Constrained Multi-objective Optimization Research Articles

A Multiobjective Optimization Algorithm for Fluid Catalytic Cracking Process with Constraints and Dynamic Environments

The optimization problems in a fluid catalytic cracking process with dynamic constraints and conflicting objectives are challenging due to the complicated constraints and dynamic environments. The decision variables need to be reoptimized to obtain the best objectives when dynamic environments arise. To solve these problems, we established a mathematical model and proposed a dynamic constrained multiobjective optimization evolution algorithm for the fluid catalytic cracking process. In this algorithm, we design an offspring generation strategy based on minimax solutions, which can explore more feasible regions and converge quickly. Additionally, a dynamic response strategy based on population feasibility is proposed to improve the feasible and infeasible solutions by different perturbations, respectively. To verify the effectiveness of the algorithm, we test the algorithm on ten instances based on the hypervolume metric. Experimental results show that the proposed algorithm is highly competitive with several state-of-the-art competitors.

A federated GAN network-based evolutionary constrained optimization approach to integrated coal mine energy system

The integrated coal mine energy system (ICMES) is a kind of system with multiple scenarios, variables and parameters, which belongs to dynamic constrained multi-objective optimization problem (DCMOP). One of the challenges in solving ICMES lies in searching for feasible solutions when the frequency of changes is quick. To solve the above mentioned issues, this paper proposes a federated GAN network-based evolutionary constrained optimization for ICMES (FGECO). Firstly, multiple GAN networks are utilized in the framework of federated learning (FL) to estimate the distribution of feasible regions that satisfy each constraint. Following that, they are fused to realize the intersection of all feasible regions, and generate one feasible region that can meet all constrained requirements. Subsequently, an initial population with guidance of evolution is generated based on the proposed shared GAN network model. Finally, FGECO is compared with four popular dynamic constrained multi-objective evolutionary algorithms (DCMOEAs) on ICMES. Experimental results indicate its superiority.

A federated GAN network-based evolutionary constrained optimization approach to integrated coal mine energy system

The integrated coal mine energy system (ICMES) is a kind of system with multiple scenarios, variables and parameters, which belongs to dynamic constrained multi-objective optimization problem (DCMOP). One of the challenges in solving ICMES lies in searching for feasible solutions when the frequency of changes is quick. To solve the above mentioned issues, this paper proposes a federated GAN network-based evolutionary constrained optimization for ICMES (FGECO). Firstly, multiple GAN networks are utilized in the framework of federated learning (FL) to estimate the distribution of feasible regions that satisfy each constraint. Following that, they are fused to realize the intersection of all feasible regions, and generate one feasible region that can meet all constrained requirements. Subsequently, an initial population with guidance of evolution is generated based on the proposed shared GAN network model. Finally, FGECO is compared with four popular dynamic constrained multi-objective evolutionary algorithms (DCMOEAs) on ICMES. Experimental results indicate its superiority.

Multipopulation Evolution-Based Dynamic Constrained Multiobjective Optimization Under Diverse Changing Environments

Dynamic constrained multiobjective optimization involves irregular changes in the distribution of the true Pareto-optimal fronts, drastic changes in the feasible region caused by constraints, and the movement directions and magnitudes of the optimal distance variables due to diverse changing environments. To solve these problems, we propose a multi-population evolution based dynamic constrained multiobjective optimization algorithm. In this algorithm, we design a tribe classification operator to divide the population into different tribes according to a feasibility check and the objective values, which is beneficial for driving the population toward the feasible region and Pareto-optimal fronts. Meanwhile, a population selection strategy is proposed to identify promising solutions from tribes and exploit them to update the population. The optimal values of the distance variables vary differently with dynamic environments, thus, we design a dynamic response strategy for solutions in different tribes that estimates their distances to approach the Pareto-optimal fronts and regenerates a promising population when detecting environmental changes. In addition, a scalable generator is designed to simulate diverse movement directions and magnitudes of the optimal distance variables in real-world problems under dynamic environments, obtaining a set of improved test problems. Experimental results show the effectiveness of test problems, and the proposed algorithm is impressively competitive with several chosen state-of-the-art competitors.

