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Model predictive control (MPC) algorithm which can predict future states and generate accurate control sequences is adopted to control multiple measurement points collaboratively in a temperature system. To carry out the multiobjective optimization problem (MOP) according to MPC, multiobjective evolutionary algorithms based on decomposition (MOEA/D) and its improved version have been employed. The improved MOEA/D algorithm was compared with its original version through simulation, and the practical effectiveness is verified by tests on a self-made dual-point temperature control system. Finally, the improved MOEA/D algorithm was embedded into the control system of the experimental device, and temperature-tracking control experiments were conducted. The results show that the algorithm applied here can simultaneously control the temperature of two points and keep them close to the target temperature curve. It helps optimize the multiobjective control by virtue of MPC, and particularly opens up new possibilities to achieve optimal temperature control in different engineering applications. [ABSTRACT FROM AUTHOR]

This paper proposes a multi‐objective evolutionary algorithm based on bilayered decomposition (MOEA/BLD) for solving constrained multi‐objective optimization problems. MOEA/D is an effective method for solving unconstrained multi‐objective optimization problems. It decomposes the objective space using weight vectors and simultaneously searches for solutions for the subproblems. However, real‐world applications impose many constraints, and these constraints must be handled appropriately when searching for good feasible solutions. The proposed MOEA/BLD treats such constraints as an additional objective function. Furthermore, in addition to the conventional weight vector, an augmented weight vector is introduced that decomposes the objective space and constraint violation space hierarchically. In the first stage, the objective space is decomposed by conventional weight vectors. In the next stage, the bi‐objective space consisting of the scalarizing function and constraint violation is decomposed by augmented weight vectors. The augmented weights are adjusted so that they decrease linearly in the search process as the search gradually moves from infeasible regions to feasible regions. The proposed algorithm is compared to several state‐of‐the‐art constrained MOEA/Ds using multi‐ and many‐objective problems. The results show that the proposed method outperforms existing methods, in terms of search performance, under various conditions. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

The decomposition-based multi-objective optimization algorithm MOEA/D (multi-objective evolutionary algorithm based on decomposition) introduces the concept of neighborhood, where each sub-problem requires optimization through solutions within its neighborhood. Due to the comparison being only with solutions in the neighborhood, the obtained set of solutions is not sufficiently diverse, leading to poorer convergence properties. In order to adequately acquire a high-quality set of solutions, this algorithm requires a large number of population iterations, which in turn results in relatively low computational efficiency. To address this issue, this paper proposes an algorithm termed MOEA/D-NRD, which is based on neighborhood region domination in the MOEA/D framework. In the improved algorithm, domination relationships are determined by comparing offspring solutions against neighborhood ideal points and neighborhood worst points. By selecting appropriate solution sets within these comparison regions, the solution sets can approach the ideal points more and faster, thereby accelerating population convergence and enhancing the computational efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

Local search (LS) algorithms are efficient metaheuristics to solve combinatorial problems. The performance of LS highly depends on the neighborhood exploration of solutions. Many methods have been developed over the years to improve the efficiency of LS on different problems of operations research. In particular, the exploration strategy of the neighborhood and the exclusion of irrelevant neighboring solutions are design mechanisms that have to be carefully considered when tackling NP‐hard optimization problems. An MOEA/D framework including an LS‐based mutation and knowledge discovery mechanisms is the core algorithm used to solve a bi‐objective vehicle routing problem with time windows (bVRPTW) where the total traveling cost and the total waiting time of drivers have to be minimized. We enhance the classical LS exploration strategy of the neighborhood from the literature of scheduling and propose new metrics based on customer distances and waiting times to reduce the neighborhood size. We conduct a deep analysis of the parameters to give a fine tuning of the MOEA/D framework adapted to the LS variants and to the bVRPTW. Experiments show that the proposed neighborhood strategies lead to better performance on both Solomon's and Gehring and Homberger's benchmarks. [ABSTRACT FROM AUTHOR]

