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Balancing between the convergence, feasibility, and diversity of the population is the key to solving constrained multi-objective optimization problems (CMOPs). However, the existing constrained multi-objective optimization evolutionary algorithm (CMOEAs) face challenges in converging to the constrained pareto front (CPF) with well-distributed feasible solutions. To address this issue, this paper proposes a dynamic tri-population multi-objective evolutionary algorithm, called TDPSCMO. In the initial phase, the first and second populations evolve dynamically to solve the original CMOP and the unconstrained Multi-Objective Optimization Problem (MOP). This dynamic offspring generation emphasizes convergence and feasibility. In the later stages, the allocation of computing resources to the first population is adjusted based on the variation in offspring numbers. Simultaneously, a third population is introduced to enhance population diversity by treating Constraint Violation degrees as an additional objective function, thus capturing more valuable information. The performance of TDPSCMO is further tested through 57 benchmark test problems and 21 real-world applications using several state-of-the-art algorithms. The results show the competitiveness of the proposed algorithm when addressing CMOPs. [ABSTRACT FROM AUTHOR]

Financial market has systemic complexity and uncertainty. For investors, return and risk often coexist. How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization (PO). At present, due to the influence of modeling and algorithm solving, the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multi-objective models. PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios. It is more difficult than the previous single-stage PO model for meeting the realistic requirements. In this paper, the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate (M-ISTARR-MD) PO model which effectively characterizes the real investment scenario. In order to solve the multi-stage multi-objective PO model with complex multi-constraints, the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning (MSCMOEA-OL). Comparing with four well-known intelligence algorithms, the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset. This paper provides a new way to construct and solve the complex PO model. [ABSTRACT FROM AUTHOR]

As a new technology, Internet of Vehicles (IoV) needs high bandwidth and low delay. However, the current on-board mobile terminal equipment cannot meet the needs of the IoV. Therefore, using mobile edge computing (MEC) can solve the problems of energy consumption and time delay in the IoV. In the MEC, task offloading can solve the problem of resource constraint on mobile devices effectively, but it is not optimal to offload all tasks to edge servers. In this paper, the vehicle computation task is regarded as a directed acyclic graph (DAG), and task nodes' execution location and scheduling order are optimized. Considering the energy consumption and delay of the system, the vehicle computation offloading is considered as a constrained multi-objective optimization problem (CMOP), and then a Non-dominated Sorting Genetic Strategy(NSGS) is proposed to solve the CMOP. The proposed algorithm can realize local and edge parallel processing to reduce delay and energy consumption. Finally, a large number of experiments are carried to prove the performance of the algorithm. The experimental results show that the algorithm can make the optimal decision in practical applications. [ABSTRACT FROM AUTHOR]

In this paper, a numerical approximation method is developed to find approximate solutions to a class of constrained multi-objective optimization problems. All the functions of the problem are not necessarily convex functions. At each iteration of the method, a particular type of subproblem is solved using the trust region technique, and the step is evaluated using the notions of actual reduction and predicted reduction. A non-differentiable $ l_{\infty } $ l∞ penalty function restricts the constraint violations. An adaptive BFGS update formula is introduced. Global convergence of the proposed algorithm is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. Furthermore, it is justified that the proposed algorithm displays a super-linear convergence rate. Numerical results are provided to show the efficiency of the algorithm in the quality of the approximated Pareto front. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms have been effective in obtaining near-optimal solutions for NP-Complete problems like task scheduling. However, most of these algorithms still suffer from inadequate balance between local and global search when seeking a global solution, which often results in sub-optimal solutions. In this paper, an adaptive benefit factors based symbiotic organisms search (ABFSOS) is proposed, that adaptively tune SOS control parameters to strike a balance between local and global search procedures for faster convergence speed. Moreover, an adaptive constrained handling strategy is integrated into the proposed algorithm to effectively tune the values of the penalty function, thereby avoiding infeasible solutions and premature convergence. The performance of the proposed constrained multi-objective ABFSOS (CMABFSOS) was evaluated using large instances of both standard, and synthetic workloads, on a standard toolkit simulator (CloudSim). The non-dominated solutions obtained by the proposed CMABFSOS algorithm outperforms the compared algorithms (EMS-C, and ECMSMOO) for all the workload instances. The proposed CMABFSOS algorithm obtained significant improvement of hypervolume (convergence and diversity) over the compared algorithms for the workload instances. The performance improvement of CMABFSOS over EMS-C ranges from 17.02 to 47.73% across the workloads, while the performance improvement over ECMSMOO is between 19.98 to 52.18%. [ABSTRACT FROM AUTHOR]

