Multi-objective Evolutionary Algorithm Research Articles

Multi-Objective Automatic Clustering Algorithm Based on Evolutionary Multi-Tasking Optimization

Data mining technology is the process of extracting hidden knowledge and potentially useful information from a large number of incomplete, noisy, and random practical application data. The clustering algorithm based on multi-objective evolution has obvious advantages compared with the traditional single-objective method. In order to further improve the performance of evolutionary multi-objective clustering algorithms, this paper proposes a multi-objective automatic clustering model based on evolutionary multi-task optimization. Based on the multi-objective clustering algorithm that automatically determines the value of k, evolutionary multi-task optimization is introduced to deal with multiple clustering tasks simultaneously. A set of non-dominated solutions for clustering results is obtained by concurrently optimizing the overall deviation and connectivity index. Multi-task adjacency coding based on a locus adjacency graph was designed to encode the clustered data. Additionally, an evolutionary operator based on relevance learning was designed to facilitate the evolution of individuals within the population. It also facilitates information transfer between individuals with different tasks, effectively avoiding negative transfer. Finally, the proposed algorithm was applied to both artificial datasets and UCI datasets for testing. It was then compared with traditional clustering algorithms and other multi-objective clustering algorithms. The results verify the advantages of the proposed algorithm in clustering accuracy and algorithm convergence.

A Hybrid Strategy Improved SPEA2 Algorithm for Multi-Objective Web Service Composition

Service-oriented architectures have become increasingly prevalent in internet application design, leading to a proliferation of services. Managing and composing these web services pose a classic non-deterministic polynomial-time hard problem. The web service composition problem (WSCP) based on the input–output model (IOM) involves the automatic composition of services without relying on a pre-defined workflow. Multi-objective evolutionary algorithms offer a solution that goes beyond simple weighted average calculations for quality of service, catering to diverse user needs in service composition. This paper introduces a multi-objective heuristic algorithm based on the SPEA2 called MSPEA2+. Specific modifications are incorporated in MSPEA2+ to support the breeding, crossover, and mutation processes, tailored for IOM-based WSCP. Validating the algorithm performance through finding suitable combination results for each task in the WSC-08 dataset, our experiments showed that MSPEA2+ has better iterative efficiency than existing multi-objective methods and outperforms them in terms of quality of service. MSPEA2+ achieved the lowest IGD value across all seven tasks, an improvement of 81.7% IGD value compared with the SPEA2 algorithm in WSC-0804.

Multi-objective reinforcement learning based on nonlinear scalarization and long-short-term optimization

Purpose Many practical control problems require achieving multiple objectives, and these objectives often conflict with each other. The existing multi-objective evolutionary reinforcement learning algorithms cannot achieve good search results when solving such problems. It is necessary to design a new multi-objective evolutionary reinforcement learning algorithm with a stronger searchability. Design/methodology/approach The multi-objective reinforcement learning algorithm proposed in this paper is based on the evolutionary computation framework. In each generation, this study uses the long-short-term selection method to select parent policies. The long-term selection is based on the improvement of policy along the predefined optimization direction in the previous generation. The short-term selection uses a prediction model to predict the optimization direction that may have the greatest improvement on overall population performance. In the evolutionary stage, the penalty-based nonlinear scalarization method is used to scalarize the multi-dimensional advantage functions, and the nonlinear multi-objective policy gradient is designed to optimize the parent policies along the predefined directions. Findings The penalty-based nonlinear scalarization method can force policies to improve along the predefined optimization directions. The long-short-term optimization method can alleviate the exploration-exploitation problem, enabling the algorithm to explore unknown regions while ensuring that potential policies are fully optimized. The combination of these designs can effectively improve the performance of the final population. Originality/value A multi-objective evolutionary reinforcement learning algorithm with stronger searchability has been proposed. This algorithm can find a Pareto policy set with better convergence, diversity and density.