With the improvement of people's living standards, the issue of dietary health has received extensive attention. In order to simultaneously meet people's demands for dietary preferences and nutritional balance, we have conducted research on the issue of personalized food recommendations. For this purpose, we have proposed a hybrid food recommendation model, which can provide users with scientific, reasonable, and personalized dietary advice. Firstly, the collaborative filtering (CF) algorithm is adopted to recommend foods to users; then, the improved Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is used to adjust the nutritional balance and symmetry of the recommended foods. In view of the existing problems in the current nutritional balance algorithm, such as slow convergence speed and insufficient local search ability, the autonomous optimization (AO) adjustment strategy, the self-adaptive adjustment strategy, and the two-sided mirror principle to optimize boundary strategy are introduced in the MOEA/D. According to the characteristics of the food nutrition regulation problem, an adaptive food regulation (AFR) adjustment strategy is designed to achieve more accurate nutritional regulation. Based on the above improvements, a food nutritional recommendation algorithm based on MOEA/D (FNR-MOEA/D) is proposed. Experiments show that compared with MOPSO, MOABC, and RVEA, FNR-MOEA/D performs more superiorly in solving the problem of nutritional balance in food recommendation. [ABSTRACT FROM AUTHOR]

This article proposes two novel mechanisms to improve the performance of many-objective evolutionary algorithms based on Chebyshev scalarization. One mechanism improves the efficiency and effectiveness of the adaptation of the descent directions in criteria space, while the other ensures that extreme solutions are preserved. Weight adaptation via WS-transformation has shown promising results, but its performance is dependent on the choice of the start of the adaptation process. In order to overcome this limitation, in this article an efficient entropy-based trigger is proposed with fast calculation of the entropy that scales favourably with the number of dimensions. The novel entropy-based method is complemented by a dual-archiving mechanism that preserves extreme solutions. The dual-archiving strategy mitigates the possibility to discard those critical individuals whose loss affects the whole evolutionary process. The new algorithm proposed in this article (called aMOEA/D-2A-ET) is compared against a set of state-of-the-art MOEAs and shown to have competitive performance. [ABSTRACT FROM AUTHOR]

Purposes Aiming at the performance conflict between optimization parameters in prior optimization method, a hybrid optimization model based on MOEA/D is proposed, which integrates CNN and genetic algorithm into MOEA/D framework to balance the correlation and complexity between various objective functions. Methods First, the deep learning method is used as a supplement to the conventional fluid mechanics analysis method to establish a highly reliable CNN response prediction model for airfoil aerodynamic characteristics, which can be used to quickly evaluate the aerodynamic parameters of airfoil. Then, the response model and genetic operator are interpolated into the MOEA/D framework to construct a multi-objective hybrid optimization model based on MOEA/D. And the lift drag ratio and moment coefficient of a NACA high lift airfoil under cruise condition are taken as the optimization objectives for testing. Finally, through the analysis of aerodynamic performance and flow field structure of the airfoil on the Pareto front, the distribution law of different airfoil configurations on the front is studied, which further guides the designer to explore the potential basic airfoil in the airfoil selection.

Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing these subproblems in a collaborative manner. However, most existing MOEA/Ds maintain population diversity by limiting the replacement region or scale, which come at the cost of decreasing convergence. To better balance convergence and diversity, we introduce auction theory into algorithm design and propose an auction-based matching (ABM) mechanism to coordinate the replacement procedure in MOEA/D. In the ABM mechanism, each subproblem can be associated with its preferred individual in a competitive manner by simulating the auction process in economic activities. The integration of ABM into MOEA/D forms the proposed MOEA/D-ABM. Furthermore, to make the appropriate distribution of weight vectors, a modified adjustment strategy is utilized to adaptively adjust the weight vectors during the evolution process, where the trigger timing is determined by the convergence activity of the population. Finally, MOEA/D-ABM is compared with six state-of-the-art multi-objective evolutionary algorithms (MOEAs) on some benchmark problems with two to ten objectives. The experimental results show the competitiveness of MOEA/D-ABM in the performance of diversity and convergence. They also demonstrate that the use of the ABM mechanism can greatly improve the convergence rate of the algorithm. [ABSTRACT FROM AUTHOR]

