Performance Of Multi-objective Evolutionary Algorithms Research Articles

Study on the performance and efficiency of multi-objective evolutionary algorithms for trimaran outrigger layout seakeeping optimization problem

Trimaran as a high-performance vessel, possesses excellent characteristics such as high speed, low wave-making resistance, and good seakeeping performance. Different from conventional monohull ship, the design of a trimaran requires additional consideration of the outrigger layout, as the position of two outriggers can affect its hydrodynamic performance. In this study, high-speed slender body potential flow theory (also named the 2D+t theory or the 2.5D method) was employed to calculate the heave and pitch motion in order to evaluate the seakeeping performance of trimarans with different outrigger layouts at varying speeds. Model experiments were subsequently conducted to validate the effectiveness of the 2.5D method in simulating the motion of trimarans under different outrigger layouts. Three multi-objective evolutionary algorithms, including Non-dominated sorting genetic algorithm II (NSGA-II), Non-dominated sorting genetic algorithm III (NSGA-III), and Multi-objective evolutionary algorithm based on decomposition (MOEA/D), as well as their applications in the optimization of trimaran outrigger layouts were introduced. Utilizing the 2.5D method based computational program as the solver, the efficiency and performance of these multi-objective evolutionary algorithms were compared. Discuss the advantages and disadvantages of three multi-objective evolutionary algorithms in solving trimaran outrigger layout optimization problem by comparing the optimization results from two aspects: optimization efficiency, and optimal solution performance. The results indicate that for optimization efficiency, the weighted sum approach based MOEA/D exhibits best optimization efficiency. NSGA-II and NSGA-III show a good advantage in terms of optimal solution performance, and compared to NSGA-II, NSGA-III can obtain more Pareto solutions.

MOAAA/D: a decomposition-based novel algorithm and a structural design application

When real-world engineering challenges are examined adequately, it becomes clear that multi-objective need to be optimized. Many engineering problems have been handled utilizing the decomposition-based optimization approach according to the literature. The performance of multi-objective evolutionary algorithms is highly dependent on the balance of convergence and diversity. Diversity and convergence are not appropriately balanced in the decomposition technique, as they are in many approaches, for real-world problems. A novel Multi-Objective Artificial Algae Algorithm based on Decomposition (MOAAA/D) is proposed in the paper to solve multi-objective structural problems. MOAAA/D is the first multi-objective algorithm that uses the decomposition-based method with the artificial algae algorithm. MOAAA/D, which successfully draws a graph on 24 benchmark functions within the area of two common metrics, also produced promising results in the structural design problem to which it was applied. To facilitate the design of the "rectangular reinforced concrete column" using MOAAA/D, a solution space was derived by optimizing the rebar ratio and the concrete quantity to be employed.

Multiobjective Evolutionary Component Effect on Algorithm Behaviour

The performance of multiobjective evolutionary algorithms (MOEAs) varies across problems, making it hard to develop new algorithms or apply existing ones to new problems. To simplify the development and application of new multiobjective algorithms, there has been an increasing interest in their automatic design from their components. These automatically designed metaheuristics can outperform their human-developed counterparts. However, it is still unknown what are the most influential components that lead to performance improvements. This study specifies a new methodology to investigate the effects of the final configuration of an automatically designed algorithm. We apply this methodology to a tuned Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) designed by the iterated racing (irace) configuration package on constrained problems of 3 groups: (1) analytical real-world problems, (2) analytical artificial problems and (3) simulated real-world. We then compare the impact of the algorithm components in terms of their Search Trajectory Networks (STNs), the diversity of the population, and the anytime hypervolume values. Looking at the objective space behavior, the MOEAs studied converged before half of the search to generally good HV values in the analytical artificial problems and the analytical real-world problems. For the simulated problems, the HV values are still improving at the end of the run. In terms of decision space behavior, we see a diverse set of the trajectories of the STNs in the analytical artificial problems. These trajectories are more similar and frequently reach optimal solutions in the other problems.