Satisfying various constraints and multiple objectives simultaneously is a significant challenge in solving constrained multi-objective optimization problems. To address this issue, a new approach is proposed in this paper that combines multi-population and multi-stage methods with a Carnivorous Plant Algorithm. The algorithm employs the ϵ -constraint handling method, with the ϵ value adjusted according to different stages to meet the algorithm's requirements. To improve the search efficiency, a cross-pollination is designed based on the trapping mechanism and pollination behavior of carnivorous plants, thus balancing the exploration and exploitation abilities and accelerating the convergence speed. Moreover, a quasi-reflection learning mechanism is introduced for the growth process of carnivorous plants, enhancing the optimization efficiency and improving its global convergence ability. Furthermore, the quadratic interpolation method is introduced for the reproduction process of carnivorous plants, which enables the algorithm to escape from local optima and enhances the optimization precision and convergence speed. The proposed algorithm's performance is evaluated on several test suites, including DC-DTLZ, FCP, DASCMOP, ZDT, DTLZ, and RWMOPs. The experimental results indicate competitive performance of the proposed algorithm over the state-of-the-art constrained multi-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

The balance of convergence, diversity, and feasibility plays a pivotal role in constrained multi-objective optimization problems. To address this issue, in this paper a novel method named PeCMOEA is proposed, in which the pivotal solutions, which are designed for estimating the constrained Pareto front, are identified through an achievement scalarizing function. In addition, two different adaptive fitness functions are formulated to evaluate convergence- and diversity-oriented populations, respectively. Finally, the promising solutions from the two populations are reserved by their fitness values in the environmental selection while a self-adaptive penalty function is designed to repair infeasible solutions and ensure their feasibility. The performance of PeCMOEA is compared with five state-of-the-art constrained multi-objective evolutionary algorithms on five test suites. The experimental results illustrate that PeCMOEA exhibits competitive performance when utilised for this family of problems. [ABSTRACT FROM AUTHOR]

Infeasible solutions are helpful for finding the feasible regions, but how many feasible and infeasible solutions should be invested to achieve the optimal search efficiency remains to be further studied. Combined with the recently proposed collaborative constrained multi-objective framework, the contributions of the helper population and original population in different types of CMOPs are discussed. It is unreasonable to assign equal resources to these two populations in different CMOPs and different searching stages. This paper aims to investigate resource allocation in a constraint environment to efficiently utilize the limited resources and obtain a better performance. Therefore, the concept of return on investment (ROI) is first introduced to measure the contributions of two populations, and then guide the population size allocation (APS). To prevent the ROI from continuously declining as the population size decreases, an evolutionary resource allocation strategy (AER) is proposed to adjust their evolutionary state according to the cooperative relationship, and to further increase their ROI and again compete for population size, to maximize the evolutionary efficiency of the two populations in competition and cooperation. The proposed CCMODRA is compared with seven popular algorithms that cover three types of CMOEAs and test them on three benchmarks that cover four types of CMOPs. The comprehensive performance of CCMODRA is better than the other seven CMOEAs on 71% of the 3-objective CDTLZs, 57% of the 5-objective CDTLZs and 46% of the MWs. The effectiveness of the APS and AER strategies are verified on generating contribution solutions and DOC test problems. In addition, the total profit obtained by CCMODRA in the knapsack problem with capacity constraints is improved by 0.2% to 216% compared with the other seven algorithms. [ABSTRACT FROM AUTHOR]

Objective optimization and constraint satisfaction should be considered simultaneously when dealing with constrained multi-objective optimization problems (CMOPs). But it is difficult for existing constraint multi-objective evolutionary algorithms (CMOEAs) to strike a good balance between them, especially for CMOPs with complex constraints. To address this issue, this paper proposes a tri-stage competitive swarm optimizer (CSO), namely TSCSO, where objective optimization and constraint satisfaction receive different attention in different stages. In Stage-I, the population converges to the vicinity of the unconstrained Pareto front (PF) without considering any constraints. In Stage-II, a balance strategy and ranking approach based on convergence, diversity, and feasibility are proposed to enhance the diversity of the population and explore more feasible regions. An external archive is used to store the feasible solutions explored during the evolutionary process. In Stage-III, the population is first initialized by the feasible solutions in the archive, and the CSO operator with efficient search is used to search for the feasible regions omitted in Stage-II. Statistical results on two benchmark suites with twenty-eight problems and five real-world problems indicate that the proposed algorithm performs better than other state-of-the-art CMOEAs overall. [ABSTRACT FROM AUTHOR]