A Dynamic Tasking-Based Evolutionary Algorithm for Bi-Objective Feature Selection

Feature selection in classification is a complex optimization problem that cannot be solved in polynomial time. Bi-objective feature selection, aiming to minimize both selected features and classification errors, is challenging due to the conflict between objectives, while one of the most effective ways to tackle this is to use multi-objective evolutionary algorithms. However, very few of these have ever reflected an evolutionary multi-tasking framework, despite the implicit parallelism offered by the population-based search characteristic. In this paper, a dynamic multi-tasking-based multi-objective evolutionary algorithm (termed DTEA) is proposed for handling bi-objective feature selection in classification, which is not only suitable for datasets with relatively lower dimensionality of features, but is also suitable for datasets with relatively higher dimensionality of features. The role and influence of multi-tasking on multi-objective evolutionary feature selection were studied, and a dynamic tasking mechanism is proposed to self-adaptively assign multiple evolutionary search tasks by intermittently analyzing the population behaviors. The efficacy of DTEA is tested on 20 classification datasets and compared with seven state-of-the-art evolutionary algorithms. A component contribution analysis was also conducted by comparing DTEA with its three variants. The empirical results show that the dynamic-tasking mechanism works efficiently and enables DTEA to outperform other algorithms on most datasets in terms of both optimization and classification.

Multi-objective capacity configuration optimization of a nuclear-renewable hybrid system

Integrating the energy storage and the base-load energy can be an efficient solution to cover the fluctuation of renewable energy. A nuclear-renewable hybrid energy system consisting of a small modular thorium molten salt reactor, solar photovoltaics, wind turbines, thermal energy storage and battery storage with two operation modes is proposed to meet the community load demand. The methodology combining multi-objective evolutionary algorithms with multi-criteria decision-making method is used to identify the optimal operation mode and gain the optimal configuration of the proposed nuclear-renewable hybrid energy system. In the first stage, the multi-objective evolutionary algorithm with better performance is utilized to gain Pareto solutions to minimize the levelized cost of energy while ensuring an acceptable level of deficiency of power supply probability. In the second stage, the multi-criteria decision-making method is adopted to select the best solution from the obtained Pareto frontiers. The optimization results demonstrate that the nondominated sorting genetic algorithm has the best performance compared with other algorithms and the operation mode with battery discharged first is more cost competitive. It is concluded from the results analysis that the selection of optimal mode is influenced by seasonal variation that contributes to large energy storage capacity requirement.

Multi-objective Evolutionary Algorithm with Variable Neighborhood Search for Optimizing Green Scheduling in a Re-Entrant Hybrid Flow Shop with Dynamic Events

In previous studies on re-entrant hybrid flow shops, the impact of dynamic events was often ignored despite being a common occurrence in practical production. To address this issue and simultaneously reduce energy consumption, a multi-objective evolutionary algorithm with variable neighborhood search (MOEA-VNS) has been proposed to optimize the green scheduling problem in a re-entrant hybrid flow shop with dynamic events (RHFS-GDS).The approach involves creating a green dynamic scheduling optimization model, which aims to minimize the makespan, total energy consumption, and stability of rescheduling solutions. A hybrid green scheduling decoding method is then employed to select machines for each operation and calculate fitness. Additionally, three neighborhood structures are designed to improve the population diversity and optimality of the MOEA-VNS algorithm. Two rescheduling strategies are also adopted to handle dynamic events that may occur during production. Experimental results demonstrate that these approaches are effective in solving the RHFS-GDS problem and can guide actual production. By incorporating dynamic events and rescheduling strategies into the optimization process, the proposed MOEA-VNS algorithm provides a comprehensive solution to the complex challenges faced by re-entrant hybrid flow shops in practical production environments.

Reinforcement learning for decision-making under deep uncertainty

Planning under complex uncertainty often asks for plans that can adapt to changing future conditions. To inform plan development during this process, exploration methods have been used to explore the performance of candidate policies given uncertainties. Nevertheless, these methods hardly enable adaptation by themselves, so extra efforts are required to develop the final adaptive plans, hence compromising the overall decision-making efficiency. This paper introduces Reinforcement Learning (RL) that employs closed-loop control as a new exploration method that enables automated adaptive policy-making for planning under uncertainty. To investigate its performance, we compare RL with a widely-used exploration method, Multi-Objective Evolutionary Algorithm (MOEA), in two hypothetical problems via computational experiments. Our results indicate the complementarity of the two methods. RL makes better use of its exploration history, hence always providing higher efficiency and providing better policy robustness in the presence of parameter uncertainty. MOEA quantifies objective uncertainty in a more intuitive way, hence providing better robustness to objective uncertainty. These findings will help researchers choose appropriate methods in different applications.