The study of the flexible job shop scheduling problem (FJSP) is of great importance in the context of green manufacturing. In this paper, with the optimization objectives of minimizing the maximum completion time and the total machine energy consumption, an improved multi-objective evolutionary algorithm with decomposition (MOEA/D) based on reinforcement learning is proposed. Firstly, three initialization strategies are used to generate the initial population in a certain ratio, and four variable neighborhood search strategies are combined to increase the local search capability of the algorithm. Second, a parameter adaptation strategy based on Q-learning is proposed to guide the population to select the optimal parameters to increase diversity. Finally, the performance of the proposed algorithm is analyzed and evaluated by comparing Q-MOEA/D with IMOEA/D and NSGA-II through different sizes of Kacem and BRdata benchmark cases and production examples of automotive engine cooling system manufacturing. The results show that the Q-MOEA/D algorithm outperforms the other two algorithms in solving the energy-efficient scheduling problem for flexible job shops. [ABSTRACT FROM AUTHOR]

In the future intelligent transportation system (ITSs), there will be a lot of negotiation work between vehicle and vehicle (V2V) and between vehicle and infrastructure (V2I), so it is very necessary to design efficient and energy-saving offloading strategy. Aiming at the three conflicting optimization objectives of offloading delay, energy consumption and load balancing, an efficient and energy-saving offloading decision scheme in the scenario of Internet of vehicles was proposed in this paper. Firstly, the task segmentation model, offloading delay model, energy consumption model, load balancing model and multi-objective optimization model were constructed. Then, based on the comprehensive consideration of data offloading delay, energy consumption and load balance, a task offloading scheme based on MOEA/D was proposed. Finally, the proposed scheme was compared with NSGA-II-based scheme, NSGA-III-based scheme,PESA-II-based scheme and SPEA-II-based scheme. The simulation results show that a task offloading scheme based on MOEA/D is obviously superior to the above schemes in terms of offloading delay, energy consumption and load balancing, and can provide efficient and energy-saving offloading service. [ABSTRACT FROM AUTHOR]

Flux Balance Analysis (FBA) is a constraint-based method that is commonly used to guide metabolites through restricting pathways that often involve conditions such as anaplerotic cycles like Calvin, reversible or irreversible reactions, and nodes where metabolic pathways branch. The method can identify the best conditions for one course but fails when dealing with the pathways of multiple metabolites of interest. Recent studies on metabolism consider it more natural to optimize several metabolites simultaneously rather than just one; moreover, they point out the use of metaheuristics as an attractive alternative that extends FBA to tackle multiple objectives. However, the literature also warns that the use of such techniques must not be wild. Instead, it must be subject to careful fine-tuning and selection processes to achieve the desired results. This work analyses the impact on the quality of the pathways built using the NSGAII and MOEA/D algorithms and several novel optimization models; it conducts a study on two case studies, the pigment biosynthesis and the node in glutamate metabolism of the microalgae Chlorella vulgaris, under three culture conditions (autotrophic, heterotrophic, and mixotrophic) while optimizing for three metabolic intermediaries as independent objective functions simultaneously. The results show varying performances between NSGAII and MOEA/D, demonstrating that the selection of an optimization model can greatly affect predicted phenotypes. [ABSTRACT FROM AUTHOR]

The flying foxes optimization (FFO) algorithm stimulated by the strategy used by flying foxes for subsistence in heat wave environments has shown good performance in the single-objective domain. Aiming to explore the effectiveness and benefits of the subsistence strategy used by flying foxes in solving optimization challenges involving multiple objectives, this research proposes a decomposition-based multi-objective flying foxes optimization algorithm (MOEA/D-FFO). It exhibits a great population management strategy, which mainly includes the following features. (1) In order to improve the exploration effectiveness of the flying fox population, a new offspring generation mechanism is introduced to improve the efficiency of exploration of peripheral space by flying fox populations. (2) A new population updating approach is proposed to adjust the neighbor matrices to the corresponding flying fox individuals using the new offspring, with the aim of enhancing the rate of convergence in the population. Through comparison experiments with classical algorithms (MOEA/D, NSGA-II, IBEA) and cutting-edge algorithms (MOEA/D-DYTS, MOEA/D-UR), MOEA/D-FFO achieves more than 11 best results. In addition, the experimental results under different population sizes show that the proposed algorithm is highly adaptable and has good application prospects in optimization problems for engineering applications. [ABSTRACT FROM AUTHOR]