When solving constrained multi-objective optimization problems (CMOPs), multiple conflicting objectives and multiple constraints need to be considered simultaneously, which are challenging to handle. Although some recent constrained multi-objective evolutionary algorithms (CMOEAs) have been developed to solve CMOPs and have worked well on most CMOPs. However, for CMOPs with small feasible regions and complex constraints, the performance of most algorithms needs to be further improved, especially when the feasible region is composed of multiple disjoint parts or the search space is narrow. To address this issue, an efficient global diversity CMOEA (EGDCMO) is proposed in this paper to solve CMOPs, where a certain number of infeasible solutions with well-distributed feature are maintained in the evolutionary process. To this end, a set of weight vectors are used to specify several subregions in the objective space, and infeasible solutions are selected from each subregion. Furthermore, a new fitness function is used in this proposed algorithm to evaluate infeasible solutions, which can balance the importance of constraints and objectives. In addition, the infeasible solutions are ranked higher than the feasible solutions to focus on the search in the undeveloped areas for better diversity. After the comparison tests on three benchmark cases and an actual engineering application, EGDCMO has more impressive performance compared with other constrained evolutionary multi-objective algorithms. [ABSTRACT FROM AUTHOR]

For solving constrained multi-objective optimization problems (CMOPs), an effective constraint-handling technique (CHT) is of great importance. Recently, many CHTs have been proposed for solving CMOPs. However, no single CHT can outperform all kinds of CMOPs. This paper proposes an algorithm, namely, ACHT-M2M, which adaptively allocates the existing CHTs in an M2M framework for solving CMOPs. To be more specific, a CMOP is first decomposed into several constrained multi-objective optimization subproblems by ACHT-M2M. Each subproblem has a subpopulation in a subregion. CHT for each subregion is adaptively allocated according to a proposed composite performance measure. Population for the next generation is selected from subregions by selection operators with different CHTs and the obtained nondominated feasible solutions in each generation are used to update a predefined archive. ACHT-M2M assembles the advantages of different CHTs and makes them cooperate with each other. The proposed ACHT-M2M is finally compared with the other 12 representative algorithms on benchmark CMOPs and the experimental results further confirm the effectiveness of ACHT-M2M for solving CMOPs. [ABSTRACT FROM AUTHOR]

Stay cables exhibit both great slenderness and low damping, which make them sensitive to resonant phenomena induced by the dynamic character of external actions. Furthermore, for these same reasons, their modal properties may vary significantly while in service due to the modification of the operational and environmental conditions. In order to cope with these two limitations, passive damping devices are usually installed at these structural systems. Robust design methods are thus mandatory in order to ensure the adequate behavior of the stay cables without compromising the budget of the passive control systems. To this end, a motion-based design method under uncertainty conditions is proposed and further implemented in this paper. In particular, the proposal focuses on the robust design of different passive damping devices when they are employed to control the response of stay cables under wind-induced vibrations. The proposed method transforms the design problem into a constrained multi-objective optimization problem, where the objective function is defined in terms of the characteristic parameters of the passive damping device, together with an inequality constraint aimed at guaranteeing the serviceability limit state of the structure. The performance of the proposed method was validated via its application to a benchmark structure with vibratory problems: The longest stay cable of the Alamillo bridge (Seville, Spain) was adopted for this purpose. Three different passive damping devices are considered herein, namely: (i) viscous; (ii) elastomeric; and (iii) frictions dampers. The results obtained by the proposed approach are analyzed and further compared with those provided by a conventional method adopted in the Standards. This comparison illustrates how the newly proposed method allows reduction of the cost of the three types of passive damping devices considered in this study without compromising the performance of the structure. [ABSTRACT FROM AUTHOR]

This paper proposes an improved epsilon constraint-handling mechanism and combines it with a decomposition-based multi-objective evolutionary algorithm (MOEA/D) to solve constrained multi-objective optimization problems (CMOPs). The proposed constrained multi-objective evolutionary algorithm (CMOEA) is named MOEA/D-IEpsilon. It adjusts the epsilon level dynamically according to the ratio of feasible to total solutions in the current population. In order to evaluate the performance of MOEA/D-IEpsilon, a new set of CMOPs with two and three objectives is designed, having large infeasible regions (relative to the feasible regions), and they are called LIR-CMOPs. Then, the 14 benchmarks, including LIR-CMOP1-14, are used to test MOEA/D-IEpsilon and four other decomposition-based CMOEAs, including MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP and CMOEA/D. The experimental results indicate that MOEA/D-IEpsilon is significantly better than the other four CMOEAs on all of the test instances, which shows that MOEA/D-IEpsilon is more suitable for solving CMOPs with large infeasible regions. Furthermore, a real-world problem, namely the robot gripper optimization problem, is used to test the five CMOEAs. The experimental results demonstrate that MOEA/D-IEpsilon also outperforms the other four CMOEAs on this problem. [ABSTRACT FROM AUTHOR]