A surrogate-assisted a priori multiobjective evolutionary algorithm for constrained multiobjective optimization problems

AbstractWe consider multiobjective optimization problems with at least one computationally expensive constraint function and propose a novel surrogate-assisted evolutionary algorithm that can incorporate preference information given a priori. We employ Kriging models to approximate expensive objective and constraint functions, enabling us to introduce a new selection strategy that emphasizes the generation of feasible solutions throughout the optimization process. In our innovative model management, we perform expensive function evaluations to identify feasible solutions that best reflect the decision maker’s preferences provided before the process. To assess the performance of our proposed algorithm, we utilize two distinct parameterless performance indicators and compare them against existing algorithms from the literature using various real-world engineering and benchmark problems. Furthermore, we assemble new algorithms to analyze the effects of the selection strategy and the model management on the performance of the proposed algorithm. The results show that in most cases, our algorithm has a better performance than the assembled algorithms, especially when there is a restricted budget for expensive function evaluations.

An away-step Frank–Wolfe algorithm for constrained multiobjective optimization

An away-step Frank–Wolfe algorithm for constrained multiobjective optimization

Dual-stage and dual-population cooperative evolutionary algorithm for solving constrained multiobjective problems

During the search process, the characteristics of the feasible regions encountered by the population continually change in Constrained Multiobjective Optimization Problems (CMOPs). This variability poses a challenge for traditional evolutionary algorithms, which often struggle to adapt to the diverse problem characteristics of the encountered feasible regions. To overcome this limitation, we propose a Dual-Stage and Dual-Population Cooperative Evolutionary Algorithm (DDCEA) to address CMOPs characterized by diverse feasible regions. DDCEA employs a dual-stage mechanism to adapt the offspring generation strategy and establishes two distinct populations to evaluate offspring using constraint-sensitive and constraint-free strategies. Comparative analyses reveal that DDCEA surpasses chosen state-of-the-art CMOEAs in adapting to the changing feasible regions and then approximating the constrained Pareto fronts.

An adaptive uniform search framework for constrained multi-objective optimization

This paper proposes an adaptive uniform search framework designed for constrained multi-objective optimization. The framework comprises three key components: a global uniform exploration strategy, a local greedy exploitation strategy, and a search switch mechanism. These components work together to facilitate comprehensive exploration of promising areas while maintaining a balance between global exploration and local exploitation. Specifically, the global uniform exploration strategy ensures even distribution within promising areas, preventing any oversights during exploration. The local greedy exploitation strategy divides these areas into sub-areas and employs a feasibility-led constraint handling technique to enhance efficiency in identifying optimal solutions. Additionally, the search switch dynamically adjusts the search strategy between global exploration and local exploitation. Numerical simulations on various benchmark suites and real-world problem demonstrate the strong performance of the framework in addressing constrained multi-objective optimization problems. The comparison results show that compared with eight recently proposed algorithms, the proposed framework is more robust in solving diverse constrained multi-objective optimization problems.

An inexact nonmonotone projected gradient method for constrained multiobjective optimization

An inexact nonmonotone projected gradient method for constrained multiobjective optimization

A novel multi-population evolutionary algorithm based on hybrid collaboration for constrained multi-objective optimization

Multi-population-based methods are widely employed for solving constrained multiobjective optimization problems (CMOPs). The population collaboration strategy is a critical part of multi-population algorithms, and different collaboration strategies perform well on different complex CMOPs. However, these single-population collaboration strategies are still challenging to adapt to various CMOPs with different characteristics. To address this issue, we propose a novel tri-population hybrid collaboration evolutionary algorithm called TP-HCEA, which includes a constraint-relaxed population (denoted as mainpop), a constraint-ignored auxiliary population (denoted as auxpop1), and an auxiliary population (denoted as auxpop2) for the original CMOP, to search optimal solutions in the feasible region. Specifically, due to the different complementarities of the two auxiliary populations, mainpop collaborates with auxpop1 and auxpop2 in a dynamic choice between strong and weak cooperation. The effectiveness of TP-HCEA is validated through comparative analysis with seven state-of-the-art algorithms in four CMOP benchmark suites and nine real-world problems.

