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Evolutionary algorithms (EAs) are general-purpose optimization algorithms, inspired by natural evolution. Recent theoretical studies have shown that EAs can achieve good approximation guarantees for solving the problem classes of submodular…
Many real-world optimization problems can be stated in terms of submodular functions. Furthermore, these real-world problems often involve uncertainties which may lead to the violation of given constraints. A lot of evolutionary…
As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical…
In the area of multi-objective evolutionary algorithms (MOEAs), there is a trend of using an archive to store non-dominated solutions generated during the search. This is because 1) MOEAs may easily end up with the final population…
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…
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…
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…
Parameter control has succeeded in accelerating the convergence process of evolutionary algorithms. While empirical and theoretical studies have shed light on the behavior of algorithms for single-objective optimization, little is known…
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…
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…
Evolutionary Algorithms (EAs) have become the most popular tool for solving widely-existed multi-objective optimization problems. In Multi-Objective EAs (MOEAs), there is increasing interest in using an archive to store non-dominated…
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 major difficulty in Multi-objective Optimization Evolutionary Algorithms (MOEAs) is how to find an appropriate solution that is able to converge towards the true Pareto Front with high diversity. Most existing methodologies, which have…
The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is one of the most prominent algorithms to solve multi-objective optimization problems. Recently, the first mathematical runtime guarantees have been obtained for this algorithm,…
In solving multi-modal, multi-objective optimization problems (MMOPs), the objective is not only to find a good representation of the Pareto-optimal front (PF) in the objective space but also to find all equivalent Pareto-optimal subsets…
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…
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…
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…
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…
Apart from few exceptions, the mathematical runtime analysis of evolutionary algorithms is mostly concerned with expected runtimes. In this work, we argue that stochastic domination is a notion that should be used more frequently in this…