In this paper, an improved ϵCMOEA/D-DE is proposed to improve the performance of CMOP algorithm and achieve parameter optimization in carbon fibre drawing process. In order to avoid overusing the infeasible solutions, two repair operators are introduced in the population evolution model. More specially, during the evolutionary process, when the constraint violation of infeasible solution exceeds a tolerance threshold, the proposed two repair operators are used to find a better solution to repair the infeasible solution. On the other hand, in order to enhance the convergence rate of the Differential Evolution (DE), a modified DE is proposed. Then, an ϵCMOEA/D-mDE-RO is proposed by incorporating these two improved strategies into the ϵCMOEA/D-DE. Subsequently, the performance of the proposed ϵCMOEA/D-mDE-RO is evaluated on the constrained test problem series and the experiment shows that the proposed algorithm outperforms the existing ϵCMOEA/D-DE. Finally, in order to further illustrate the application potential, the proposed algorithm is successfully applied in optimizing carbon fibre drawing process and the optimal draw ratio vector is obtained. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problem (CMOP) considers the convergence, diversity and feasibility of the population in the optimization process, so it is challenging to find desirable solutions of CMOP. Existing evolutionary multi-objective optimization algorithms have good performance on unconstrained multi-objective optimization problems, but have difficulties in solving CMOPs in discrete feasible regions. Aiming at this issue, this paper proposes a novel multi-level population hybrid search evolution algorithm (MLHSEA). First, a new multi-level hybrid search strategy (i.e. MHSS) is designed in the algorithm, which divides the population into three-level subpopulations based on Pareto ranks, constraint violation degree values, and feasible thresholds. Each subpopulation has its own unique evolution strategy to maximize the evolutionary potential of each subpopulation, which is beneficial to make some feasible solutions break through the discrete feasible region and reach the Pareto frontier. Then, a new population fusion degree strategy (i.e. PFDS) is proposed to timely perform population fusion and information exchange according to the population fusion degree (PFD) of each sub-population, thus improving the searchability of the target space. Finally, a novel detection reset strategy (i.e. DRS) is proposed for the lowest inferior subpopulation. This strategy can make inferior subpopulations avoid unnecessary evolutionary iterations and improve population diversity. Based on constrained test suites with four different characteristics, the experimental results show that the proposed MLHSEA outperforms other state-of-the-art constrained multi-objective optimization algorithms in performance. [ABSTRACT FROM AUTHOR]

• A dynamic task mechanism is designed to improve the generality of the algorithm. • The main task processes constraints with higher constraint priority in turn. • Auxiliary task P 2 stops the evolution adaptively after converging to UPF. • The entire solution process is divided into exploration and exploitation stages. Compared with common multi-objective optimization problems, constrained multi-objective optimization problems demand additional consideration of the treatment of constraints. Recently, many constrained multi-objective evolutionary algorithms have been presented to reconcile the relationship between constraint satisfaction and objective optimization. Notably, evolutionary multi-task mechanisms have also been exploited in solving constrained multi-objective problems frequently with remarkable outcomes. However, previous methods are not fully applicable to solving problems possessing all types of constraint landscapes and are only superior for a certain type of problem. Thus, in this paper, a novel dynamic-multi-task-assisted constrained multi-objective optimization algorithm, termed DTCMO, is proposed, and three dynamic tasks are involved. The main task approaches the constrained Pareto front by adding new constraints dynamically. Two auxiliary tasks are devoted to exploring the unconstrained Pareto front and the constrained Pareto front with dynamically changing constraint boundaries, respectively. In addition, the first auxiliary task stops the evolution automatically after reaching the unconstrained Pareto front, avoiding the waste of subsequent computational resources. A series of experiments are conducted with eight mainstream algorithms on five benchmark problems, and the results confirm the generality and superiority of DTCMO. [ABSTRACT FROM AUTHOR]

Using infeasible information to balance objective optimization and constraint satisfaction is a very promising research direction to address constrained multi-objective problems (CMOPs) via evolutionary algorithms (EAs). The existing constrained multi-objective evolutionary algorithms (CMOEAs) still face the issue of striking a good balance when solving CMOPs with diverse characteristics. To alleviate this issue, in this paper we develop a two-stage different evolution with a dynamic population assignment strategy for CMOPs. In this approach, two cooperative populations are used to provide feasible driving forces and infeasible guiding knowledge. To adequately utilize the infeasibility information, a dynamic population assignment model is employed to determine the primary population, which is used as the parents to generate offspring. The entire search process is divided into two stages, in which the two populations work in weak and strong cooperative ways, respectively. Furthermore, multistrategy-based differential evolution operators are adopted to create aggressive offspring. The superior exploration and exploitation ability of the proposed algorithm is validated via some state-of-the-art CMOEAs over artificial benchmarks and real-world problems. The experimental results show that our proposed algorithm gained a better, or more competitive, performance than the other competitors, and it is an effective approach to balancing objective optimization and constraint satisfaction. [ABSTRACT FROM AUTHOR]

