Showing papers on "Multi-objective optimization published in 2021"

A novel hybrid antlion optimization algorithm for multi-objective task scheduling problems in cloud computing environments

Abstract: Efficient task scheduling is considered as one of the main critical challenges in cloud computing. Task scheduling is an NP-complete problem, so finding the best solution is challenging, particularly for large task sizes. In the cloud computing environment, several tasks may need to be efficiently scheduled on various virtual machines by minimizing makespan and simultaneously maximizing resource utilization. We present a novel hybrid antlion optimization algorithm with elite-based differential evolution for solving multi-objective task scheduling problems in cloud computing environments. In the proposed method, which we refer to as MALO, the multi-objective nature of the problem derives from the need to simultaneously minimize makespan while maximizing resource utilization. The antlion optimization algorithm was enhanced by utilizing elite-based differential evolution as a local search technique to improve its exploitation ability and to avoid getting trapped in local optima. Two experimental series were conducted on synthetic and real trace datasets using the CloudSim tool kit. The results revealed that MALO outperformed other well-known optimization algorithms. MALO converged faster than the other approaches for larger search spaces, making it suitable for large scheduling problems. Finally, the results were analyzed using statistical t-tests, which showed that MALO obtained a significant improvement in the results.

A Coevolutionary Framework for Constrained Multiobjective Optimization Problems

Abstract: Constrained multiobjective optimization problems (CMOPs) are challenging because of the difficulty in handling both multiple objectives and constraints While some evolutionary algorithms have demonstrated high performance on most CMOPs, they exhibit bad convergence or diversity performance on CMOPs with small feasible regions To remedy this issue, this article proposes a coevolutionary framework for constrained multiobjective optimization, which solves a complex CMOP assisted by a simple helper problem The proposed framework evolves one population to solve the original CMOP and evolves another population to solve a helper problem derived from the original one While the two populations are evolved by the same optimizer separately, the assistance in solving the original CMOP is achieved by sharing useful information between the two populations In the experiments, the proposed framework is compared to several state-of-the-art algorithms tailored for CMOPs High competitiveness of the proposed framework is demonstrated by applying it to 47 benchmark CMOPs and the vehicle routing problem with time windows

Multi-Objective Design Optimization of an IPMSM Based on Multilevel Strategy

Abstract: The multiobjective optimization design of interior permanent magnet synchronous motors (IPMSMs) is a challenge due to the high dimension and huge computation cost of finite element analysis. This article presents a new multilevel optimization strategy for efficient multiobjective optimization of an IPMSM. To determine the multilevel optimization strategy, Pearson correlation coefficient analysis and cross-factor variance analysis techniques are employed to evaluate the correlations of design parameters and optimization objectives. A three-level optimization structure is obtained for the investigated IPMSM based on the analysis results, and different optimization parameters and objectives are assigned to different levels. To improve the optimization efficiency, the Kriging model is employed to approximate the finite element analysis for the multiobjective optimization in each level. It is found that the proposed method can provide optimal design schemes with a better performance, such as smaller torque ripple and lower power loss for the investigated IPMSM, while the needed computation cost is reduced significantly. Finally, experimental results based on a prototype are provided to validate the effectiveness of the proposed optimization method. The proposed method can be applied for the efficient multiobjective optimization of other electrical machines with high dimensions.

Robust multi-objective optimal design of islanded hybrid system with renewable and diesel sources/stationary and mobile energy storage systems

Abstract: Planning of an islanded hybrid system (IHS) with different sources and storages to supply clean, flexible, and highly reliable energy at consumption sites is of high importance. To this end, this paper presents the design of an IHS with a wind turbine, photovoltaic, diesel generator, and stationary (battery) and mobile (electrical vehicles) energy storage systems (ESS). The proposed method includes a multi-objective optimization to minimize the total cost of construction, maintenance, and operation of sources and ESSs within the IHS and the emission level of the system using two separate objective functions. The problem is subject to operational and planning constraints of sources and ESSs and power. Employing the Pareto optimization technique based on the e-constraint method forms a single-objective optimization problem for the proposed design. The problem involves uncertainties of load, renewable energy, and energy demand of mobile ESSs and has a nonlinear form. Adaptive robust optimization based on a hybrid meta-heuristic algorithm that utilizes a combination of the sine-cosine algorithm (SCA) and crow search algorithm (CSA) is proposed to achieve an optimal robust structure for the suggested scheme. In this scheme, operation model of the mobile storage systems in the IHS considering the uncertainties prediction errors and its model using HMA-based ARO besides adopting the HMA to achieve a unique optimal solution are among the novelties of this research. Eventually, considering the climate data and energy consumption of a region in Rafsanjan, Iran, capabilities of the method in extracting a robust IHS for sources and ESSs are validated depending on optimal economic and environmental conditions. The HMA succeeds to reach an optimal solution with an SD of 0.92% in the final response and this underlines its capability in achieving approximate conditions of unique responsiveness. The proposed scheme with proper planning and operation of sources and storages in the form of a HIS finds optimal values for economic and environmental conditions so that the difference between pollution and cost values from its minimum values at the compromise point is roughly 22%. For 17% uncertainty parameters prediction errors, the scheme obtains a robust structure for the IHS.