A two-stage direction-guided evolutionary algorithm for large-scale multiobjective optimization

Large-scale multiobjective optimization problems (LSMOPs) have exponential growth in the search space as the decision variables increase, and the vast search space poses a challenge to the performance of multiobjective evolutionary algorithms (MOEAs). Many current large-scale MOEAs need to consume a large amount of computational resources to get good performance. This paper proposes a two-stage direction-guided evolutionary algorithm for large-scale multiobjective optimization (LMOEA-S2D) to balance the performance and computational resource overhead. The algorithm exploits the Pareto-optimality property of domination and the diversity-preserving property of decomposition to optimize the performance in the two stages, respectively, and designs a corresponding direction-guided mechanism to improve search efficiency. LMOEA-S2D designs global direction search and local direction search in the domination-based stage for efficient exploitation to accelerate population convergence. To promote greater population diversity, a hybrid direction search was devised to aid diversity exploration in the decomposition-based stage, and this facilitates even distribution of candidate solutions across the Pareto optimal frontier. LMOEA-S2D is compared with five state-of-the-art large-scale MOEAs on some large-scale multiobjective test suites with 100 to 5,000 decision variables. The experimental results show that LMOEA-S2D significantly outperformed all compared algorithms under limited computational resources.

Parameter Control Framework for Multiobjective Evolutionary Computation Based on Deep Reinforcement Learning

To address the challenge of parameter adjustment in complex environments, this paper introduces a transfer learning-based parameter control framework via deep reinforcement learning for multiobjective evolutionary algorithms (MOEAs). To avoid the requirement for accurate Pareto front information, this framework is proposed with comprehensive global-state information, including basic problem features, the relative position of individuals, the distribution of fitness value, and the grid-IGD. Building on this framework, four reinforced multiobjective evolutionary algorithms (r-MOEAs) are proposed and tested on four DTLZ benchmarks and eight WFG benchmarks. The results of the comparative analyses reveal that compared with the original MOEAs, the four r-MOEAs exhibit faster convergence and stronger robustness. It is also confirmed that our proposed parameter control framework has the capability to learn knowledge from different experiences and improve the performance of MOEAs.

Dual-Fuzzy-Classifier-Based Evolutionary Algorithm for Expensive Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have been widely used to solve multiobjective optimization problems (MOPs). Conventional MOEAs usually require a large number of function evaluations (FEs) for evaluating the quality of solutions. However, only a limited number of FEs are affordable in many real-world optimization problems where the FEs are computationally or economically expensive. The use of a large number of FEs decreases the effectiveness of MOEAs in solving these problems. This article proposes a dual fuzzy classifier-based surrogate model (DFC) and a DFC-based multiobjective evolutionary algorithm framework (DFC-MOEA) for expensive optimization problems. The DFC model is used for offspring pre-selection to choose high-quality offspring solutions and for categorization to divide unevaluated solutions into three categories. In the proposed framework, two fuzzy classifiers are built to predict the quality of each unevaluated solution. To strike a balance between convergence and diversity, one classifier is designed for predicting the dominance relation of unevaluated solutions (i.e., convergence), and another classifier is designed for predicting the crowdedness of unevaluated solutions (i.e., diversity). The integration of the proposed framework in three different types of MOEAs (i.e., a dominance-based MOEA, an indicator-based MOEA, and a decomposition-based MOEA) demonstrates its usefulness in handling expensive optimization problems. Comprehensive experiments on four well-known test suites and several real-world optimization problems demonstrate that the proposed framework is able to improve the performance of MOEAs under a limited number of FEs.

Improving multi-objective evolutionary algorithms using Grammatical Evolution

Multi-objective evolutionary algorithms (MOEAs) have become an effective choice to solve multi-objective optimization problems (MOPs). However, it is well known that Pareto dominance-based MOEAs struggle in MOPs with four or more objective functions due to a lack of selection pressure in high dimensional spaces. The main choices for dealing with such problems are decomposition-based and indicator-based MOEAs. In this work, we propose the use of Grammatical Evolution (an evolutionary computation search technique) to generate functions that can improve decomposition-based and indicator-based MOEAs. Namely, we propose a methodology to generate new scalarizing functions, which are known to have a great impact in the performance of decomposition-based MOEAs and in some indicator-based MOEAs. Additionally, we propose another methodology to generate hypervolume approximations, since the hypervolume is a popular performance indicator used not only in indicator-based MOEAs but also to assess performance of MOEAs. Using our first methodology, we generate two new scalarizing functions and provide their corresponding experimental validation to show that they exhibit a competitive behavior when compared against some well-known scalarizing functions such as ASF, PBI and the Tchebycheff scalarizing function. Using our second methodology, we produce 4 different hypervolume approximations and compare their performance against the Monte Carlo method and against two other state-of-the-art hypervolume approximations. The experimental results show that our functions exhibit a good compromise in terms of quality and execution time.