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.

Reinforcement Learning-Based Multiobjective Evolutionary Algorithm for Mixed-Model Multimanned Assembly Line Balancing Under Uncertain Demand.

In practical assembly enterprises, customization and rush orders lead to an uncertain demand environment. This situation requires managers and researchers to configure an assembly line that increases production efficiency and robustness. Hence, this work addresses cost-oriented mixed-model multimanned assembly line balancing under uncertain demand, and presents a new robust mixed-integer linear programming model to minimize the production and penalty costs simultaneously. In addition, a reinforcement learning-based multiobjective evolutionary algorithm (MOEA) is designed to tackle the problem. The algorithm includes a priority-based solution representation and a new task-worker-sequence decoding that considers robustness processing and idle time reductions. Five crossover and three mutation operators are proposed. The Q -learning-based strategy determines the crossover and mutation operator at each iteration to effectively obtain Pareto sets of solutions. Finally, a time-based probability-adaptive strategy is designed to effectively coordinate the crossover and mutation operators. The experimental study, based on 269 benchmark instances, demonstrates that the proposal outperforms 11 competitive MOEAs and a previous single-objective approach to the problem. The managerial insights from the results as well as the limitations of the algorithm are also highlighted.

An indicator-based evolutionary algorithm with adaptive archive update cycle for multi-objective multi-robot task allocation

The multi-robot task allocation problem has garnered significant attention in research and development. This paper addresses the multi-robot task allocation problem by introducing a unified model that seamlessly transforms into four popular mathematical models through simple parameter adjustments. We propose an efficient indicator-based multi-objective evolutionary algorithm with a hybrid encoding scheme for task execution order and robot starting point information. The algorithm employs the hypervolume indicator for environmental selection to enhance convergence and the modified crowding distance for archive updates to promote diversity. Additionally, an adaptive archive update mechanism is designed for time efficiency. In experiments comparing our proposed algorithm with 8 state-of-the-art algorithms on 18 randomly generated instances of various sizes, along with 4 real-world problems from the TSPLIB benchmark, our algorithm consistently outperformed the comparison algorithms in five key indicators. These results underscore the effectiveness of our approach in addressing real-world multi-robot task allocation problems.

A multi-objective particle swarm optimization based on local ideal points

Numerous multi-objective evolutionary algorithms have recently been proposed for the leader selection or archive maintenance process via using reference sets. Despite the potential of this strategy has been demonstrated in the existing literatures, a significant drawback is that this methodology requires additional parameters or predefined reference points, which leads to increasing the complexity in real-world applications and reducing the versatility in addressing various optimization challenges. Novel to this study, a new convergence contribution (CC) evaluator without extra parameters and predefined reference points is presented for convergence evaluation, where the inspiration is drawn from the concept of an ideal point on a Pareto front and the divide-and-conquer technique. Specifically, the local ideal points are introduced in this paper by dynamically fabricating from the approximate Pareto front. Furthermore, the CC evaluator and parallel cell distance (PCD) are cooperatively integrated into a multi-objective particle swarm optimization (MOPSO/CP) to enhance both the global best solution selection and archive maintenance strategies. Comparative experiments on 21 benchmark test functions exhibited that the performances in terms of inverted generational distance and hypervolume of the proposed MOPSO/CP was the best among those of the chosen competitive algorithms. The significant role of the cooperative mechanism and the CC evaluator is further verified by ablation studies. The superiority of the designed algorithm against its competitors is unequivocally highlighted by the experimental results.

A Multiobjective Evolutionary Algorithm for Network Planning in In-Building Distributed Antenna Systems

A Multiobjective Evolutionary Algorithm for Network Planning in In-Building Distributed Antenna Systems

A Synergistic Multi-Objective Evolutionary Algorithm with Diffusion Population Generation for Portfolio Problems

