers of objectives. In…
Multi-objective evolutionary algorithms (MOEAs) are among the most widely and successfully applied optimizers for multi-objective problems. However, to store many optimal trade-offs (the Pareto optima) at once, MOEAs are typically run with…
Recent theoretical works have shown that the NSGA-II can have enormous difficulties to solve problems with more than two objectives. In contrast, algorithms like the NSGA-III or SMS-EMOA, differing from the NSGA-II only in the secondary…
Evolutionary algorithms (EAs) have been widely used to solve multi-objective optimization problems, and have become the most popular tool. However, the theoretical foundation of multi-objective EAs (MOEAs), especially the essential…
Evolutionary algorithms (EAs) are widely used for multi-objective optimization due to their population-based nature. Traditional multi-objective EAs (MOEAs) generate a large set of solutions to approximate the Pareto front, leaving a…
This paper conducts the first rigorous runtime analysis of the SMS-EMOA for many-objective optimization. To this aim, we first propose a many-objective counterpart of the bi-objective OJZJ benchmark. We prove that SMS-EMOA computes the full…
Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update, a key component in multi-objective EAs (MOEAs), is…
NSGA-III is one of the most widely adopted algorithms for tackling many-objective optimization problems. However, its CPU-based design severely limits scalability and computational efficiency. To address the limitations, we propose…
The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications. However, in contrast to several simple MOEAs analyzed also via mathematical…
The NSGA-III algorithm relies on uniformly distributed reference points to promote diversity in many-objective optimization problems. However, this strategy may underperform when facing irregular Pareto fronts, where certain vectors remain…