A pareto fronts relationship identification-based two-stage constrained evolutionary algorithm

Striking a balance between diverse constraints and conflicting objectives is one of the most crucial issues in solving constrained multi-objective optimization problems (CMOPs). However, it remains challenging to existing methods, due to the reduced search space caused by the constraints. For this issue, this paper proposes a Pareto fronts relationship identification-based two-stage constrained evolutionary algorithm called RITEA, which balances objective optimization and constraint satisfaction by identifying and utilizing the relationship between the unconstrained Pareto front (UPF) and the constrained Pareto front (CPF). Specifically, the evolutionary process is divided into two collaborative stages: training stage and reinforcement stage. In the training stage, a relationship identification method is developed to estimate the relationship between UPF and CPF, which guides the population search direction. In the reinforcement stage, the corresponding evolutionary strategies are designed based on the identified relationship to enhance the accurate search on the CPF. Furthermore, a dynamic preference fitness function (termed DPF) is designed to adaptively maintain the balance of search preference between convergence and diversity. Compared to seven state-of-the-art algorithms on 36 benchmark CMOPs in three popular test suites, RITEA obtains 77.8% of the best IGD values and 66.7% of the best HV values. The experimental results show that RITEA exhibits highly competitively when dealing with CMOPs.

A two-stage bidirectional coevolution algorithm with reverse search for constrained multiobjective optimization

Constrained multiobjective optimization problems (CMOPs) are widespread in reality. The presence of constraints complicates the feasible region of the original problem and increases the difficulty of problem solving. There are not only feasible regions, but also large areas of infeasible regions in the objective space of CMOPs. Inspired by this, this paper proposes a bidirectional coevolution method with reverse search (BCRS) combined with a two-stage approach. In the first stage of evolution, constraints are ignored and the population is pushed toward promising regions. In the second stage, evolution is divided into two parts, i.e., the main population evolves toward the constrained Pareto front (CPF) within the feasible region, while the reverse population approaches the CPF from the infeasible region. Then a solution exchange strategy similar to weak cooperation is used between the two populations. The experimental results on benchmark functions and real-world problems show that the proposed algorithm exhibits superior or at least competitive performance compared to other state-of-the-art algorithms. It demonstrates BCRS is an effective algorithm for addressing CMOPs.Graphical

Multidisciplinary Design Methodology for Micro-Gas-Turbines—Part II: System Analysis and Optimization

Abstract Owing to their high specific energy capabilities, ultramicrogas turbines (UMGT) are a high-potential technology to provide portable electric power supply for applications with demand of less than 1 kW. UMGT conceptual design is challenged by small-scale effects augmenting interdisciplinary dependencies leading to highly coupled, nonlinear component interactions. This work provides a novel approach to conceptual UMGT design by combining reduced order component and system modeling with constrained multi-objective optimization. Hereby, Part I presents integrated design and performance modeling of compressor, turbine, combustor, and generator. In Part II, the heat engine and generator modules are merged into a system framework by establishing conceptual UMGT rotor geometry and engine design. Following bearing selection and lifetime assessment, experimentally validated reduced order models are developed for heat transfer and rotordynamic analysis. Using the elaborated framework, a constrained multi-objective system optimization of a 300 W engine is performed based on ten design parameters and comparing SiAlON and Inconel 718 as potential rotor materials available for additive manufacturing. Hereby, bearing lifetime, system efficiency, and specific power are maximized while meeting rotordynamic, structural, and thermal requirements. Evaluating the results, interdisciplinary effects are highlighted, and two optimum engine configurations are suggested.

A Multi-Stage Constraint-Handling Multi-Objective Optimization Method for Resilient Microgrid Energy Management

In recent years, renewable energy has seen widespread application. However, due to its intermittent nature, there is a need to develop energy management systems for its scheduling and control. This paper introduces a multi-stage constraint-handling multi-objective optimization method tailored for resilient microgrid energy management. The microgrid encompasses diesel generators, energy storage systems, renewable energy sources, and various load types. The intelligent management of generators, batteries, switchable loads, and controllable loads ensures a reliable power supply for the critical loads. Beyond operational costs, our model also considers grid dependency as a key objective, making it particularly suited for energy management in extreme environments such as islands, border regions, and military bases. Managing complex controls of generators, batteries, switchable loads, and controllable loads presents challenging constraints that the management strategy must meet. To tackle this challenge, we propose an multi-objective optimization algorithm with multi-stage constraint-handling strategy to handle the high-dimensional complex constraints of the resilient energy management problem. Our proposed approach demonstrates superior performance compared to nine leading constrained multi-objective optimization algorithms across various test scenarios. Furthermore, the benefits of our method become increasingly evident as the complexity of the problem increases. Compared to the classical NSGA-II, the proposed NSGA-II-MC method achieved a 49.7% improvement in the Hypervolume metric on large-scale problems.