The penalty-based boundary cross-aggregation (PBI) method is a common decomposition method of the MOEA/D algorithm, but the strategy of using a fixed penalty parameter in the boundary cross-aggregation function affects the convergence of the populations to a certain extent and is not conducive to the maintenance of the diversity of boundary solutions. To address the above problems, this paper proposes a penalty boundary crossing strategy (DPA) for MOEA/D to adaptively adjust the penalty parameter. The strategy adjusts the penalty parameter values according to the state of uniform distribution of solutions around the weight vectors in the current iteration period, thus helping the optimization process to balance convergence and diversity. In the experimental part, we tested the MOEA/D-DPA algorithm with several MOEA/D improved algorithms on the classical test set. The results show that the MOEA/D with the DPA has better performance than the MOEA/D with the other decomposition strategies. [ABSTRACT FROM AUTHOR]

Infrastructures can be modeled as large‐scale networks consisting of nodes and arcs, making network optimization a popular modeling option for arising problems. In specific, providing timely restoration plans for interdependent infrastructures facing disruptions has been a challenge for decision makers. In this study, we focus on geospatial (co‐location) and functional interdependencies to capture the impact of cascading failures on infrastructure systems. The dynamics of real networks are more complicated to be captured by one objective function. Therefore, we define three objective functions in three pillars of sustainability: (a) economic, (b) social, and (c) environmental. To solve the multiobjective optimization model, we develop a learn‐to‐decompose framework, consisting of a multiobjective evolutionary algorithm based on decomposition module and a Gaussian process regression (GPR) module to periodically learn from the obtained Pareto front and guide the search direction. We also included a heuristic module to address two significant challenges in restoring interdependent infrastructures: the island scenario and co‐location interdependencies. We applied the proposed framework to benchmark problems and interdependent water and transportation networks in the City of Tampa, FL. We carried out sensitivity analyses to monitor the performance of the GPR by different kernel functions. We also provided insights for decision makers by finding the trade‐off between fortification (proactive) and restoration (reactive) costs. The result demonstrates the proposed framework is feasible and applicable for large‐scale networks. [ABSTRACT FROM AUTHOR]

Accurate wind speed forecasting can effectively improve the balance of wind power generation and reduce the consumption of power system. However, many previous studies have only carried out wind speed point prediction or interval prediction, which may lead to incomplete analysis of wind speed. In this article, A nonlinear fuzzy forecasting system is designed for wind speed forecasting, and it is composed of four modules: the self-adaption feature selecting module, the point forecasting module, the fuzzy interval forecasting module and the evaluation module. In the first module, the weights of Intrinsic Mode Functions (IMFs) are calculated by the multi-objective optimization algorithm to reconstruct time series data, which can enhance the stability of forecasting effectively. In the point forecasting module, the nonlinear combined model based on Bi-directional Long Short-Term Memory (Bi-LSTM) are used for reducing the forecasting error and assisting the formulation of power dispatching strategy. Meanwhile, the fuzzy interval forecasting can analyze the wind speed fluctuation and help to arrange the rotating reserve. The results show the nonlinear hybrid forecasting system can not only give accurate wind speed forecasting for wind power generation management by point forecasting, but also provide effective reference for the grid rotating reserve through interval forecasting. [ABSTRACT FROM AUTHOR]

Engineering optimization typically involves a large number of nonlinear constraints; therefore, effective constraint handling techniques (CHTs) are sought for metaheuristic optimization algorithms. Modified repair-based CHT is proposed here for a multi-objective evolutionary algorithm based on decomposition (MOEA/D). This CHT is: (1) adaptive to the share of infeasible solutions in a population; (2) free of problem-specific heuristics that users typically need to provide for repair; and (3) without control parameters. Infeasible solutions with superior decomposition function value are repaired using information contained in the neighbourhoods of the current population. The approach is tested on four multi-objective problems: a common mathematical optimization benchmark problem, two truss optimization problems and a real-world structural design of a tanker ship. A few prominent CHTs and metaheuristic algorithms are used for comparison. With the proposed CHT, MOEA/D shows improved convergence speed and spread of the Pareto front, providing competitive results in comparison to the other algorithms. [ABSTRACT FROM AUTHOR]