Evaluating the choice of radial basis functions in multiobjective optimal control applications

Evolutionary Multi-Objective Direct Policy Search (EMODPS) is a prominent framework for designing control policies in multi-purpose environmental systems, combining direct policy search with multi-objective evolutionary algorithms (MOEAs) to identify Pareto approximate control policies. While EMODPS is effective, the choice of functions within its global approximator networks remains underexplored, despite their potential to significantly influence both solution quality and MOEA performance. This study conducts a rigorous assessment of a suite of Radial Basis Functions (RBFs) as candidates for these networks. We critically evaluate their ability to map system states to control actions, and assess their influence on Pareto efficient control policies. We apply this analysis to two contrasting case studies: the Conowingo Reservoir System, which balances competing water demands including hydropower, environmental flows, urban supply, power plant cooling, and recreation; and The Shallow Lake Problem, where a city navigates the trade-off between environmental and economic objectives when releasing anthropogenic phosphorus. Our findings reveal that the choice of RBF functions substantially impacts model outcomes. In complex scenarios like multi-objective reservoir control, this choice is critical, while in simpler contexts, such as the Shallow Lake Problem, the influence is less pronounced, though distinctive differences emerge in the characteristics of the prescribed control strategies.

Enhancing Multi-Objective Optimization with Automatic Construction of Parallel Algorithm Portfolios

It has been widely observed that there exists no universal best Multi-Objective Evolutionary Algorithm (MOEA) dominating all other MOEAs on all possible Multi-Objective Optimization Problems (MOPs). In this work, we advocate using the Parallel Algorithm Portfolio (PAP), which runs multiple MOEAs independently in parallel and gets the best out of them, to combine the advantages of different MOEAs. Since the manual construction of PAPs is non-trivial and tedious, we propose to automatically construct high-performance PAPs for solving MOPs. Specifically, we first propose a variant of PAPs, namely MOEAs/PAP, which can better determine the output solution set for MOPs than conventional PAPs. Then, we present an automatic construction approach for MOEAs/PAP with a novel performance metric for evaluating the performance of MOEAs across multiple MOPs. Finally, we use the proposed approach to construct an MOEAs/PAP based on a training set of MOPs and an algorithm configuration space defined by several variants of NSGA-II. Experimental results show that the automatically constructed MOEAs/PAP can even rival the state-of-the-art multi-operator-based MOEAs designed by human experts, demonstrating the huge potential of the automatic construction of PAPs in multi-objective optimization.

A many-objective evolutionary algorithm with estimating the convexity-concavity of Pareto fronts and clustering

Many real-world applications involve several conflicting objectives that can be solved using multiobjective evolutionary algorithms (MOEAs). Nevertheless, when considering the convexity-concavity of Pareto fronts (PFs), which is not common in the existing MOEAs, it may improve the performance of MOEAs. Spurred by this advantage, we propose a many-objective evolutionary algorithm with estimating the Convexity-Concavity of PFs and Clustering, named MaOEA-3C. Specifically, the convexity-concavity of PF is estimated according to a well-converged and well-distributed elitist archive that is updated periodically using non-dominated sorting and a niche-based method. Then, the solution fitness is computed according to the estimation result, enhancing the selection pressure and promoting the convergence when the Pareto dominance fails to select solutions. Additionally, the solutions in the elitist archive guide evolving directions for the current population by clustering, acting like reference vectors in decomposition-based algorithms, thus maintaining the diversity of solutions. The performance of MaOEA-3C is compared with seven state-of-the-art algorithms, and the results demonstrate the effectiveness and competitiveness of MaOEA-3C on many-objective optimization problems.