Constrained Multi-Objective Optimization With Deep Reinforcement Learning Assisted Operator Selection

Constrained Multi-Objective Optimization With Deep Reinforcement Learning Assisted Operator Selection

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

The 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 Pop1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Pop}}_1$$\\end{document} and Pop2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Pop}}_2$$\\end{document}. Throughout the three stages, Pop1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Pop}}_1$$\\end{document} is tasked with converging to the constrained Pareto front (CPF). However, Pop2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Pop}}_2$$\\end{document} 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.

Constraint subsets-based evolutionary multitasking for constrained multiobjective optimization

Constrained multiobjective optimization problems (CMOPs) are challenging because they need to optimize multiple conflicting objectives and satisfy various constraints simultaneously. To solve CMOPs, various constrained multiobjective evolutionary algorithms have been proposed in recent years. However, most of them tackle constraints by considering all constraints or zero constraint scenarios, these extreme treatment methods may be unable to utilize the information of multiple constraint subsets composed of partial constraints to maintain more promising infeasible solutions. To remedy this issue, a constraint subsets-based evolutionary multitasking method is developed, where a CMOP is transformed into a multitasking optimization problem by creating multiple simple auxiliary CMOPs. Particularly, the original CMOP is the main task, while the newly created CMOPs with different constraint subsets are the auxiliary tasks. Each task will be evolved by one specific population, and the knowledge transfer is conducted among tasks to realize the collaborative search. Meanwhile, the updating of the auxiliary task involves two stages. In the first stage, each auxiliary population will evolve to approach the pareto front of the constraint subset (s-CPF), promoting crossing the infeasible regions. While in the second stage, a feasible region-based search mechanism is proposed to approach the pareto front of the main task from each s-CPF, by utilizing unique and promising infeasible solutions. In addition, systematic experiments are carried out on three benchmark test suites and four real-world CMOPs. The experimental results fully demonstrate that the proposed algorithm is highly competitive with other state-of-the-art constrained multiobjective evolutionary algorithms.

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.

Multi-objective optimization and integrated indicator-driven two-stage project recommendation in time-dependent software ecosystem

Context:Time-dependent software ecosystem is a complex system, where there are many projects and developers. Recommending projects to developers in a time-dependent software ecosystem can improve their quality and development speeds. However, the time-dependence of projects and developers results in an increased difficulty of project recommendation. Objective:To better recommend projects to developers in a time-dependent software ecosystem, we propose a method of multi-objective optimization and integrated indicator-driven two-stage project recommendation, which is fulfilled according to the change of developer communities and their projects. Method:According to the change of developer communities and their projects, a method of multi-objective optimization and integrated indicator-driven two-stage project recommendation is fulfilled. In the first stage, a constrained multi-objective optimization model for project recommendation to developer communities is established, and an improved NSGA-II algorithm is adopted to solve this model, with the purpose of obtaining the recommended projects to a developer community. For the second stage, an integrated indicator for project recommendation to developers is built to determine the developers of a project. Results:The proposed method is applied to project recommendation for nine time-dependent software ecosystems in GitHub, and compared with six state-of-the-art ones. The experimental results show that our method has significant advantages in recommendation accuracy and efficiency. Conclusion:According to the experimental results, we conclude that the proposed method can timely and accurately recommend projects to developers in a time-dependent software ecosystem, which reduces the difficulty of solving the problem of project recommendation.

An Improved Particle Swarm Optimization Algorithm for Automated Test Resource Allocation

With the rapid increase of software complexity, automated testing has become the mainstream of software testing. However, the current automated test tools adopt a large number of common test equipment resource. At the beginning of the test, for specific test scenarios, the testers need to plan the test equipment resources according to the requirements of the software under test. An automatic test equipment resource planning and optimization algorithm based on group optimization is proposed IPSO (Improved Particle Swarm Optimization) to solve this problem. This method maps the requirement description to the equipment description to obtain the matching matrix, and then establishes a multi-objective constrained optimization model for test equipment resource planning. The solution is obtained through improved particle swarm optimization algorithm to achieve the optimal planning of test equipment resources. Compared with traditional manual planning methods, this algorithm reduces the workload of testers, and improves the automation and efficiency of testing. Experimental results demonstrate that the optimal solutions found by the algorithm proposed in this paper is superior to those of the PSO (Particle Swarm Optimization)) and Linearly Decreasing Inertia Weight Particle Swarm Optimization (LWPSO) algorithms.