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into several scalar subproblems and then optimizes them cooperatively in their respective neighborhoods. Since the neighborhood size remains constant during the evolution process, striking a balance between diversity and convergence is a challenging for the conventional MOEA/D. In this study, a density estimation-based dynamical neighborhood (DEDN) strategy is proposed and integrated into MOEA/D to form MOEA/D-DEDN. In the MOEA/D-DEDN, an angle-based evolutionary state evaluation (AESE) scheme is first developed to evaluate the evolutionary state of the algorithm. Second, a distance-based density estimation (DDE) scheme is designed to calculate the population density for all the subproblems. Finally, the neighborhood size and penalty parameters of each subproblem are adjusted based on the AESE scheme and DDE schemes during the evolutionary process to overcome the disadvantages of computational resource waste and premature convergence. The performance of the proposed MOEA/D-DEDN is validated using the ZDT, DTLZ, and UF test suits in terms of IGD, HV, and Spacing metrics. The experimental results show that MOEA/D-DEDN has a significant improvement over the traditional MOEA/D and six state-of-the-art MOEA/D variants. Furthermore, to verify its effectiveness and usefulness, the proposed MOEA/D-DEDN is applied to address MOPs for three engineering applications: trajectory planning for parafoil UAVs, structural optimization for space trusses, and parameters optimization for wastewater treatment processes. [ABSTRACT FROM AUTHOR]

A cryptocurrency is a non-centralized form of money that facilitates financial transactions using cryptographic processes. It can be thought of as a virtual currency or a payment mechanism for sending and receiving money online. Cryptocurrencies have gained wide market acceptance and rapid development during the past few years. Due to the volatile nature of the crypto-market, cryptocurrency trading involves a high level of risk. In this paper, a new normalized decomposition-based, multi-objective particle swarm optimization (N-MOPSO/D) algorithm is presented for cryptocurrency algorithmic trading. The aim of this algorithm is to help traders find the best Litecoin trading strategies that improve their outcomes. The proposed algorithm is used to manage the trade-offs among three objectives: the return on investment, the Sortino ratio, and the number of trades. A hybrid weight assignment mechanism has also been proposed. It was compared against the trading rules with their standard parameters, MOPSO/D, using normalized weighted Tchebycheff scalarization, and MOEA/D. The proposed algorithm could outperform the counterpart algorithms for benchmark and real-world problems. Results showed that the proposed algorithm is very promising and stable under different market conditions. It could maintain the best returns and risk during both training and testing with a moderate number of trades. [ABSTRACT FROM AUTHOR]

A multi-objective evolutionary algorithm based on decomposition (MOEA/D) serves as a robust framework for addressing multi-objective optimization problems (MOPs). However, it is widely recognized that the applicability of a fixed offspring-generating strategy in MOEA/D can be limited, despite its foundation in the MOEA/D methodology. Consequently, hybrid algorithms have gained popularity in recent years. This study proposes a novel hyper-heuristic approach that integrates the estimation of distribution (ED) and crossover (CX) strategies into the MOEA/D framework based on the view of successful replacement rate (SSR) and attempts to explain the potential reasons for the advantages of hybrid algorithms. The proposed approach dynamically switches from the differential evolution (DE) operator to the covariance matrix adaptation evolution strategy (CMA-ES) operator. Simultaneously, certain subproblems in the neighbourhood denoted as B (i) employ the Improved Differential Evolution (IDE) operator to generate new individuals for balancing the high evaluation costs associated with CMA-ES. Numerical experiments unequivocally demonstrate that the suggested approach offers distinct advantages when applied to a three-objective test suite. These experiments also validate a significant enhancement in the efficiency (SRR) of the DE operator within this context. The perspectives and experimental findings, with a focus on the Success Rate Ratio (SRR), have the potential to provide valuable insights and inspire further research in related domains. [ABSTRACT FROM AUTHOR]

