Over the last three decades, a large number of evolutionary algorithms have been developed for solving multi-objective optimization problems. However, there lacks an upto-date and comprehensive software platform researchers to properly benchmark existing practitioners apply selected solve their real-world The demand such common tool becomes even more urgent, when source code many proposed has not made publicly available. To address these issues, we MATLAB in this paper, called PlatEMO, which...

Evolutionary algorithms (EAs) have shown to be promising in solving many-objective optimization problems (MaOPs), where the performance of these heavily depends on whether solutions that can accelerate convergence toward Pareto front and maintaining a high degree diversity will selected from set nondominated solutions. In this paper, we propose knee point-driven EA solve MaOPs. Our basic idea is points are naturally most preferred among if no explicit user preferences given. A bias current...

During the past two decades, a variety of multiobjective evolutionary algorithms (MOEAs) have been proposed in literature. As pointed out some recent studies, however, performance an MOEA can strongly depend on Pareto front shape problem to be solved, whereas most existing MOEAs show poor versatility problems with different shapes fronts. To address this issue, we propose based enhanced inverted generational distance indicator, which adaptation method is suggested adjust set reference points...

The current literature of evolutionary many-objective optimization is merely focused on the scalability to number objectives, while little work has considered decision variables. Nevertheless, many real-world problems can involve both objectives and large-scale To tackle such (MaOPs), this paper proposes a specially tailored algorithm based variable clustering method. begin with, method divides variables into two types: 1) convergence-related 2) diversity-related Afterward, optimize types...

Evolutionary algorithms have been shown to be powerful for solving multiobjective optimization problems, in which nondominated sorting is a widely adopted technique selection. This technique, however, can computationally expensive, especially when the number of individuals population becomes large. mainly because most existing algorithms, solution needs compared with all other solutions before it assigned front. In this paper we propose novel, efficient approach sorting, termed sort (ENS)....

Constrained multiobjective optimization problems (CMOPs) are challenging because of the difficulty in handling both multiple objectives and constraints. While some evolutionary algorithms have demonstrated high performance on most CMOPs, they exhibit bad convergence or diversity CMOPs with small feasible regions. To remedy this issue, article proposes a coevolutionary framework for constrained optimization, which solves complex CMOP assisted by simple helper problem. The proposed evolves one...

In the real world, it is not uncommon to face an optimization problem with more than three objectives. Such problems, called many-objective problems (MaOPs), pose great challenges area of evolutionary computation. The failure conventional Pareto-based multi-objective algorithms in dealing MaOPs motivates various new approaches. However, contrast rapid development algorithm design, performance investigation and comparison have received little attention. Several test suites which were designed...

Surrogate-assisted evolutionary algorithms (SAEAs) have been developed mainly for solving expensive optimization problems where only a small number of real fitness evaluations are allowed. Most existing SAEAs designed low-dimensional single or multiobjective problems, which not well suited many-objective optimization. This paper proposes surrogate-assisted algorithm that uses an artificial neural network to predict the dominance relationship between candidate solutions and reference instead...

There exist many multiobjective optimization problems (MOPs) containing a large number of decision variables in real-world applications, which are known as large-scale MOPs. Due to the ineffectiveness existing operators finding optimal solutions huge space, some variable division-based algorithms have been tailored for improving search efficiency solving However, these will encounter difficulties when with complicated landscapes, division is likely be inaccurate and time consuming. In this...

Both convergence and diversity are crucial to evolutionary many-objective optimization, whereas most existing dominance relations show poor performance in balancing them, thus easily leading a set of solutions concentrating on small region the Pareto fronts. In this paper, novel relation is proposed better balance for optimization. relation, an adaptive niching technique developed based angles between candidate solutions, where only best converged solution identified be nondominated each...

In the last two decades, a variety of different types multiobjective optimization problems (MOPs) have been extensively investigated in evolutionary computation community. However, most existing algorithms encounter difficulties dealing with MOPs whose Pareto optimal solutions are sparse (i.e., decision variables zero), especially when number is large. Such large-scale exist wide range applications, for example, feature selection that aims to find small subset features from large candidate...

In this paper, we propose a framework to accelerate the computational efficiency of evolutionary algorithms on large-scale multiobjective optimization. The main idea is track Pareto optimal set (PS) directly via problem reformulation. To begin with, algorithm obtains reference directions in decision space and associates them with weight variables for locating PS. Afterwards, original optimization reformulated into low-dimensional single-objective problem. problem, reconstructed by objective...

Both objective optimization and constraint satisfaction are crucial for solving constrained multiobjective problems, but the existing evolutionary algorithms encounter difficulties in striking a good balance between them when tackling complex feasible regions. To address this issue, article proposes two-stage algorithm, which adjusts fitness evaluation strategies during process to adaptively satisfaction. The proposed algorithm can switch two stages according status of current population,...

Over the last three decades, a large number of evolutionary algorithms have been developed for solving multiobjective optimization problems. However, there lacks an up-to-date and comprehensive software platform researchers to properly benchmark existing practitioners apply selected solve their real-world The demand such common tool becomes even more urgent, when source code many proposed has not made publicly available. To address these issues, we MATLAB multi-objective in this paper,...

Due to the curse of dimensionality search space, it is extremely difficult for evolutionary algorithms approximate optimal solutions large-scale multiobjective optimization problems (LMOPs) by using a limited budget evaluations. If Pareto-optimal subspace approximated during process, space can be reduced and difficulty encountered highly alleviated. Following above idea, this article proposes an algorithm solve sparse LMOPs learning subspace. The proposed uses two unsupervised neural...

Evolutionary algorithms (EAs) have become one of the most effective techniques for multi-objective optimization, where a number variation operators been developed to handle problems with various difficulties. While EAs use fixed operator all time, it is labor-intensive process determine best EA new problem. Hence, some recent studies dedicated adaptive selection during search process. To address exploration versus exploitation dilemma in selection, this paper proposes novel method based on...

Axon P systems are computing models with a linear structure in the sense that all nodes (i.e., units) arranged one by along axon. Such have good biological motivation: an axon nervous system is complex information processor of impulse signals. Because linear, computational power such has been proved to be greatly restricted; particular, not universal as language generators. It remains open whether number In this paper, we prove both generators and function devices, investigate needed...

Diversity preservation plays an important role in the design of multi-objective evolutionary algorithms, but diversity performance assessment these algorithms remains challenging. To address this issue, paper proposes a metric and test suite for multiobjective algorithms. The proposed assesses both evenness spread solution set by projecting it to lower-dimensional hypercube calculating "volume" projected set. contains eight benchmark problems, which pose stiff challenges existing obtain...

Since non-dominated sorting was first adopted in NSGA 1995, most evolutionary algorithms have employed as one of the major criteria their environmental selection for solving multi- and many-objective optimization problems. In this paper, we focus on analyzing effectiveness efficiency algorithms. The is verified by considering two popular algorithms, NSGA-II KnEA, which were designed problems, respectively. evaluated comparing several state-of-the-art These results provide important insights...