Evolutionary Multi-objective Optimization Research Articles

Population Feasibility State Guided Autonomous Constrained Multi-Objective Evolutionary Optimization

Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering the integration of multiple constraint handling techniques. Given this, this paper combines the objective and constraint separation method with the multi-operator method, proposing a population feasibility state guided autonomous constrained evolutionary optimization method. This method first defines the feasibility state of the population based on both feasibility and ε feasibility of the solutions. Subsequently, a reinforcement learning model is employed to construct a mapping model between the population state and reproduction operators. Finally, based on the real-time population state, the mapping model is utilized to recommend the promising reproduction operator for the next generation. This approach demonstrates significant performance improvement for ε constrained mechanisms in constrained multi-objective optimization algorithms, and shows considerable advantages in comparison with state-of-the-art constrained multi-objective optimization algorithms.

Adaptive operator selection with dueling deep Q-network for evolutionary multi-objective optimization

Adaptive operator selection is an online method that automatically adjusts the application rate of different operators based on their actual performance. This paper proposes an adaptive operator selection paradigm based on dueling deep Q-network (DDQN), aiming to improve the training efficiency of the Q-network for solving multi-objective optimization problems. The Q-network is decomposed into state value and action advantage networks, allowing the agent to learn state values more frequently and accurately. A novel state space and reward mechanism are designed to adapt to the characteristics of evolutionary multi-objective optimization. Combining adaptive operator selection with a multi-objective evolutionary algorithm with adaptive weights (AdaW), an AdaW-DDQN algorithm with high adaptability is proposed. Experimental results on three complex benchmark suites demonstrate that the proposed adaptive operator selection paradigm significantly improves the performance of multi-objective optimization algorithms. The AdaW-DDQN algorithm provides an effective and efficient solution for solving multi-objective optimization problems.

Multigranularity Surrogate Modeling for Evolutionary Multiobjective Optimization With Expensive Constraints.

Multiobjective optimization problems (MOPs) with expensive constraints pose stiff challenges to existing surrogate-assisted evolutionary algorithms (SAEAs) in a very limited computational cost, due to the fact that the number of expensive constraints for an MOP is often large. For existing SAEAs, they always approximate constraint functions in a single granularity, namely, approximating the constraint violation (CV, coarse-grained) or each constraint (fine-grained). However, the landscape of CV is often too complex to be accurately approximated by a surrogate model. Although the modeling of each constraint function may be simpler than that of CV, approximating all the constraint functions independently may result in tremendous cumulative errors and high computational costs. To address this issue, in this article, we develop a multigranularity surrogate modeling framework for evolutionary algorithms (EAs), where the approximation granularity of constraint surrogates is adaptively determined by the position of the population in the fitness landscape. Moreover, a dedicated model management strategy is also developed to reduce the impact resulting from the errors introduced by constraint surrogates and prevent the population from trapping into local optima. To evaluate the performance of the proposed framework, an implementation called K-MGSAEA is proposed, and the experimental results on a large number of test problems show that the proposed framework is superior to seven state-of-the-art competitors.

Crossover can guarantee exponential speed-ups in evolutionary multi-objective optimisation

Evolutionary algorithms are popular algorithms for multi-objective optimisation (also called Pareto optimisation) as they use a population to store trade-offs between different objectives. Despite their popularity, the theoretical foundation of multi-objective evolutionary optimisation (EMO) is still in its early development. Fundamental questions such as the benefits of the crossover operator are still not fully understood. We provide a theoretical analysis of the well-known EMO algorithms GSEMO and NSGA-II to showcase the possible advantages of crossover: we propose classes of “royal road” functions on which these algorithms cover the whole Pareto front in expected polynomial time if crossover is being used. But when disabling crossover, they require exponential time in expectation to cover the Pareto front. The latter even holds for a large class of black-box algorithms using any elitist selection and any unbiased mutation operator. Moreover, even the expected time to create a single Pareto-optimal search point is exponential. We provide two different function classes, one tailored for one-point crossover and another one tailored for uniform crossover, and we show that some immune-inspired hypermutations cannot avoid exponential optimisation times. Our work shows the first example of an exponential performance gap through the use of crossover for the widely used NSGA-II algorithm and contributes to a deeper understanding of its limitations and capabilities.

