Evolutionary Multiobjective Optimization Algorithms Research Articles

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.

A Hydrodynamic Model and Data-Driven Evolutionary Multi-Objective Optimization Algorithm Based Optimal Operation Method for Multi-barrage Flood Control

A Hydrodynamic Model and Data-Driven Evolutionary Multi-Objective Optimization Algorithm Based Optimal Operation Method for Multi-barrage Flood Control

A neighborhood-assisted evolutionary algorithm for multimodal multi-objective optimization

A neighborhood-assisted evolutionary algorithm for multimodal multi-objective optimization

Neural Architecture Search as Multiobjective Optimization Benchmarks: Problem Formulation and Performance Assessment

The ongoing advancements in network architecture design have led to remarkable achievements in deep learning across various challenging computer vision tasks. Meanwhile, the development of neural architecture search (NAS) has provided promising approaches to automating the design of network architectures for lower prediction error. Recently, the emerging application scenarios of deep learning (e.g., autonomous driving) have raised higher demands for network architectures considering multiple design criteria: number of parameters/weights, number of floating-point operations, inference latency, among others. From an optimization point of view, the NAS tasks involving multiple design criteria are intrinsically multiobjective optimization problems; hence, it is reasonable to adopt evolutionary multiobjective optimization (EMO) algorithms for tackling them. Nonetheless, there is still a clear gap confining the related research along this pathway: on the one hand, there is a lack of a general problem formulation of NAS tasks from an optimization point of view; on the other hand, there are challenges in conducting benchmark assessments of EMO algorithms on NAS tasks. To bridge the gap: (i) we formulate NAS tasks into general multi-objective optimization problems and analyze the complex characteristics from an optimization point of view; (ii) we present an end-to-end pipeline, dubbed EvoXBench, to generate benchmark test problems for EMO algorithms to run efficiently -without the requirement of GPUs or Pytorch/Tensorflow; (iii) we instantiate two test suites comprehensively covering two datasets, seven search spaces, and three hardware devices, involving up to eight objectives. Based on the above, we validate the proposed test suites using six representative EMO algorithms and provide some empirical analyses. The code of EvoXBench is available at https://github.com/EMI-Group/EvoXBench.

Detecting Hidden and Irrelevant Objectives in Interactive Multiobjective Optimization

Evolutionary multi-objective optimization algorithms (EMOAs) typically assume that all objectives that are relevant to the decision-maker (DM) are optimized by the EMOA. In some scenarios, however, there are irrelevant objectives that are optimized by the EMOA but ignored by the DM, as well as, hidden objectives that the DM considers when judging the utility of solutions but are not optimized. This discrepancy between the EMOA and the DM’s preferences may impede the search for the most-preferred solution and waste resources evaluating irrelevant objectives. Research on objective reduction has focused so far on the structure of the problem and correlations between objectives and neglected the role of the DM. We formally define here the concepts of irrelevant and hidden objectives and propose methods for detecting them, based on uni-variate feature selection and recursive feature elimination, that use the preferences already elicited when a DM interacts with a ranking-based interactive EMOA (iEMOA). We incorporate the detection methods into an iEMOA capable of dynamically switching the objectives being optimized. Our experiments show that this approach can efficiently identify which objectives are relevant to the DM and reduce the number of objectives being optimized, while keeping and often improving the utility, according to the DM, of the best solution found.

Improved Evolutionary Operators for Sparse Large-Scale Multiobjective Optimization Problems

Many critical science, societal, and engineering fields contain large-scale multiobjective optimization problems (LSMOPs), comprised of many decision variables. However, as the number of decision variables increases, optimization algorithms face exponentially large search spaces, thereby exhibiting a degraded performance. Nonetheless, LSMOPs whose optimal solutions correspond to sparse variable vectors can be solved more efficiently by evolutionary multiobjective optimization (EMO) algorithms. Despite the great recent strides in developing generic EMO algorithms for sparse LSMOPs, there is still room for improvement. Specifically, algorithms still struggle to find convergent and diverse Pareto fronts in an acceptable amount of time when solving sparse LSMOPs with thousands of decision variables. To better solve sparse LSMOPs, we propose a novel set of evolutionary operators to adapt small-scale EMO algorithms for sparse LSMOPs. These simple, novel, and effective operators include varied striped sparse population sampling (VSSPS), sparse simulated binary crossover (S-SBX), and sparse polynomial mutation (S-PM). These operators, combined with NSGA-II, make the proposed S-NSGA-II algorithm. S-NSGA-II runs near-universally faster than existing methods for problems containing up to 6,400 decision variables, while performing as well as or better than contemporary sparse LSMOP algorithms with respect to hypervolume, especially with problems with larger than 5,000 decision variables.