Result diversification with negative type distances by multi-objective evolutionary algorithms

The result diversification problem is to select an optimal subset with high “quality” and “diversity” from a given ground set of items, which is popular in various applications such as web-based search, multi-document summarization and ensemble pruning. The diversity relies on the distance between items. Previous works mainly focused on metric distances, and applied a greedy or local search algorithm with theoretical guarantees. As a kind of global search algorithm inspired by Darwin’s theory of evolution, evolutionary algorithms (EAs) can have a better optimization ability than greedy and local search, but often lack theoretical support. Recently, EAs have been introduced to result diversification, achieving good theoretical guarantees besides superior empirical performances. In this paper, we study whether EAs can still achieve good theoretical guarantees for result diversification with negative type distances, which are also a class of important dissimilarity measures, especially in information retrieval and sketching techniques. We propose to reformulate the result diversification problem with negative type distances as a bi-objective maximization problem, and solve it by multi-objective evolutionary algorithms (MOEAs). We prove that a simple MOEA (i.e., GSEMO) can achieve the best-known polynomial-time approximation ratio. Experiments are also performed to examine the performance of different MOEAs on the application of web-based search.

Unified space approach-based Dynamic Switched Crowding (DSC): A new method for designing Pareto-based multi/many-objective algorithms

This study proposes a robust method to improve the search performance of multi-objective evolutionary algorithms (MOEAs) using a Pareto-based archiving mechanism and a crowding distance-based archive handling mechanism. The aim of the proposed method is to provide a sustainable diversity in the objective and decision spaces and to establish a stable exploitation-exploration balance in both spaces. To this purpose: 1) reference space combinations are defined, 2) strategies consisting of reference space combinations are developed to improve the performance of the crowding-distance calculation, and 3) a dynamic switching mechanism is proposed to implement these strategies. In the proposed DSC method, non-dominated solutions are represented in three different reference spaces: the decision space, the objective space, and the unified result of these two spaces. Binary combinations of these three spaces were created and strategies using different reference spaces were developed. The switching mechanism was designed to implement these strategies dynamically. Crowding-distance calculation was performed with reference to the space vector selected by this switching mechanism. The proposed DSC method was tested on multimodal multi-objective optimization problems (MMOPs) and real-world engineering problems incorporating both alternating current optimal power flow (AC-OPF) and alternating current/direct current optimal power flow (AC/DC-OPF). According to the experimental study results, the proposed DSC-MOAGDE algorithm has about 30% better success rate on MMOPs compared to its competitors. Similarly, the proposed method was able to optimize cost by 6.66%, 24.15%, 52.13%, 56.72%, and 120.21% better than the MMODE_ICD, MO_RING_PSO_SCD, MOAGDE, NSWOA and SSMOPSO algorithms in AC-OPF and AC/DC-OPF real-world problems.

On Performance of a Simple Multi-objective Evolutionary Algorithm on the Constrained Minimum Spanning Tree Problem

The constrained optimization problems can be transformed into multi-objective optimization problems, and thus can be optimized by multi-objective evolutionary algorithms. This method has been successfully used to solve the constrained optimization problems. However, little theoretical work has been done on the performance of multi-objective evolutionary algorithms for the constrained optimization problems. In this paper, we theoretically analyze the performance of a multi-objective evolutionary algorithms on the constrained minimum spanning tree problem. First, we theoretically prove that the multi-objective evolutionary algorithm is capable of finding a (2,1)-approximation solution for the constrained minimum spanning tree problem in a pseudopolynomial runtime. Then, this simple multi-objective evolutionary algorithm is shown to be efficient on a constructed instance of the problem.

Comparing the Performance of Evolutionary Algorithms for Sparse Multi-Objective Optimization via a Comprehensive Indicator [Research Frontier

Many real-world multi-objective optimization problems (MOPs) are characterized by a large number of decision variables, where the decision variables are mostly set to zero in the Pareto optimal solutions. Although some multi-objective evolutionary algorithms (MOEAs) have been tailored for large-scale MOPs in recent years, most of them do not consider the sparse nature of Pareto optimal solutions, and their effectiveness to sparse MOPs has not been investigated. Therefore, this work aims to compare the performance of MOEAs on sparse MOPs by suggesting a comprehensive performance indicator. In comparison to existing indicators assessing the convergence and diversity of a solution set according to predefined reference points, the proposed indicator can assess the convergence, diversity, and sparsity without using any reference point. Based on the proposed indicator, an experiment is conducted to compare the performance of 11 state-of-the-art MOEAs on 60 test instances taken from benchmark suites and real-world applications. The statistical results show that some MOEAs are significantly better than the others for solving sparse MOPs, and the proposed indicator is effective for the performance assessment on sparse MOPs.