Exploring the Explainable Aspects and Performance of a Learnable Evolutionary Multiobjective Optimization Method

Multiobjective optimization problems have multiple conflicting objective functions to be optimized simultaneously. The solutions to these problems are known as Pareto optimal solutions, which are mathematically incomparable. Thus, a decision maker must be employed to provide preferences to find the most preferred solution. However, decision makers often lack support in providing preferences and insights in exploring the solutions available. We explore the combination of learnable evolutionary models with interactive indicator-based evolutionary multiobjective optimization to create a learnable evolutionary multiobjective optimization method. Furthermore, we leverage interpretable machine learning to provide decision makers with potential insights about the problem being solved in the form of rule-based explanations. In fact, we show that a learnable evolutionary multiobjective optimization method can offer advantages in the search for solutions to a multiobjective optimization problem. We also provide an open source software framework for other researchers to implement and explore our ideas in their own works. Our work is a step toward establishing a new paradigm in the field on multiobjective optimization: explainable and learnable multiobjective optimization . We take the first steps toward this new research direction and provide other researchers and practitioners with necessary tools and ideas to further contribute to this field.

Evolutionary multiobjective optimization assisted by scalarization function approximation for high-dimensional expensive problems

Surrogate-assisted evolutionary algorithms (SAEAs) are a promising approach for solving expensive multiobjective optimization problems, but they often cannot address high-dimensional problems. Although one common approach to overcoming this challenge is to construct reliable surrogates, their accuracy inevitably deteriorates in a high-dimensional search space. Thus, this paper presents a novel SAEA based on scalarization function approximation, which is designed to strengthen its robustness against this deterioration. The proposed algorithm constructs an approximation model for each scalarization function defined in a decomposition-based framework. Each decomposed problem is then solved using multiple independent models trained for its neighbor problems. The intent is to decrease the risk of search performance degradations caused by unreliable approximations and retain the redundancy of the surrogate-assisted search to hedge the risk of over-fitting. Furthermore, each approximation model is adapted to a promising region of its corresponding decomposed problem to reduce the complexity of model fitting given a limited number of training samples. Experimental results show that the proposed algorithm is competitive with state-of-the-art SAEAs adapted for high-dimensional problems.

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.

A Weighted multi-objective evolutionary algorithm optimization

Weight Based Genetic Algorithms (WBGA) have a computational efficacy and non-cumbersome for multi-objective optimization. The solutions obtained in the converged region do not always produce maximum optimization for all the objective functions simultaneously. But, the combination of the solutions from different iteration may yield optimized values for all the objective functions to a satisfactory level. The paper attempts to find a method which keeps the simplicity and computational efficiency of WBGA intact, but at the same time counters the problem of inferior pareto-optimal solutions. This is done by finding such a combinational set of solutions which yields strong values for all the objectives. The paper proposes neutrosophic logic (NL) as a postprocessor to the outcome of the WBGA. The NL assigns a percentage of truth, false and indeterminant value to the obtained solutions. The proposed postprocessor operation has been demonstrated with hand calculations on a test problem, and a complex practical example. The results obtained as compared to WBGA show the emergence of a superior solution-set and reaches in close agreement with NSGA-II, while maintaining the computational efficiency.

Process Knowledge-Guided Autonomous Evolutionary Optimization for Constrained Multiobjective Problems

Various real-world problems can be attributed to constrained multi-objective optimization problems. Although there are various solution methods, it is still very challenging to automatically select efficient solving strategies for constrained multi-objective optimization problems. Given this, a process knowledge-guided constrained multi-objective autonomous evolutionary optimization method is proposed. Firstly, the effects of different solving strategies on population states are evaluated in the early evolutionary stage. Then, the mapping model of population states and solving strategies is established. Finally, the model recommends subsequent solving strategies based on the current population state. This method can be embedded into existing evolutionary algorithms, which can improve their performances to different degrees. The proposed method is applied to 41 benchmarks and 30 dispatch optimization problems of the integrated coal mine energy system. Experimental results verify the effectiveness and superiority of the proposed method in solving constrained multi-objective optimization problems.

Multimodal Multiobjective Differential Evolutionary Optimization With Species Conservation

Multimodal Multiobjective Differential Evolutionary Optimization With Species Conservation

Evolutionary Multi-Objective Bayesian Optimization Based on Multisource Online Transfer Learning

Evolutionary Multi-Objective Bayesian Optimization Based on Multisource Online Transfer Learning

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.