During the past two decades, evolutionary algorithms have seen great achievements in solving complex optimization problems owing to the advantages brought by their properties, especially constrained multi-objective optimization problems (CMOPs) with multiple conflicting objective functions and constraints which widely exist in industry, scientific research, and daily life. Among the real-world CMOPs, mechanical design problems (MDPs) from the industry widely exist and are important, while unfortunately, most constrained multi-objective evolutionary algorithms (CMOEAs), developed based on benchmark CMOPs, neglect the specific features and challenges of MDPs and thus cannot solve them well to provide the practitioners promising Pareto optimal solutions for decision making. To overcome this limitation, this paper analyzes the features and challenges of MDPs, including badly scaled objective space, decision space properties, and decision variable linkages. Then, we propose a new CMOEA named CMORWMDP. First, instead of the homogeneous operator in existing CMOEAs, a heterogeneous operator strategy is adopted to use the operator of Genetic Algorithm to enhance the convergence and the operator of Differential Evolution to tackle variable linkages. In addition, an improved fitness function that considers normalization is designed for environmental and mating selections. The proposed algorithm is simple, parameter-free, and easy to implement. Experiments on 21 real-world MDPs show its superiority compared to 20 state-of-the-art CMOEAs under the Friedman test and Wilcoxon test on different metrics, demonstrating the effectiveness of the heterogeneous operator and normalization-based fitness for selections for real-world MDPs. Moreover, the effectiveness of the proposed algorithm in solving other real-world CMOPs is also verified, revealing that our methods are very promising in tackling real-world problems. • Challenges of real-world constrained multi-objective mechanical design problems. • Heterogeneous operator strategy to tackle the challenges. • Improved fitness function with normalization. • A parameter-free constrained multi-objective optimization evolutionary algorithm. [ABSTRACT FROM AUTHOR]

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. [Display omitted] • RITEA, a two-stage constrained evolutionary algorithm for CMOPs. • Identify and utilize the relationship between UPF and CPF to balance optimization and constraint satisfaction. • Utilizes collaborative training stage and reinforcement stage to guide population search accurately. • Introduction of a dynamic preference fitness function to adaptively balance the search preferences between convergence and diversity. [ABSTRACT FROM AUTHOR]

When dealing with Constrained Multi-objective Optimization Problems (CMOPs) and struggling to enhance feasibility, convergence and diversity, the researchers of Constrained Multi-objective Optimization Evolutionary Algorithms (CMOEAs) gravitate toward feasibility or take precedence to preserve well-converged solutions ignoring diversity in the past. To compensate for the defects, the paper proposes CMOEA-MSWA to guide the search of infeasible regions by coordinated strategy of archive and weight vectors. Firstly, the archive carrying the information of population diversity updates the weight vectors. Secondly, the updated weight vectors perpetuate the diversity information to the search of infeasible regions. The circular effects between strategies promote the detection of infeasible solutions with good objectives and exhibit competitive performance in terms of spread and evenness. To testify the versatility the CMOEA-MSWA in enhancing diversity, the comprehensive performance is evaluated firstly and the diversity analysis of the CMOEA-MSWA is carried out on four benchmark suites with 34 test instances, where the number of objectives for some of test problems is scaled from three to five. In comparison with five state-of-the-art CMOEAs, the proposed algorithm yields highly competitive performance in diversity on different types of CMOPs. In addition, the effectiveness of collaboration between archive and weight vectors on handling infeasible solutions is also verified. [ABSTRACT FROM AUTHOR]

When solving constrained multi-objective optimization problems (CMOPs), keeping infeasible individuals with good objective values and small constraint violations in the population can improve the performance of the algorithms, since they provide the information about the optimal direction towards Pareto front. By taking the constraint violation as an objective, we propose a novel constraint-handling technique based on directed weights to deal with CMOPs. This paper adopts two types of weights, i.e. feasible and infeasible weights distributing on feasible and infeasible regions respectively, to guide the search to the promising region. To utilize the useful information contained in infeasible individuals, this paper uses infeasible weights to maintain a number of well-diversified infeasible individuals. Meanwhile, they are dynamically changed along with the evolution to prefer infeasible individuals with better objective values and smaller constraint violations. Furthermore, 18 test instances and 2 engineering design problems are used to evaluate the effectiveness of the proposed algorithm. Several numerical experiments indicate that the proposed algorithm outperforms four compared algorithms in terms of finding a set of well-distributed non-domination solutions. [ABSTRACT FROM AUTHOR]