When constructing an investment portfolio, it is important to maximize returns while minimizing risks. This portfolio optimization can be considered as a multi-objective optimization problem that is solved by means of multi-objective evolutionary algorithms. The use of multi-objective evolutionary algorithms (MOEAs) provides an effective approach for dealing with the complex data involved in multi-objective optimization problems. However, current MOEAs often rely on a single strategy to obtain optimal solutions, leading to premature convergence and an insufficient population diversity. In this paper, a new MOEA called the Synergistic MOEA with Diffusion Population Generation (DPG-SMOEA) is proposed to address these limitations by integrating MOEAs with diffusion models. To train the diffusion model, a mixed memory pool strategy is optimized, which collects improved solutions from the MOEA/D-AEE, an optimized MOEA, as training samples. The trained model is then used to generate offspring. Considering the cold-start mechanism of the diffusion model, particularly during the training phase where it is not suitable for generating initial offspring, this paper adjusts and optimizes the collaborative strategy to enhance the synergy between the diffusion model and MOEA/D-AEE. Experimental validation of the DPG-SMOEA demonstrates the advantages of using diffusion models in low-dimensional and relatively continuous data analysis. The results show that the DPG-SMOEA performs well on the low-dimensional Hang Seng Index test dataset, while achieving average performance on other high-dimensional datasets, consistent with theoretical predictions. Overall, the DPG-SMOEA achieves better results compared to MOEA/D-AEE and other multi-objective optimization algorithms.

Multi-Objective Design of a Horizontal Flow Subsurface Wetland

An artificial wetland is used to treat gray, waste, storm or industrial water. This is an engineering system that uses natural functions of vegetation, soil and organisms to provide secondary treatment to gray water. In the physical design of each artificial wetland, there are various action factors that must meet certain characteristics so that the level of gray-water pollution is reduced. In this sense, several design methodologies have been developed and reported in the literature, but some are customized designs and often do not meet the required decontamination objectives. This challenge increases as the complexity of the task in its structure also increases. Particularly in this work, a multi-objective evolutionary algorithm is used to optimize the physical design of a horizontal flow subsurface wetland (HFSW) for gray-water treatment. The study aims to achieve two objectives: first, to minimize the physical volume, and second, to maximize the contaminant removal efficiency. The defined objective functions depend on six design variables called hydraulic retention time, width, length, water depth inside the wetland, substrate depth and slope. Three constraint functions are also defined: removal efficiency greater than 95%, physical volume below 500 m3 and compliance with a length–width ratio is 3:1, varying the population size and number of generations equal to 200, 400, and 600. The set of solutions according to the number of generations as well as the Pareto front corresponds to the best solution that complies with the constraints of the problem of oversizing the HFSW, and the Pareto front shows the interaction between the objectives and their behavior, reflecting the problem’s nature as minimization–maximization.

A Systematic Review of Multi-Objective Evolutionary Algorithms Optimization Frameworks

The study of evolutionary algorithms (EAs) has witnessed an impressive increase during the last decades. The need to explore this area is determined by the growing request for design and the optimization of more and more engineering problems in society, such as highway construction processes, food and agri-technologies processes, resource allocation problems, logistics and transportation systems, microarchitectures, suspension systems optimal design, etc. All of these matters refer to specific highly computational problems with a huge design space, hence the obvious need for evolutionary algorithms and frameworks, or platforms that allow for the implementing and testing of such algorithms and methods. This paper aims to comparatively analyze the existing software platforms and state-of-the-art multi-objective optimization algorithms and make a review of what features exist and what features might be included next as further developments in such tools, from a researcher’s perspective. Additionally, it is essential for a framework to be easily extendable with new types of problems and optimization algorithms, metrics and quality indicators, genetic operators or specific solution representations and results analysis and comparison features. After presenting the most relevant existing features in these types of platforms, we suggest some future steps and the developments we have been working on.

Correction: Bu et al. A Decomposition-Based Multi-Objective Evolutionary Algorithm for Solving Low-Carbon Scheduling of Ship Segment Painting. Coatings 2024, 14, 368

In the original publication [...]