Dynamic Multiobjective Evolutionary Optimization via Knowledge Transfer and Maintenance

Dynamic Multiobjective Evolutionary Optimization via Knowledge Transfer and Maintenance

An Interactive Knowledge-Based Multiobjective Evolutionary Algorithm Framework for Practical Optimization Problems

Experienced users often have useful knowledge and intuition in solving real-world optimization problems. User knowledge can be formulated as inter-variable relationships to assist an optimization algorithm in finding good solutions faster. Such inter-variable interactions can also be automatically learned from high-performing solutions discovered at intermediate iterations in an optimization run – a process called innovization. These relations, if vetted by the users, can be enforced among newly generated solutions to steer the optimization algorithm towards practically promising regions in the search space. Challenges arise for large-scale problems where the number of such variable relationships may be high. This paper proposes an interactive knowledge-based evolutionary multi-objective optimization () framework that extracts hidden variable-wise relationships as knowledge from evolving high-performing solutions, shares them with users to receive feedback, and applies them back to the optimization process to improve its effectiveness. The knowledge extraction process uses a systematic and elegant graph analysis method which scales well with number of variables. The working of the proposed is demonstrated on three large-scale real-world engineering design problems. The simplicity and elegance of the proposed knowledge extraction process and achievement of high-performing solutions quickly indicate the power of the proposed framework. The results presented should motivate further such interaction-based optimization studies for their routine use in practice.

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.

A Synergistic MOEA Algorithm with GANs for Complex Data Analysis

The multi-objective evolutionary algorithm optimization (MOEA) is a challenging but critical approach for tackling complex data analysis problems. However, prevailing MOEAs often rely on single strategies to obtain optimal solutions, leading to concerns such as premature convergence and insufficient population diversity, particularly in high-dimensional data scenarios. In this paper, we propose a novel adversarial population generation algorithm, APG-SMOEA, which synergistically combines the benefits of MOEAs and Generative Adversarial Networks (GANs) to address these limitations. In order to balance the efficiency and quality of offspring selection, we introduce an adaptive population entropy strategy, which includes control parameters based on population entropy and a learning pool for storing and retrieving optimal solutions. Additionally, we attempt to alleviate the training complexity and model collapse problems common in GANs with APG-SMOEA. Experimental results on benchmarks demonstrate that the proposed algorithm is superior to the existing algorithms in terms of solution quality and diversity of low-dimensional or high-dimensional complex data.

Exoplanet host star classification: multi-objective optimization of incomplete stellar abundance data

Abstract The presence of a planetary companion around its host star has been repeatedly linked with stellar properties, affecting the likelihood of substellar object formation and stability in the protoplanetary disc, thus presenting a key challenge in exoplanet science. Furthermore, abundance and stellar parameter data sets tend to be incomplete, which limits the ability to infer distributional characteristics harnessing the entire data set. This work aims to develop a methodology using machine learning (ML) and multi-objective optimization for reliable imputation for subsequent comparison tests and host star recommendation. It integrates fuzzy clustering for imputation and ML classification of hosts and comparison stars into an evolutionary multi-objective optimization algorithm. We test several candidates for the classification model, starting with a binary classification for giant planet hosts. Upon confirmation that the eXtreme Gradient Boosting algorithm provides the best performance, we interpret the performance of both the imputation and classification modules for binary classification. The model is extended to handle multilabel classification for low-mass planets and planet multiplicity. Constraints on the model’s use and feature/sample selection are given, outlining strengths and limitations. We conclude that the careful use of this technique for host star recommendation will be an asset to future missions and the compilation of necessary target lists.

An adaptive evolutionary multi-objective clustering based on the data properties of the base partitions

Evolutionary multi-objective clustering (EMOC) is a modern clustering technique in which the general concepts of evolutionary multi-objective optimization are applied to the clustering problem. The design and definition of clustering are difficult problems, and the choice of the objective functions and parameter setting of the algorithms are still challenges. In this paper, we propose the adaptive evolutionary multi-objective clustering approach based on data properties (AEMOC). AEMOC considers a new metric to evaluate the base partitions (candidate solutions used in the initial population) generated by minimum spanning tree clustering. This metric is applied to: (1) determine properties of the data, such as separation and overlap; and (2) define an offline selection of objective functions and parameter settings of the multi-objective algorithm. The information regarding the data properties allows AEMOC to avoid unnecessary data processing in datasets in which the initialization provides optimal solutions and optimization is not required. AEMOC presented promising results considering a diverse set of artificial and real-life datasets, based on two aspects: (1) it succeeded in the determination of the data properties of the base partitions and verifying the potential clustering quality, presenting a correlation of 0.8 with a reference metric, and (2) it provided better clustering results than reference EMOC approaches, achieving a general gain in the clustering performance of 3% in real-life datasets and 7% in artificial datasets.

Migrant Resettlement by Evolutionary Multi-objective Optimization

Migrant Resettlement by Evolutionary Multi-objective Optimization