A similarity-detection-based evolutionary algorithm for large-scale multimodal multi-objective optimization

In recent years, there has been a surge in the development of evolutionary algorithms tailored for multimodal multi-objective optimization problems (MMOPs). These algorithms aim to find multiple equivalent Pareto optimal solution sets (PSs). However, little work has been done on MMOPs with large-scale decision variables, especially when the Pareto optimal solutions are sparse. These problems pose significant challenges due to the dimension curse, the unknown sparsity, and the unknown number of equivalent PSs. In this paper, we propose an evolutionary algorithm based on similarity detection called SD-MMEA to solve large-scale MMOPs with sparse Pareto-optimal solutions. Specifically, it employs a multi-population independent evolution to explore multiple PSs and distinguishes different PSs by double detection of the similarity between subpopulations. Simultaneously, develop online scoring mechanisms for decision variables to guide the subpopulations to explore in different directions. In addition, during the latter stage of evolution, the decision variables of individuals are further optimized by a double-layer grouping process. The proposed algorithm is compared with six state-of-the-art algorithms. Experimental results show that SD-MMEA has significant advantages in solving large-scale MMOPs with sparse solutions.

Offline Data-Driven Multiobjective Optimization Evolutionary Algorithm Based on Generative Adversarial Network

Usually, data-driven multi-objective optimiza -tion problems (DD-MOPs) are indirectly solved by evolutionary algorithms through the built surrogate model which is well-trained from sample data. However, in most DD-MOPs, only a few available data can be practicably collected from real engineering experiments due to the unaffordable cost and time. The key challenge in such a DD-MOP is to prevent the serious deterioration on the accuracy of the obtained approximate Pareto front. In this paper, two novel strategies, critical fitness for evolutionary algorithms and data augmentation for a surrogate model, are complementarily imposed by a generative adversarial network (GAN) to tackle with the challenges in DD-MOPs. In the critical fitness strategy, a new critical fitness, composed of the critical score from the discriminator of GAN and the prediction value of surrogate model, is proposed to improve the accuracy of approximate Pareto front of a DD-MOP. In the data augmentation strategy, some new samples are synthetized by the generator of GAN to build a better-trained surrogate model. As a result, the GAN concurrently serves the critical fitness strategy and the data augmentation strategy as the roles of “killing two birds with one stone”. The performance of the proposed algorithm for DD-MOPs was well-verified over 26 benchmark problems and successfully applied to discover new NdFeB materials.

Evolutionary Multi-Objective Optimization Algorithm for Resource Allocation Using Deep Neural Network in Ultra-Dense Networks

Evolutionary Multi-Objective Optimization Algorithm for Resource Allocation Using Deep Neural Network in Ultra-Dense Networks

A novel tri-stage with reward-switching mechanism for constrained multiobjective optimization problems

AbstractThe effective exploitation of infeasible solutions plays a crucial role in addressing constrained multiobjective optimization problems (CMOPs). However, existing constrained multiobjective optimization evolutionary algorithms (CMOEAs) encounter challenges in effectively balancing objective optimization and constraint satisfaction, particularly when tackling problems with complex infeasible regions. Subsequent to the prior exploration, this paper proposes a novel tri-stage with reward-switching mechanism framework (TSRSM), including the push, pull, and repush stages. Each stage consists of two coevolutionary populations, namely $${\text {Pop}}_1$$ Pop 1 and $${\text {Pop}}_2$$ Pop 2 . Throughout the three stages, $${\text {Pop}}_1$$ Pop 1 is tasked with converging to the constrained Pareto front (CPF). However, $${\text {Pop}}_2$$ Pop 2 is assigned with distinct tasks: (i) converging to the unconstrained Pareto front (UPF) in the push stage; (ii) utilizing constraint relaxation technique to discover the CPF in the pull stage; and (iii) revisiting the search for the UPF through knowledge transfer in the repush stage. Additionally, a novel reward-switching mechanism (RSM) is employed to transition between different stages, considering the extent of changes in the convergence and diversity of populations. Finally, the experimental results on three benchmark test sets and 30 real-world CMOPs demonstrate that TSRSM achieves competitive performance when compared with nine state-of-the-art CMOEAs. The source code is available at https://github.com/Qu-jq/TSRSM.