A novel evolutionary algorithm for structural model updating with a hybrid initialization and multi-stage update strategy

Measurement errors, spatial incompleteness, and parameter uncertainties frequently lead to significant deviations between the estimated correction coefficients of structural model updating and their actual values. To address the limitations, a novel multi-objective evolutionary algorithm called MOEA-HiMs is proposed for structural model updating, which incorporates a hybrid initialization and multi-stage update strategy. Two main contributions are summarized: (a) the introduction of optimal point and elite set initialization to enhance population diversity, which is achieved through the use of Latin hypercube sampling and a regularization technique, respectively; (b) the division of the optimization process into multiple stages, where solutions are corrected to improve converging efficiency using an appropriate update strategy. Additionally, the elite set is selected through the execution of sensitivity classification using a novel mathematical sensitivity index. The effectiveness and robustness of the MOEA-HiMs are demonstrated by the numerical offshore jacket platform and an experimentally-scaled platform structure. Both numerical and experimental results prove that the novel proposed MOEA-HiMs is more effective and robust than the traditional MOEA when using limited information, even under heavy noise conditions. The algorithm can serve as preliminary methods for online structural model updating of offshore platforms.

Parameter-less Pareto local search for multi-objective neural architecture search with the Interleaved Multi-start Scheme

With the emerging deployment of deep neural networks, such as in mobile devices and autonomous cars, there is a growing demand for neural architecture search (NAS) to automatically design powerful network architectures. It is more reasonable to formulate NAS as a multi-objective optimization problem. In addition to prediction performance, multi-objective NAS (MONAS) problems take into account other criteria like the number of parameters and inference latency. Multi-objective evolutionary algorithms (MOEAs) are the preferred approach for tackling MONAS due to their effectiveness in dealing with multi-objective optimization problems. Recently, local search-based NAS algorithms have demonstrated their efficiency over MOEAs for MONAS problems. However, their performance has been only verified on bi-objective NAS problems. In this article, we propose a local search algorithm for multi-objective NAS (LOMONAS), an efficient local search framework for solving not only bi-objective NAS problems but also NAS problems having more than two objectives. We additionally present a parameter-less version of LOMONAS, namely IMS-LOMONAS, by combining LOMONAS with the Interleaved Multi-start Scheme (IMS) to help NAS practitioners avoid manual control parameter settings. Experimental results from a series of benchmark problems in the CEC’23 Competition demonstrate the competitiveness of LOMONAS and IMS-LOMONAS compared to MOEAs in tackling MONAS within both small-scale and large-scale search spaces. Source code is available at: https://github.com/ELO-Lab/IMS-LOMONAS.

Multi-objective path planning for multi-UAV connectivity and area coverage

In this paper, we assume that a team of drones equipped with sensing and networking capabilities explore an unknown area via onboard sensors for surveillance, monitoring, target search or data collection purposes and deliver the sensed data to a ground control station (GCS) over multi-hop links. We propose a multi-drone path planner that jointly optimizes area coverage time and connectivity among the drones. We propose a novel connectivity metric that includes not only percentage connectivity of the drones to GCS, but also the maximum duration of consecutive time that the drones are disconnected from the GCS. To solve this optimization formulation, we propose a multi-objective evolutionary algorithm with novel operations. We use our solver to test single, two and many objective path planning problems and compare our Pareto-optimal solutions to benchmark weighted-sum based solutions. We show that as opposed to the single solution that weighted-sum methods provide based on prior information from the user, the proposed evolutionary multi-objective optimizers can provide a diverse set of solutions that cover a range of mission time and connectivity performance illustrating the trade-off between these conflicting objectives. The end-user can then choose the best path solution based on the mission priorities during operation.

Comparison of MOEAs in an Optimization-Decision Methodology for a Joint Order Batching and Picking System

This paper investigates the performance of a two-stage multi-criteria decision-making procedure for order scheduling problems. These problems are represented by a novel nonlinear mixed integer program. Hybridizations of three Multi-Objective Evolutionary Algorithms (MOEAs) based on dominance relations are studied and compared to solve small, medium, and large instances of the joint order batching and picking problem in storage systems with multiple blocks of two and three dimensions. The performance of these methods is compared using a set of well-known metrics and running an extensive battery of simulations based on a methodology widely used in the literature. The main contributions of this paper are (1) the hybridization of MOEAs to deal efficiently with the combination of orders in one or several picking tours, scheduling them for each picker, and (2) a multi-criteria approach to scheduling multiple picking teams for each wave of orders. Based on the experimental results obtained, it can be stated that, in environments with a large number of different items and orders with high variability in volume, the proposed approach can significantly reduce operating costs while allowing the decision-maker to anticipate the positioning of orders in the dispatch area.