A Self-adaptive Evolutionary Algorithm for Multi-objective Optimization

Various evolutionary multiobjective optimization (EMO) algorithms have been used in the field of evolutionary fuzzy systems (EFS), because EMO algorithms can easily handle multiple objective functions such as the accuracy maximization and complexity minimization for fuzzy system design. Most EMO algorithms used in EFS are Pareto dominance-based algorithms such as NSGA-II, SPEA2, and PAES. There are a few studies where other types of EMO algorithms are used in EFS. In this paper, we apply a multiobjective evolutionary algorithm based on decomposition called MOEA/D to EFS for fuzzy classifier design. MOEA/D is one of the most well-known decomposition-based EMO algorithms. The key idea is to divide a multiobjective optimization problem into a number of single-objective problems using a set of uniformly distributed weight vectors in a scalarizing function. We propose a new scalarizing function called an accuracy-oriented function (AOF) which is specialized for classifier design. We examine the effects of using AOF in MOEA/D on the search ability of our multiobjective fuzzy genetics-based machine learning (GBML). We also examine the synergy effect of MOEA/D with AOF and parallel distributed implementation of fuzzy GBML on the generalization ability.

A ring-hierarchy-based evolutionary algorithm for multimodal multi-objective optimization

In recent years, evolutionary multiobjective optimization (EMO) algorithms have frequently been used for engineering problems with some conflicting objective functions to be simultaneously optimized. EMO algorithms can provide a number of Pareto optimal solutions to users. Two scenarios are considered in the practical use of EMO algorithms. One is that a decision maker selects a single solution from the obtained ones after the EMO process. The other is that a decision maker utilizes the solutions to analyze the relationship between design variables and objective functions of the corresponding problem. In this paper, we apply fuzzy genetics-based machine learning to the second scenario in order to generate if-then rule-based classifiers which represent the relationship between design variables and objective functions. We also utilize this method during the EMO process to pre-screen candidate offspring solutions. The classifier detects non-promising offspring solutions. Then, they are discarded before their fitness evaluation, so that the computation resource is used only for promising solutions. We apply this method to one engineering problem and examine its effect on the search performance of an EMO algorithm.

A method of designing fuzzy rule based classification systems (FRBCSs) using multi-objective optimization evolutionary algorithms (MOEAs) clearly depends on evolutionary quality. There are two types of such algorithms: Genetic Algorithms (GAs) and Swarm Intelligence (SI). Naturally arises a question how strongly utilized evolutionary algorithms influence on the efficiency of a method of designing FRBCS making this better than another. Particle swarm optimization (PSO) algorithm [13, 14] is among SI series. This paper represents an application of the multi-objective PSO algorithm with fitness sharing (MO-PSO) proposed in [8] to optimize the semantic parameters of linguistic variables and fuzzy rule selection in designing FRBCSs based on hedge algebras proposed as in [7] (using GSA-genetic simulated annealing algorithm). By simulation, MO-PSO is shown to be more efficient and produces better results than GSA-algorithm. That is to show a method of the FRBCS design is better than another one using MOEA, the same MOEA must be used.

Evolutionary algorithms have been widely used to tackle multi-objective optimization problems. Despite many successful applications there is a lack of theoretical knowledge on how and why this type of algorithm works particularly well for multi-objective problems. This special issue presents current advances to the theoretical understanding of evolutionary algorithms for multi-objective optimization. It comprises four very high quality papers which have been selected via a rigorous reviewing process. The first paper “On the Effect of Populations in Evolutionary Multi-Objective Optimisation” by Oliver Giel and Per Kristian Lehre studies the basic question whether a population is provably useful to compute the whole Pareto front of a multi-objective optimization problem. They compare restart strategies of several single-objective approaches based on one individual to a natural multi-objective approach using a population. Their analyses point out the benefits of the multi-objective evolutionary algorithm in a rigorous way. Using illustrative example functions they provide not only proven results but also a good intuition about why population-based approaches can outperform individual-based approaches in multi-objective optimization. The paper “Exploring the Runtime of an Evolutionary Algorithm for the Multi-Objective Shortest Path Problem” by Christian Horoba examines the behavior of evolutionary algorithms for the classical NP-hard multi-objective shortest path problem. The author considers an evolutionary approach based on -dominance and proves that this algorithm constitutes a fully polynomial-time randomized approximation scheme (FPRAS) for the problem. The algorithm achieves this by mimicking a problemspecific algorithm for that problem. This provides general insight into why evolutionary algorithms can perform well for problems that allow for efficient problem-specific algorithms. Hypervolume-based algorithms have become very popular in evolutionary multiobjective optimization. In the paper, “An Efficient Algorithm for Computing Hypervolume Contributions,” Karl Bringmann and Tobias Friedrich present a faster algorithm for determining the individual with the smallest hypervolume contribution in a given population. Furthermore, they study the problem of removing λ > 1 individuals with the smallest hypervolume contribution from a given population and present an elegant and fast method to carry out this task.

Immunity-based hybrid evolutionary algorithm for multi-objective optimization in global container repositioning

Evolutionary Multi-objective Optimization (EMO) is a hot research direction nowadays and one of the state-of-the-art evolutionary multi-objective optimization algorithms ——NSGA-II has gain wide attention and application in many fields. Gene Expression Programming (GEP) has a powerful search capability, but falls into local optimum easily. Based on the transformed GEP, NSGA-II and the virus evolution mechanism, a new multi-objective evolutionary algorithm GEP Virus NSGA-II is proposed. With the infection operation of virus population, the diversity of the host population is increased, and it’s much easier to jump out of the local optimum. And this algorithm has got good experimental results on 9 standard test problems.