The helium cryo-plant is an indispensable subsystem for the application of low temperature superconductors in large-scale scientific facilities. However, it is important to note that the cryo-plant requires stable operation and consumes a substantial amount of electrical power for its operation. Additionally, the construction of the cryo-plant incurs significant economic costs. To achieve the necessary cooling capacity while reducing power consumption and ensuring stability and economic feasibility, constrained multi-objective optimization is performed using the interior point method in this work. The Collins cycle, which uses liquid nitrogen precooling, is selected as the representative helium liquefaction cycle for optimization. The discharge pressure of the compressor, flow ratio of turbines, and effectiveness of heat exchangers are taken as decision parameters. Two objective parameters, cycle exergy efficiency, ηex,cycle, and liquefaction rate, ṁL, are chosen, and the wheel tip speed of turbines and UA of heat exchangers are selected as stability and economic cost constraints, respectively. The technique for order of preference by similarity to the ideal solution (TOPSIS) is utilized to select the final optimal solution from the Pareto frontier of constrained multi-objective optimization. Compared to the constrained optimization of ηex,cycle, the TOPSIS result increases the ṁL by 23.674%, but there is an 8.162% reduction in ηex,cycle. Similarly, compared to the constrained optimization of ṁL, the TOPSIS result increases the ηex,cycle by 57.333%, but a 10.821% reduction in ṁL is observed. This approach enables the design of helium cryo-plants with considerations for cooling capacity, exergy efficiency, economic cost, and stability. Furthermore, the wheel tip speed and UA of heat exchangers of the solutions in the Pareto frontier are also studied. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach to address the optimal design of a Feed-forward Neural Network (FNN) based classifier. The originality of the proposed methodology, called CMOA, lie in the use of a new constraint handling technique based on a self-adaptive penalty procedure in order to direct the entire search effort towards finding only Pareto optimal solutions that are acceptable. Neurons and connections of the FNN Classifier are dynamically built during the learning process. The approach includes differential evolution to create new individuals and then keeps only the non-dominated ones as the basis for the next generation. The designed FNN Classifier is applied to six binary classification benchmark problems, obtained from the UCI repository, and results indicated the advantages of the proposed approach over other existing multi-objective evolutionary neural networks classifiers reported recently in the literature. [ABSTRACT FROM AUTHOR]

This paper studied modeling and optimizing problems on first batch of emergency materials scheduling when large-scale disaster occurs. After extending loss evaluation function of affected point from linear to nonlinear, it constructed multi to multi constrained scheduling models with multiple objectives on disposable and consumable supplies. Then this paper applied artificial bee colony aigtrithm to solve this model based on Pareto dominance and crowding distance, and improved the algorithm by following policies; on the defmition of backward food source, proposed foods initialization with backward learning to improve the quality of initial solutions; adder! back wan! learning and comprehensive learning into bee search procedure to affect searching direction by the information of backward and other better food source. Experiment results on randomly generated data of three scales scheduling problems show that non dominated front solutions set solver! by the improver! algorithm is more diverse, more extensive anti more uniform, so it can be user! to support for emergency scheduling decision on first batch of emergency supplies. [ABSTRACT FROM AUTHOR]

In order to solve the dynamic emission economic dispatch (DEED) problem with high-dimensional and large scale constraints, this paper proposed an adaptive multiobjective differential evolutionary algorithm (ADEA). The ADEA designed an adaptive differential crossover module, developed an improving current to best 1 crossover scheme to enhance the diversity of population. These strategies improved the exploration and exploitation ability of the ADEA, it also applied a repair strategy to deal with the equality and inequality constrains in DEED problem. Numerical experiments tested the effectiveness of ADEA on 10-unit system, and compared with several peer algorithms. Simulation results indicate that ADEA has good convergence. The uniformity and ductility of the Pareto front obtained by ADEA is better than that of the compared algorithms. It provides a more efficient scheduling decision-making method for power system dispatcher by a fuzzy decision method. [ABSTRACT FROM AUTHOR]