The importance of electric vehicle charging stations (EVCS) is increasing as electric vehicles (EV) become more widely used. EVCS with multiple low-carbon energy sources can promote sustainable energy development. This paper presents an optimization methodology for direct energy exchange between multi-geographic dispersed EVCSs in London, UK. The charging stations (CSs) incorporate solar panels, hydrogen, battery energy storage systems, and grids to support their operations. EVs are used to allow the energy exchange of charging stations. The objective function of the solar-hydrogen-battery storage electric vehicle charging station (SHS-EVCS) includes the minimization of both capital and operation and maintenance (O&M) costs, as well as the reduction in greenhouse gas emissions. The system constraints encompass the power output limits of individual components and the need to maintain a power balance between the SHS-EVCSs and the EV charging demand. To evaluate and compare the proposed SHS-EVCSs, two multi-objective optimization algorithms, namely the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), are employed. The findings indicate that NSGA-II outperforms MOEA/D in terms of achieving higher-quality solutions. During the optimization process, various factors are considered, including the sizing of solar panels and hydrogen storage tanks, the capacity of electric vehicle chargers, and the volume of energy exchanged between the two stations. The application of the optimized SHS-EVCSs results in substantial cost savings, thereby emphasizing the practical benefits of the proposed approach. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has achieved great success in the field of evolutionary multi-objective optimization. It decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems. Each sub-problem is optimized by using information from its neighboring sub-problems. Therefore, the neighborhood size of each sub-problem plays an important role in MOEA/D. Different neighborhood sizes are tested in this paper. Experimental results demonstrate that larger neighborhood size helps achieve better convergence and diversity with more CPU time and vice versa. MOEA/D uses constant neighborhood size during the whole process, and it is difficult to balance the convergence, diversity and running time. Therefore, this paper propose an algorithm based on MOEA/D. The algorithm adjusts the neighborhood size dynamically in different generations and different sub-problems to reduce the running time while the convergence and diversity of this algorithm are similar or better than other state-of-the-art algorithms. Compared to the original MOEA/D, experimental results show that adjusting the neighborhood size dynamically is a good way to reduce the running time significantly while maintaining the convergence and diversity. Furthermore, the algorithm proposed in this paper is compared with five state-of-the-art algorithms based on MOEA/D. The experimental results show that the proposed algorithm outperforms the others in efficiency while performs similarly in convergence and diversity.

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) is effective to solve most multi-objective optimization problems (MOPs) in the past 20 years. However, the algorithm MOEA/D with constant weight vectors has bad performance in solving several MOPs with discontinuous Pareto front (PF). This paper analyses the limitations of the constant weight vectors in MOEA/D and explains the necessity of adjusting the weight vectors in the processing. This paper proposes a weight vector adjustment method for MOEA/D (MOEA/D-WVA). It deletes the weight vectors which have bad search direction, and adds some new weight vectors in the processing. Experimental studies are conducted on several MOPs with discontinuous PF to compare the MOEA/D-WVA with other state-of-the-art multi-objective optimization algorithms in solving those MOPs with complex PF. The results show MOEA/D-WVA performs better than other algorithms on those MOPs with discontinuous PF.

The penalty-based boundary cross-aggregation (PBI) method is a common decomposition method of the MOEA/D algorithm, but the strategy of using a fixed penalty parameter in the boundary cross-aggregation function affects the convergence of the populations to a certain extent and is not conducive to the maintenance of the diversity of boundary solutions. To address the above problems, this paper proposes a penalty boundary crossing strategy (DPA) for MOEA/D to adaptively adjust the penalty parameter. The strategy adjusts the penalty parameter values according to the state of uniform distribution of solutions around the weight vectors in the current iteration period, thus helping the optimization process to balance convergence and diversity. In the experimental part, we tested the MOEA/D-DPA algorithm with several MOEA/D improved algorithms on the classical test set. The results show that the MOEA/D with the DPA has better performance than the MOEA/D with the other decomposition strategies.

Most genetic operators use random mating selection strategy and fixed rate crossover operator to solve various optimization problems. In order to improve the convergence and diversity of the algorithm, an adaptive adjacent maximum distance crossover operator is proposed in this paper. A new mating selection strategy (distance-based mating selection strategy) and an adaptive mechanism (adaptive crossover strategy based on population convergence) are adopted. Distance-based mating selection strategy purposefully selects parents to produce better offspring. Adaptive crossover strategy based on population convergence increases the convergence speed of the algorithm by controlling the crossover probability. The proposed crossover strategy is evaluated on the simulated binary crossover operators of non-dominated sorting genetic algorithm II and multi-objective evolutionary algorithm based on decomposition. The performance of the algorithm is verified on a series of standard test problems. Finally, the optimization results of the improved algorithm using adaptive adjacent maximum distance crossover operator and the standard algorithm are compared and analyzed. The experimental results show that the algorithm using adaptive adjacent maximum distance crossover operator has better optimization results. [ABSTRACT FROM AUTHOR]