An Autoselection Strategy of Multiobjective Evolutionary Algorithms Based on Performance Indicator and its Application

The use of ensemble approaches in the single-objective evolutionary algorithms is ubiquitous, but ensembles of multiobjective evolutionary algorithms (MOEAs) have achieved relatively little attention. On the other hand, manually selecting a suitable MOEA to solve an actual multiobjective optimization problem (MOP) is time-consuming and challenging. Therefore, developing a multiobjective hyperheuristic to allocate computational resources for multiple MOEAs in an intelligent approach is beneficial. In this work, an autoselection strategy of MOEAs based on the performance indicator (MOEAS-PI) is introduced to alleviate the abovementioned problem. In the MOEAS-PI, the performance of each constituent MOEA in the pool is assessed according to a real-time and comprehensive performance indicator, which contains both the current and future performances. The MOEAS-PI is able to easily choose the best performing MOEA during the evolutionary process. Also, it can enhance the robustness of MOEAs and reduce the application risk. The effectiveness of the MOEAS-PI is carefully evaluated on 23 MOPs. Simulation results demonstrate that the MOEAS-PI is an effective and efficient method to integrate the advantages of each individual algorithm. Finally, the MOEAS-PI is utilized to solve a translation control problem of an immersed tunnel element under current flow. Experimental results reveal that the MOEAS-PI is a reliable and effective optimization approach to solve actual MOPs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Multiobjective optimization problems (MOPs) have been commonly found in various fields. However, a single MOEA cannot guarantee its sufficient robustness and adaptability in solving MOPs. Therefore, this study aims to propose a multiobjective hyperheuristic algorithm to improve the robustness of MOEAs. The performance of the proposed algorithm is tested on benchmark test functions and an actual MOP. The results show that the proposed approach can select a suitable MOEA to solve a particular type of MOPs during the evolutionary process and provide a solution set for decision-makers to control the translation of an immersed tunnel element under different objectives/operator environments.

New Findings on Indicator-based Multi-Objective Evolutionary Algorithms: A Brief Summary

Quality indicators (QIs) are functions that assign a real value to a set that represents the Pareto front approximation of a multi-objective optimization problem. In the evolutionary multi-objective optimization community, QIs have been mainly employed in two ways: (1) for the performance assessment of multi-objective evolutionary algorithms (MOEAs), which produce Pareto front approximations, and (2) to be adopted as the backbone of selection mechanisms of MOEAs. Regardless of the continuing advances on QIs and their utilization in MOEAs, there are currently a vast number of open questions in this researcharea. In this doctoral thesis, we have focused on two main research directions: the design of new selection mechanisms based on the competition and cooperation of multiple QIs, aiming to compensate for the weaknesses (in terms of convergence and diversity properties) of individual QIs with the strengths of the others. The second research axis is the generation of new QIs that are compliant with the Pareto dominance relation extended to sets. Such QIs have a direct impact on the type of conclusions that can be drawn about the performance of MOEAs. Our experimental results have shown that the use of multiple QIs either to design new selection mechanisms or to construct new Pareto-compliant QIs is a promising research direction that can improve the capabilities of MOEAs and that allows for a performance assessment of MOEAs with a higher degree of confidence.