How to balance the satisfaction of constraints and the optimization of objective functions is one of the key issues to solve constrained multi-objective optimization problems (CMOPs), especially when the constraints are complex. Although many algorithms have been designed to handle this, most of them are still unable to effectively handle CMOPs with complex constraints. Based on the above issue, this paper proposes a framework for bi-directional search, which evolves two populations (P 1 and P 2). P 1 aims to search the constrained Pareto front (CPF) from the infeasible side of the objective space, and P 2 from the feasible side, aiming to achieve a more efficient and comprehensive bi-directional search for the CPF. To ensure the diversity, we adopt a preferred weight vector selection strategy to choose potential mating parents, which improves the search capability for the marginal CPF. Furthermore, to coordinate the interaction between the two populations, we propose an environmental selection strategy to select the offspring generated by P 1 and P 2 under the same weight vector with the better fitness to update the populations respectively, and the fitness is evaluated based on the different constraint relaxations of the two populations, to update them respectively. Extensive experiments indicate that our proposed algorithm has significantly better results or was at least competitive when compared to eight state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The main challenge in addressing constrained multi-objective optimization problems (CMOPs) lies in achieving a balance among convergence, diversity, and feasibility. To address this issue, this paper proposes a constrained multi-objective evolutionary algorithm with Pareto estimation via neural network named CMOEA-PeNN. In order to exploit and explore the decision space, the proposed algorithm employs a dual-population mechanism, which is trained with a self-organizing map (SOM). Firstly, the population distribution structure in decision space is mapped to objective space while preserving neighborhood information, and then the neuron weight is utilized to estimate the Pareto front (PF). Secondly, a novel approach is devised to preserve the feasibility of the population and enhance the estimation of the Pareto front by SOM. The achievement scalarizing function (ASF) is employed to choose promising solutions. This strategy could guide the population toward the optimal solution while exploring the small feasible regions. Finally, the performance of CMOEA-PeNN is compared with five state-of-the-art constrained multi-objective evolutionary algorithms (CMOEAs) on three widely used benchmark problems and a real-world problem. The experimental results show that CMOEA-PeNN could archive competitive performance in solving CMOPs. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) are commonly encountered in engineering practice. The key to effectively solving these problems lies in achieving a timely balance between convergence, diversity, and feasibility during iterations. Furthermore, the appropriate utilization of infeasible solutions is crucial for identifying potential feasible regions. In order to accomplish this comprehensive objective, we propose a novel dual-stage constrained multi-objective evolutionary algorithm (CMOEA) called NACMOEA in this paper. It can be characterized by the following features: 1) Introducing a novel niche-based individual selection and infeasible solution utilization strategy to enhance convergence, diversity, and feasibility. 2) Presenting a cooperative search strategy assisted by dual archives to approximate the constrained Pareto front (CPF) from both feasible and infeasible perspectives, thereby improving the efficiency of obtaining the complete CPF. 3) Designing a new stage switch method based on non-dominant coverage rate to ensure proper completion of search stage switching. Extensive experiments demonstrate that NACMOEA exhibits competitive comprehensive performance when compared with other advanced CMOEAs. • The search process of the proposed NACMOEA is divided into two stages, where a new dual archive collaboration strategy is developed iteratively. • A niche-based environmental selection and an infeasible individual utilization strategy are designed to better balance the performance. • A novel non-dominant coverage rate metric is developed to facilitate appropriate switching in the search stage. • The proposed NACMOEA performs well compared to other advanced algorithms on various complex CMOP test problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a decomposition-based evolutionary algorithm with boundary search and archive for constrained multi-objective optimization problems (CMOPs), named CM2M. It decomposes a CMOP into a number of optimization subproblems and optimizes them simultaneously. Moreover, a novel constraint handling scheme based on the boundary search and archive is proposed. Each subproblem has one archive, including a subpopulation and a temporary register. Those individuals with better objective values and lower constraint violations are recorded in the subpopulation, while the temporary register consists of those individuals ever found before. To improve the efficiency of the algorithm, the boundary search method is designed. This method makes the feasible individuals with a higher probability to perform genetic operator with the infeasible individuals. Especially, when the constraints are active at the Pareto solutions, it can play its leading role. Compared with two algorithms, i.e. CMOEA/D-DE-CDP and Gary's algorithm, on 18 CMOPs, the results show the effectiveness of the proposed constraint handling scheme. [ABSTRACT FROM AUTHOR]

The performance of evolutionary algorithms can be seriously weakened when constraints limit the feasible region of the search space. In this paper we present a constrained multi-objective optimization algorithm based on adaptive ε-truncation (ε-T-CMOA) to further improve distribution and convergence of the obtained solutions. First of all, as a novel constraint handling technique ε-truncation technique keeps an effective balance between feasible solutions and infeasible solutions by permitting some excellent infeasible solutions with good objective value and low constraint violation to take part in the evolution, so diversity is improved, and convergence is also coordinated. Next, an exponential variation is introduced after differential mutation and crossover to boost the local exploitation ability. At last, the improved crowding density method only selects some Pareto solutions and near solutions to join in calculation, thus it can evaluate the distribution more accurately. The comparative results with other state-of-the-art algorithms show that ε-T-CMOA is more diverse than the other algorithms and it gains better in terms of convergence in some extent. [ABSTRACT FROM AUTHOR]

When tackling constrained multi-objective optimization problem, evolutionary algorithms grapple with the simultaneous need to optimize the conflict objectives and satisfy constraints. The preference for the algorithm in processing objectives and constraints directly affects the feasibility, diversity and convergence of population. At the same time, the decision regarding algorithmic preference should be based on the characteristics of the current evolution. Therefore, preference decision of algorithm is a intractable challenge throughout the optimization. To address this issue, a multi-preference-based constrained multi-objective optimization algorithm is proposed in this paper, operating under the aegis of three evolutionary models. The preferences are determined by the analysis of the evolution states in concert with the actual characteristic of the population, and are implemented through the reasonable scheduling evolutionary models. When the preference changes, the algorithm identifies the useful knowledges carried by the previous populations and transfers them to the current populations. In addition, a shift-based update strategy and a new co-evolution strategy are designed for different models in the proposed algorithm, respectively. Compared to five state-of-the-art multi-objective algorithms on two benchmark suits and two real-world applications, the proposed algorithm performs better than its peers, especially in diversity difficulty and convergence difficulty multi-objective optimization problems. [ABSTRACT FROM AUTHOR]

