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Evolutionary algorithms (EAs) have emerged as a predominant approach for addressing multi-objective optimization problems. However, the theoretical foundation of multi-objective EAs (MOEAs), particularly the fundamental aspects like running…
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…
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…
Multi-objective evolutionary algorithms (MOEAs) have become essential tools for solving multi-objective optimization problems (MOPs), making their running time analysis crucial for assessing algorithmic efficiency and guiding practical…
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…
Despite significant progress in the field of mathematical runtime analysis of multi-objective evolutionary algorithms (MOEAs), the performance of MOEAs on discrete many-objective problems is little understood. In particular, the few…
Runtime analysis has recently been applied to popular evolutionary multi-objective (EMO) algorithms like NSGA-II in order to establish a rigorous theoretical foundation. However, most analyses showed that these algorithms have the same…
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…
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…
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…
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…
NSGA-III is a prominent algorithm in evolutionary many-objective optimization. It is particularly well suited for optimizing problems with more than three objectives, distinguishing it from the classical NSGA-II. However, theoretical…
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…
Together with the NSGA-II, the SPEA2 is one of the most widely used domination-based multi-objective evolutionary algorithms. For both algorithms, the known runtime guarantees are linear in the population size; for the NSGA-II, matching…
The decomposition-based multi-objective evolutionary algorithm (MOEA/D) does not directly optimize a given multi-objective function $f$, but instead optimizes $N + 1$ single-objective subproblems of $f$ in a co-evolutionary manner. It…
In single-objective optimization, it is well known that evolutionary algorithms also without further adjustments can tolerate a certain amount of noise in the evaluation of the objective function. In contrast, this question is not at all…
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…
In the real world, there exist a class of optimization problems that multiple (local) optimal solutions in the solution space correspond to a single point in the objective space. In this paper, we theoretically show that for such multimodal…
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…
Runtime analysis has produced many results on the efficiency of simple evolutionary algorithms like the (1+1) EA, and its analogue called GSEMO in evolutionary multiobjective optimisation (EMO). Recently, the first runtime analyses of the…