An evolutionary algorithm for multiobjective optimization of the structural elements of the large spatial sections of ships is presented. The evolutionary algorithm where selection takes place based on the aggregated objective function combined with domination attributes as well as distance to the asymptotic solution is proposed and applied to solve the problem of optimizing structural elements with respect to their weight and surface area on a high-speed vehicle-passenger catamaran structure with several design variables such as plate thickness, scantlings of longitudinal stiffeners and transverse frames, and spacing between longitudinal and transversal structural members. Details of the computational models were at the level typical for conceptual design. Scantlings were analyzed using the selected rules of a classification society. The results of numerical experiments with the use of the developed algorithm are presented. They show that the proposed genetic algorithm can be a foundation of the effective multiobjective optimization tool for ship structure optimization. Further development of the tool should include more advanced methods for ship structural analysis.

Within the field of evolutionary multi-objective optimization, there exists a class of problems where most evolutionary multi-objective optimization algorithms (EMOAs) suffer from a loss of diversity that remains unrecoverable for extended periods, namely “imbalanced problems”. Currently, the field of multi-objective optimization lacks rigorous quantitative characterization of imbalanced multi-objective optimization problems (MOPs) and systematic understanding of their impact on algorithmic performance. To address these limitations, we introduce two novel quantities: the global and local shrinkage-spread rates, which characterize population convergence and diversity dynamics during global exploration and local exploitation phases, respectively. Based on these quantities, we provide the first mathematical characterization of imbalanced MOPs and derive key theoretical properties through rigorous probabilistic analysis. Our theoretical result shows that the probability of achieving substantial diversity recovery is below 0.1 under given conditions, demonstrating that diversity recovery becomes extremely challenging once population diversity is lost. We further construct ten imbalanced MOPs in which the difficulty of maintaining population diversity can be precisely modulated through adjustable parameters. Using these benchmark problems, we conduct comparative experiments evaluating four representative EMOAs, i.e., NSGA-II, MOEA/D, RVEA, MOEA/D-M2M and DrEA, in terms of their diversity maintenance capabilities on imbalanced MOPs. The results provide both theoretical insights and practical guidance for designing robust EMOAs capable of handling imbalanced MOPs.

Most evolutionary multiobjective optimization algorithms are designed to approximate the entire Pareto front. During the last decade, a series of preference-based evolutionary algorithms have been developed, where a part of the Pareto front is approximated by incorporating the preferences of a Decision Maker. However, only a few such algorithms are able to obtain well-distributed solutions covering the complete “region of interest” that is determined by a reference point. In this paper, a preference-based evolutionary algorithm for approximating the region of interest is proposed. It is based on the state-of-the-art genetic algorithm NSGA-II and the CHIM approach introduced in the NBI method which is used to obtain uniformly distributed solutions in the region of interest. The efficiency of the proposed algorithm has been experimentally evaluated and compared to other state-of-the-art multiobjective preference-based evolutionary algorithms by solving a set of multiobjective optimization benchmark problems. It has been shown that the incorporation of the Decision Maker’s preferences and the CHIM approach into the NSGA-II algorithm allows approximating the whole region of interest accurately while maintaining a good distribution of the obtained solutions.

In the past few years, multi-objective optimization algorithms have been extensively applied in several fields including engineering design problems. A major reason is the advancement of evolutionary multi-objective optimization (EMO) algorithms that are able to find a set of non-dominated points spread on the respective Pareto-optimal front in a single simulation. Besides just finding a set of Pareto-optimal solutions, one is often interested in capturing knowledge about the variation of variable values over the Pareto-optimal front. Recent innovization approaches for knowledge discovery from Pareto-optimal solutions remain as a major activity in this direction. In this article, a different data-fitting approach for continuous parameterization of the Pareto-optimal front is presented. Cubic B-spline basis functions are used for fitting the data returned by an EMO procedure in a continuous variable space. No prior knowledge about the order in the data is assumed. An automatic procedure for detecting gaps in the Pareto-optimal front is also implemented. The algorithm takes points returned by the EMO as input and returns the control points of the B-spline manifold representing the Pareto-optimal set. Results for several standard and engineering, bi-objective and tri-objective optimization problems demonstrate the usefulness of the proposed procedure.

Multi-objective Cascade Control of Regulatory Process with Two Conflicting Objectives

This research proposed an integrated strategy for building performance optimization from the whole life cycle perspective to explore the optimal building scheme. After the feature elimination, the ensemble learning model (ELM) was trained to obtain a high-precision model for predicting life cycle carbon emissions (LCCE), life cycle costs (LCC), and indoor discomfort hours (IDH). Then, the optimal optimization algorithm was selected among three different optimization algorithms. Finally, the best building scheme was chosen according to the newly proposed solution. The results showed that the ELM could achieve high prediction efficiency by combining input feature evaluation and screening, multi-sampling methods, and hyperparameter optimization. The R2 value of ELM can reach 0.980, while the Two-Archive Evolutionary Algorithm for Constrained multi-objective optimization (C-TAEA) was the optimal optimization algorithm. The best equilibrium solution proposed in this study solved the problem of different optimization ranges of different objectives and maximized the optimization value. Finally, the best equilibrium scheme reduced the LCCE by 34.7%, the LCC by 13.9%, and the IDH by 26.6%. Therefore, this strategy can efficiently optimize building objectives and produce a more balanced and optimal building scheme, thus making it widely applicable in building performance optimization.

Enhanced evolutionary algorithms for single and multiobjective optimization in the job shop scheduling problem

Neuroevolution for solving multiobjective knapsack problems