Recently, SaaS applications are developed as a composition of microservices that serve diverse tenants having similar but different requirements, and hence, can be developed as variability-intensive microservices. Manual identification of these microservices is difficult, time-consuming, and costly, since, they have to satisfy a set of quality metrics for several SaaS architecture configurations at the same time. In this paper, we tackle the multi-objective optimization problem of identifying variable microservices aiming optimal granularity (new metric proposed), commonality, and data convergence, with a search-based approach employing the MOEA/D algorithm. We empirically and experimentally evaluated the proposed method following the Goal-Question-Metric approach. The results show that the method is promising in identifying fully consistent, highly reusable, variable microservices with an acceptable multi-tenancy degree. Moreover, the identified microservices, although not structurally very similar to those identified by the expert architects, provide design quality measures (granularity, etc.) close to (and even better than) the experts. [ABSTRACT FROM AUTHOR]

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Due to the high requirements for performance of antennas in the modern communication system, more and more objectives need to be considered, which makes the antenna design unendurable time-consuming and hard to converge. To obtain the Pareto solutions for antenna design effectively and efficiently, a dual reduction method is incorporated in an improved multi-objective evolutionary algorithm based on decomposition (MOEA/D). To obtain information about conflicting objectives on the Pareto front, the size of the MOEA/D neighbourhood is dynamically adjusted; to improve the speed and accuracy of finding redundant objectives, PCA and Pareto impact ratio are used as dual objective-reduction criteria. Numerical results in solving the mathematical benchmark problems, an antenna array problem and Yagi-uda optimal design demonstrate that the proposed method can reduce redundant objectives and increase the convergence speed. [ABSTRACT FROM AUTHOR]

Multi-objective welding robot path planning is becoming an important problem owing to the developing requirements of industrial production intelligence. An approach with path planning and optimization is proposed for solving the problem of arc welding. A rapidly exploring random tree* (RRT*)-based local path search algorithm is applied to generate a set of collision-free paths between any two welding seams, and the global search algorithm based on the decomposition-based multi-objective evolutionary algorithm (MOEA/D) framework is introduced to improve welding production efficiency by optimizing the requested contradictory objectives, namely, path length, trajectory smoothness and energy consumption. Both proposed algorithms are tested in different instances and on an actual welding workpiece, and the results prove that the proposed method could be useful in industrial production. [ABSTRACT FROM AUTHOR]

Vehicles route problems (VRP) are to arrange the optimal routes under the various requirements, and it is becoming significant in the logistics industry as electric commerce is rising. However, uncertainty is inevitable in VRP. In this manuscript, we consider the VRP with time windows (VRPTW) under uncertainty. We formulate the robust multi-objective VRPTW (RMOVRPTW) model and propose a robust optimization algorithm based on MOEA/D (R-MOEAD-VRP) for simultaneously optimizing the total distance and the number of vehicles required for transport. First, we use the priority of the customers being served to encode and use the defined transformation approach to form the feasible routes. Next, we employ Order Crossover and Exchange mutation operators to increase population diversity. For the new routes by reproduction, we use Monte-Carlo tests to check the feasibility of the routes after adding uncertainty. For the feasible routes, we calculate the solution robustness values based on the defined method. Finally, we consider both optimality and robustness to form a set of highly robust and relatively optimal solutions. For verifying the availability of the presented algorithm, the simulation experiments conduct on Solomon's benchmark problems compared with several related algorithms. Experimental results show that our proposed algorithm can bring more robust and non-dominated solutions under uncertainty and can achieve good performance. [ABSTRACT FROM AUTHOR]

When dealing with regular, simple Pareto fronts (PFs), the decomposition-based multi-objective optimization algorithm (MOEA/D) performs well by presetting a set of uniformly distributed weight vectors. However, its performance declines when faced with complex and irregular PFs. Many algorithms address this problem by periodically adjusting the distribution of the weight vectors, but these methods do not take into account the performance of the population and are likely to update the weight vectors at the wrong time. In addition, for the SBX crossover operator, the setting of its distribution index will largely affect the exploration and convergence ability of the algorithm, so a single parameter setting will have negative impacts. To tackle these challenges, this paper proposes a method to simultaneously adaptively update weight vectors and optimize SBX parameter via Q-learning(RL-MaOEA/D). In order to make the strategies made by Q-learning more accurate, Two different metrics (CD and NCD) are proposed that capture diversity and convergence of individual and population respectively. RL-MaOEA/D is compared with seven state-of-the-art algorithms on different problems, and the simulation results reflect that the proposed algorithm has better performance. • Determining the timing of the update of the weight vectors is difficult. • Setting a single SBX parameter can cause performance degradation. • Adaptive updating of weight vectors and optimization of SBX parameters via Q-learning. • Proposing two metrics to reflect diversity and convergence of individual and population respectively. • Experiment results demonstrate the algorithm proposed has superior performance. [ABSTRACT FROM AUTHOR]