Decomposition with adaptive composite norm for evolutionary multi-objective combinatorial optimization

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multi-objective problem into a series of single-objective subproblems for collaborative optimization. The weighted sum (WS) method and the Tchebycheff (TCH) method are the two most popular scalarization methods. They have pros and cons in solving multi-objective combinatorial optimization problems (MOCOPs) the WS method allows MOEA/D to converge faster than the TCH method; the WS-based MOEA/D cannot obtain unsupported non-dominated vectors, while the TCH-based one can overcome this shortcoming. This inspired us to use the WS method to drive the population towards the Pareto front and then switch to the TCH method to maintain a more diverse population. To better balance convergence and diversity, we propose a new scalarization strategy called adaptive composite norm (ACN). The ACN strategy can combine the WS and the TCH with dynamic weighting. The experiments consider 16 instances including 4 MOCOPs and run on the PlatEMO. Results reveal that MOEA/D-ACN can rank first and significantly outperform the other evolutionary multi-objective combinatorial optimization algorithms on almost all instances.

Regularity model based offspring generation in surrogate-assisted evolutionary algorithms for expensive multi-objective optimization

Evolutionary algorithms face significant challenges when it comes to solving expensive multi-objective optimization problems, which require costly evaluations. One of the most popular approaches to addressing this issue is to use surrogate models, which can replace the expensive real function evaluations with cheaper approximations. However, in many surrogate-assisted evolutionary algorithms (SAEAs), the process of offspring generation has not received sufficient attention. In this paper, we propose a novel framework for expensive multi-objective optimization called RM-SAEA, which utilizes a regularity model (RM) operator to generate offspring more effectively. The regularity model operator is combined with a general genetic algorithm operator to create a heterogeneous offspring generation module that can better approximate the Pareto front. Moreover, to overcome the data deficiency issue in expensive optimization scenarios, we employ a data augmentation strategy while training the regularity model. Finally, we embed three representative SAEAs into the proposed RM-SAEA to demonstrate its efficacy. Experimental results on several benchmark test suites with up to 10 objectives and real-world applications show that RM-SAEA achieves superior overall performance compared to eight state-of-the-art algorithms. By focusing on more effective offspring generation and addressing data deficiencies, our proposed framework is able to generate better approximations of the Pareto front and improve the optimization process in expensive multi-objective optimization scenarios.

A multi-granularity clustering based evolutionary algorithm for large-scale sparse multi-objective optimization

Sparse multi-objective optimization problems (SMOPs) frequently exist in a variety of disciplines such as machine learning, economy, and signal processing. Evolutionary algorithms have demonstrated their proficiency in optimizing complex problems in recent years, although their performance often deteriorates significantly on large-scale SMOPs. In an effort to accelerate the convergence, this paper suggests a multi-granularity variable clustering method for evolutionary algorithms. This method estimates the sparse distribution of decision variables at each generation and partitions them into a varying number of layers, each with a distinct probability of being zero. These clustering outcomes inspire the development of a crossover operator and a mutation operator, which prove adept at efficiently generating sparse solutions. Experimental evaluations on both benchmark and real-world SMOPs confirm that an evolutionary algorithm incorporating the new crossover operator and mutation operator converges more rapidly than its state-of-the-art counterparts.

A Bi-Objective Evolutionary Algorithm for Multimodal Multiobjective Optimization

Multimodal multi-objective optimization problems (MMOPs) possess multiple Pareto optimal sets corresponding to the identical Pareto optimal front (PF). To handle MMOPs, we propose a bi-objective evolutionary algorithm (BOEA), which transforms an MMOP into a bi-objective optimization problem. This problem is constructed by the penalty boundary intersection technique and a diversity indicator to obtain multiple Pareto optimal sets. The first objective reflects the population convergence and factors in the population diversity in the objective space, while the other objective concentrates more on the population diversity in the decision space. Furthermore, an environmental selection strategy is designed to choose the offspring solutions, which consists of non-dominated sorting based on the transformed optimization problem and hierarchical clustering for selecting promising solutions. Experiments on 34 MMOPs demonstrate that BOEA performs better than selected state-of-the-art representatives, including 22 MMOPs from CEC2019 and 12 imbalanced MMOPs. In addition, the effectiveness of BOEA is further validated by six feature selection problemsin real-world applications.

Identifying Pareto Fronts Reliably Using a Multistage Reference-Vector-Based Framework

Evolutionary multi-objective and many-objective optimization (EMO and EMaO) algorithms are increasingly being used to identify the true shape and location of the Paretooptimal front using a few representative well-converged and welldistributed solutions. The reason for their popularity is due to their ability to provide a better understanding of objective relationships for optimal solutions, and also to facilitate the choice of a preferred solution using an interactive or postoptimal multi-criterion decision analysis. However, since EMO and EMaO algorithms are stochastic, a single application may not provide a true representative set with a desired number of Pareto solutions reliably in repetitive runs and importantly with a well-distributed set of solutions. In this paper, we propose a multistage framework involving reference-vector based evolutionary multi-and many-objective algorithms (MuSt-EMO and MuSt-EMaO) that attempts to recursively rectify shortcomings of previous stages by careful executions of subsequent stages so that a prescribed number of well-distributed and well-converged solutions are achieved at the end. The proposed multi-stage approach is implemented to a number of popular reference vector based EMO/EMaO algorithms and is applied on various multiand many-objective test and real-world problems.