When solving constrained multi-objective optimization problems, the balance of convergence, diversity, and feasibility plays a pivotal role. To address this issue, this paper proposes a coevolutionary constrained multi-objective algorithm with learning constraint boundary (CCMOLCB). Firstly, the constrained multi-objective problems are transformed by adding an additional objective using the constraint violation degree. Then, the transformed problem is solved by an improved coevolutionary framework which employs two populations. The main population explores the objective space and repairs infeasible solutions to maintain the feasibility of population. Meanwhile, the feasibility and diversity of solutions are balanced by using a dynamic weight coefficient during the evolution, it changes as the number of iterations increases. The subordinate population selects solutions by taking into consideration the learning constraint boundary (LCB). This boundary guarantees convergence of solutions by constraining the search range of the main population, thereby enhancing the environmental selection pressure. The performance of CCMOLCB is compared with seven state-of-the-art constrained multi-objective evolutionary algorithms on five test suites. The experimental results illustrate that CCMOLCB exhibits competitive performance when dealing with this family of problems. • A restrictive relationship is embedded into coevolutionary framework by using the proposed learning constraint boundary. • The learning constraint boundary updates adaptively by absorbing the valuable information from population. • The self-adapting ability of the coevolutionary framework is improved by the learning mechanism. • The comparison of CCMO-LCB with state-of-the-art algorithms is presented. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) are commonly encountered in engineering practice. The key to effectively solving these problems lies in achieving a timely balance between convergence, diversity, and feasibility during iterations. Furthermore, the appropriate utilization of infeasible solutions is crucial for identifying potential feasible regions. In order to accomplish this comprehensive objective, we propose a novel dual-stage constrained multi-objective evolutionary algorithm (CMOEA) called NACMOEA in this paper. It can be characterized by the following features: 1) Introducing a novel niche-based individual selection and infeasible solution utilization strategy to enhance convergence, diversity, and feasibility. 2) Presenting a cooperative search strategy assisted by dual archives to approximate the constrained Pareto front (CPF) from both feasible and infeasible perspectives, thereby improving the efficiency of obtaining the complete CPF. 3) Designing a new stage switch method based on non-dominant coverage rate to ensure proper completion of search stage switching. Extensive experiments demonstrate that NACMOEA exhibits competitive comprehensive performance when compared with other advanced CMOEAs.

Most current evolutionary multi-objective optimization (EMO) algorithms perform well on multi-objective optimization problems without constraints, but they encounter difficulties in their ability for constrained multi-objective optimization problems (CMOPs) with low feasible ratio. To tackle this problem, this paper proposes a multi-objective differential evolutionary algorithm named MODE-SaE based on an improved epsilon constraint-handling method. Firstly, MODE-SaE self-adaptively adjusts the epsilon level in line with the maximum and minimum constraint violation values of infeasible individuals. It can prevent epsilon level setting from being unreasonable. Then, the feasible solutions are saved to the external archive and take part in the population evolution by a co-evolution strategy. Finally, MODE-SaE switches the global search and local search by self-switching parameters of search engine to balance the convergence and distribution. With the aim of evaluating the performance of MODE-SaE, a real-world problem with low feasible ratio in decision space and fourteen bench-mark test problems, are used to test MODE-SaE and five other state-of-the-art constrained multi-objective evolution algorithms. The experimental results fully demonstrate the superiority of MODE-SaE on all mentioned test problems, which indicates the effectiveness of the proposed algorithm for CMOPs which have low feasible ratio in search space. • To solve constrained multi-objective optimization problems with low feasible ratio. • An algorithm based on an improved epsilon constraint-handling method is proposed. • A co-evolution strategy of the external archive is used to save feasible solutions. • Our algorithm self-switches parameters of DE to balance convergence and distribution. • Our algorithm provides an effective tool to solve the above problems. [ABSTRACT FROM AUTHOR]

In the real-world, symmetry or asymmetry widely exists in various problems. Some of them can be formulated as constrained multi-objective optimization problems (CMOPs). During the past few years, handling CMOPs by evolutionary algorithms has become more popular. Lots of constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been proposed. Whereas different CMOEAs may be more suitable for different CMOPs, it is difficult to choose the best one for a CMOP at hand. In this paper, we propose an ensemble framework of CMOEAs that aims to achieve better versatility on handling diverse CMOPs. In the proposed framework, the hypervolume indicator is used to evaluate the performance of CMOEAs, and a decreasing mechanism is devised to delete the poorly performed CMOEAs and to gradually determine the most suitable CMOEA. A new CMOEA, namely ECMOEA, is developed based on the framework and three state-of-the-art CMOEAs. Experimental results on five benchmarks with totally 52 instances demonstrate the effectiveness of our approach. In addition, the superiority of ECMOEA is verified through comparisons to seven state-of-the-art CMOEAs. Moreover, the effectiveness of ECMOEA on the real-world problems is also evaluated for eight instances. [ABSTRACT FROM AUTHOR]