Multipopulation Particle Swarm Optimization for Evolutionary Multitasking Sparse Unmixing

Recently, the multiobjective evolutionary algorithms (MOEAs) have been designed to cope with the sparse unmixing problem. Due to the excellent performance of MOEAs in solving the NP hard optimization problems, they have also achieved good results for the sparse unmixing problems. However, most of these MOEA-based methods only deal with a single pixel for unmixing and are subjected to low efficiency and are time-consuming. In fact, sparse unmixing can naturally be seen as a multitasking problem when the hyperspectral imagery is clustered into several homogeneous regions, so that evolutionary multitasking can be employed to take advantage of the implicit parallelism from different regions. In this paper, a novel evolutionary multitasking multipopulation particle swarm optimization framework is proposed to solve the hyperspectral sparse unmixing problem. First, we resort to evolutionary multitasking optimization to cluster the hyperspectral image into multiple homogeneous regions, and directly process the entire spectral matrix in multiple regions to avoid dimensional disasters. In addition, we design a novel multipopulation particle swarm optimization method for major evolutionary exploration. Furthermore, an intra-task and inter-task transfer and a local exploration strategy are designed for balancing the exchange of useful information in the multitasking evolutionary process. Experimental results on two benchmark hyperspectral datasets demonstrate the effectiveness of the proposed method compared with the state-of-the-art sparse unmixing algorithms.

Handling multiple objectives using k‐means clustering guided multiobjective evolutionary algorithm

AbstractMultiobjective optimization problems (MOPs) are very popular these days and have gained continuous research attention. These problems involve a minimum of two conflicting objectives that need to be optimized simultaneously. Multiobjective evolutionary algorithms (MOEAs) optimize these objectives by targeting solutions on the Pareto front. To judge the performance of different MOEAs, the convergence rate and population diversity are used. In order to create a good algorithm with a high convergence rate and diversity, the k‐means clustering algorithm is combined with a real parameter version of the improved environmental adaptation method (IEAM‐RP) in this paper. This is done as IEAM‐RP converges very fast and the k‐means clustering algorithm is used to provide diversity in decision search space. To check the performance of the proposed algorithm, it has been compared with nine state‐of‐the‐art multiobjective algorithms (MOPSOtridist, MOEA/D‐STM, MOEA/D, MOPSO, NSGA‐II, MOPSOses, MOGOA, MODA, MOALO) using standard multiobjective benchmark functions. Further, the performance of the proposed algorithm is compared against IBEA and SMS‐EMOA using walking fish group (WFG) test suit. The experimental results prove the effectiveness of the proposed algorithm.

A two-stage evolutionary strategy based MOEA/D to multi-objective problems

The balance of convergence and diversity plays a significant role to the performance of multi-objective evolutionary algorithms (MOEAs). The MOEA/D is a very popular multi-objective optimization algorithm and has been used to solve various real world problems. Like many other algorithms, the MOEA/D also has insufficient ability of convergence and diversity when tackling certain complex multi-objective optimization problems (MOPs). In this paper, a novel algorithm named MOEA/D-TS is proposed for effectively solving MOPs. The new algorithm adopts two stages evolution strategies, the first stage is focused on pushing the solutions into the area of the Pareto front and speeding up its convergence ability, after that, the second stage conducts in the operating solution’s diversity and makes the solutions distributed uniformly. The performance of MOEA/D-TS is validated in the ZDT, DTLZ and IMOP problems. Compared with others popular and variants algorithms, the experimental results demonstrate that the proposed algorithm has advantage over other algorithms with regard to the convergence and diversity in most of the tested problems.

An Approach for the Generation of Multi-Objective Algorithms Applied to the Integration and Test Order Problem

Multi-Objective Evolutionary Algorithms (MOEAs) have been successfully applied to solve hard real software engineering problems. However, to choose and design a MOEA is considered a difficult task, since there are several parameters and components to be configured. These aspects directly impact the generated solutions and the performance of MOEAs. In this sense, this paper proposes an approach for the automatic generation of MOEAs applied to the Integration and Test Order (ITO) problem. Such a problem refers to the generation of optimal sequences of units for integration testing. The approach includes a set of parameters and components of different MOEAs, and is implemented with two design algorithms: Grammatical Evolution (GE) and Iterated Racing (irace). Evaluation results are presented, comparing the MOEAs generated by both design algorithms. Furthermore, the generated MOEAs are compared to two well-known MOEAs used in the literature to solve the ITO problem. Results show that the MOEAs generated with GE and irace perform similarly, and both outperform traditional MOEAs. The approach can reduce efforts spent to design and configure MOEAs, and serves as basis for implementing solutions to other software engineering problems.