Large-scale evolutionary optimization: A review and comparative study

Large-scale global optimization (LSGO) problems have widely appeared in various real-world applications. However, their inherent complexity, coupled with the curse of dimensionality, makes them challenging to solve. Continuous efforts have been devoted to designing computational intelligence-based approaches to solve them. This paper offers a comprehensive review of the latest developments in the field, focusing on the advances in both single-objective and multi-objective large-scale evolutionary optimization algorithms over the past five years. We systematically categorize these algorithms, discuss their distinct features, and highlight benchmark test suites essential for performance evaluation. After that, comparative studies are conducted using numerical solutions to evaluate the performance of state-of-the-art LSGO for both single-objective and multi-objective problems. Finally, we discuss the real-world applications of LSGO, some challenges, and possible future research directions.

Design and Maintenance Optimisation of Substation Automation Systems: A Multiobjectivisation Approach Exploration

Substation automation systems (SAS) are critical infrastructures whose design and maintenance must be optimised to guarantee a suitable performance. In order to provide a collection of solutions that balance availability and cost, this paper explores the optimisation of the design and maintenance of a section of SAS. Multiobjective evolutionary algorithms are combined with discrete event simulation while the performance of two state-of-the-art multiobjective evolutionary algorithms is studied. On the one hand, the nondominated sorting genetic algorithm II (NSGA-II), and on the other hand, the S-metric selection evolutionary multiobjective optimisation algorithm (SMS-EMOA). Such a problem is solved from 2 and 3-objective approaches by attending to the multiobjectivisation concept. The robustness of the methodology is brought to light, and benefits were observed from the multiobjectivisation approach. Decision-makers can employ this knowledge to make informed decisions based on economic and reliability criteria.

MOEA with adaptive operator based on reinforcement learning for weapon target assignment

<abstract><p>Weapon target assignment (WTA) is a typical problem in the command and control of modern warfare. Despite the significance of the problem, traditional algorithms still have shortcomings in terms of efficiency, solution quality, and generalization. This paper presents a novel multi-objective evolutionary optimization algorithm (MOEA) that integrates a deep Q-network (DQN)-based adaptive mutation operator and a greedy-based crossover operator, designed to enhance the solution quality for the multi-objective WTA (MO-WTA). Our approach (NSGA-DRL) evolves NSGA-II by embedding these operators to strike a balance between exploration and exploitation. The DQN-based adaptive mutation operator is developed for predicting high-quality solutions, thereby improving the exploration process and maintaining diversity within the population. In parallel, the greedy-based crossover operator employs domain knowledge to minimize ineffective searches, focusing on exploitation and expediting convergence. Ablation studies revealed that our proposed operators significantly boost the algorithm performance. In particular, the DQN mutation operator shows its predictive effectiveness in identifying candidate solutions. The proposed NSGA-DRL outperforms state-and-art MOEAs in solving MO-WTA problems by generating high-quality solutions.</p></abstract>

Hypervolume-Based Cooperative Coevolution with Two Reference Points for Multi-Objective Optimization

An important issue in hypervolume-based evolutionary multi-objective optimization (EMO) algorithms is the specification of a reference point for hypervolume calculation. However, its appropriate specification has not been carefully studied in the literature. Some recent studies have pointed out the importance and difficulty of the reference point specification. Its appropriate specification depends on problem characteristics such as the Pareto front shape and the number of objectives. In this paper, the difficulty of the reference point specification in hypervolume-based EMO algorithms is circumvented by using two reference points. Instead of using only a single reference point, we propose a new hypervolume-based EMO algorithm that can effectively utilize two reference points cooperatively. Experimental results show that the proposed algorithm has good and robust performance on a wide range of test problems. In comparison to hypervolume-based EMO algorithms with only a single reference point, the proposed algorithm can find a wider and more uniformly distributed solution set. On a recently proposed real-world problem suite, the proposed algorithm shows competitive performance in comparison to state-of-the-art algorithms.

A Multitask-Assisted Evolutionary Algorithm for Constrained Multimodal Multiobjective Optimization

A Multitask-Assisted Evolutionary Algorithm for Constrained Multimodal Multiobjective Optimization