A Multiobjective Optimization Problem (MOP) requires the optimization of several objective functions simultaneously, usually in conflict with each other. One of the most efficient algorithms for solving MOPs is MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition), which decomposes a MOP into single-objective optimization subproblems and solves them using information from neighboring subproblems. MOEA/D variants with other evolutionary operators have emerged over the years, improving their efficiency in various MOPs. Recently, the IWOA (Improved Whale Optimization Algorithm) was proposed, an optimization algorithm bioinspired by the whale hunting method hybridized with Differential Evolution, which presented excellent results in single-objective optimization problems. This work proposes the MOEA/D-IWOA algorithm, which associates characteristics of the evolutionary operators of the IWOA to MOEA/D. Computational experiments were accomplished to analyze the performance of the MOEA/D-IWOA in benchmark MOPs suites. The results were compared with those obtained by the MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Third Evolution Step of Generalized Differential Evolution (GDE3), Improving the Strength Pareto Evolutionary Algorithm (SPEA2), and Indicator-Based Evolutionary Algorithm (IBEA) algorithms in the Hypervolume and Inverted Generational Distance Plus (IGD+) indicators. The MOEA/D-IWOA proved to be competitive, with a good performance profile, in addition to presenting the best results in some POMs.

Network Function Virtualization (NFV) can provide the resource according to the request and can improve the flexibility of the network. It has become the key technology of next generation communication. Resource scheduling for virtual network function service chain (VNF-SC) mapping is the key issue of the NFV. A virtual network function service chain placement multi-objective optimization model and algorithm based on improved genetic algorithm is proposed. Firstly, a multi-objective optimization model, which minimizes deployment cost, transmission delay and maximizes the load balance, is established. On this basis, an improved genetic algorithm based on MOEA/D is proposed to solve the established multiobjective model. In this algorithm, the combination scheme and mapping scheme of the service request are coded by the two-level coding method in the mapping process, and then the improved sparrow search algorithm is used to obtain the service function chain deployment scheme of the request and calculate the mapping weight. In addition, an efficient individual generation strategy is proposed to generate some superior individual. Finally, some simulation experiments are conducted and the experimental results show that the algorithm can effectively reduce deployment cost and transmission delay than the compared algorithm. [ABSTRACT FROM AUTHOR]

The echo state network (ESN) has been widely applied for nonlinear system modeling. However, the too large reservoir size of ESN will lead to overfitting problem and reduce generalization performance. To balance reservoir size and training performance, the multi-objective sparse echo state network (MOS-ESN) is proposed. Firstly, the ESN design problem is formulated as a two-objective optimization problem, which is solved by the decomposition-based multi-objective optimization algorithm (MOEA/D). Secondly, to accelerate algorithm convergence, the local search strategy is designed, which combines the l1 or l0 norm regularization and coordinate descent algorithm, respectively. Thirdly, to produce more solutions around the knee point, an adaptive weight vectors updating method is proposed, which is based on decision maker interest. Experimental results show that the MOS-ESN outperforms other methods in terms of network sparseness and prediction accuracy. [ABSTRACT FROM AUTHOR]

This paper aimed at the study of solving multi-objective optimization in fuzzy flexible work workshop scheduling problems. The method used fuzzy numbers to represent relevant parameters, and the optimization objectives of minimizing the maximum completion time, total machine load and maximum machine load. This paper proposed an improved weight vector and initialization population of MOEA/D algorithm. This algorithm used initialization population of MOEA/D algorithm to optimize the global update pairing strategy. By comparing and analyzing with MOEA/D, NSGA-Ⅱ, and NSGA-Ⅲ algorithms, this study introduced enterprise engineering examples for analysis. Results reveal that the I-MOEA/D algorithm is superior than other algorithms and has excellent convergence and distribution. [ABSTRACT FROM AUTHOR]