Revealing the benefits of entropy weights method for multi-objective optimization in machining operations: A critical review

Abstract: Machining operation optimization improves the quality of the product, reduces cost, enhances overall efficiency by reducing human error, and enables consistent and efficient operation. It is a vital decision-making process and achieves the best solution within constraints. It reduces reliance on machine-tool technicians and handbooks to identify cutting parameters, as a lack of awareness of the optimal combination of machining parameters leads to several machining inefficiencies. Subsequently, the optimization of the machining process is more useful for units of production, particularly machining units. In multi-objective optimization (MOO) problems, weights of importance are assigned, mostly identical. But, nowadays, the weights assignment techniques have received a lot of consideration from the professionals and researchers in MOO problems. Various techniques are developed to assign weights of significance to responses in MOO. The Entropy weights method (EWM) continues to work pleasingly across diverse machining operations to allocate objective weights. In this paper, a literature review is conducted to classify the articles on EWM applications in machining operations. The categorization proposal for the EWM reviews included 65 academic articles from different journals, books, and conferences since the year 2009. The EWM applications were separated into 18 categories of conventional and non-conventional machining operations. The implementation procedure of EWM is presented with an example along with method development. Scholarly articles in the EWM applications are further inferred based on (1) implementation of EWM in different machining operations, (2) MOO methods used with entropy weights in machining operations, (3) application of entropy weights by citation index and publication year, and (4) entropy weights applications in other fields. The review paper provided constructive insight into the EWM applications and ended with suggestions for further research in machining and different areas.

An Adaptive Localized Decision Variable Analysis Approach to Large-Scale Multiobjective and Many-Objective Optimization.

Abstract: This article proposes an adaptive localized decision variable analysis approach under the decomposition-based framework to solve the large-scale multiobjective and many-objective optimization problems (MaOPs). Its main idea is to incorporate the guidance of reference vectors into the control variable analysis and optimize the decision variables using an adaptive strategy. Especially, in the control variable analysis, for each search direction, the convergence relevance degree of each decision variable is measured by a projection-based detection method. In the decision variable optimization, the grouped decision variables are optimized with an adaptive scalarization strategy, which is able to adaptively balance the convergence and diversity of the solutions in the objective space. The proposed algorithm is evaluated with a suite of test problems with 2-10 objectives and 200-1000 variables. Experimental results validate the effectiveness and efficiency of the proposed algorithm on the large-scale multiobjective and MaOPs.

A Survey of Evolutionary Algorithms for Multi-Objective Optimization Problems With Irregular Pareto Fronts

Abstract: Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems (MOPs). However, their performance often deteriorates when solving MOPs with irregular Pareto fronts. To remedy this issue, a large body of research has been performed in recent years and many new algorithms have been proposed. This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts. We start with a brief introduction to the basic concepts, followed by a summary of the benchmark test problems with irregular problems, an analysis of the causes of the irregularity, and real-world optimization problems with irregular Pareto fronts. Then, a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses. Finally, open challenges are pointed out and a few promising future directions are suggested.

A Comprehensive Review on NSGA-II for Multi-Objective Combinatorial Optimization Problems

Abstract: This paper provides an extensive review of the popular multi-objective optimization algorithm NSGA-II for selected combinatorial optimization problems viz. assignment problem, allocation problem, travelling salesman problem, vehicle routing problem, scheduling problem, and knapsack problem. It is identified that based on the manner in which NSGA-II has been implemented for solving the aforementioned group of problems, there can be three categories: Conventional NSGA-II, where the authors have implemented the basic version of NSGA-II, without making any changes in the operators; the second one is Modified NSGA-II, where the researchers have implemented NSGA-II after making some changes into it and finally, Hybrid NSGA-II variants, where the researchers have hybridized the conventional and modified NSGA-II with some other technique. The article analyses the modifications in NSGA-II and also discusses the various performance assessment techniques used by the researchers, i.e., test instances, performance metrics, statistical tests, case studies, benchmarking with other state-of-the-art algorithms. Additionally, the paper also provides a brief bibliometric analysis based on the work done in this study.

Deep Reinforcement Learning for Multiobjective Optimization

Abstract: This article proposes an end-to-end framework for solving multiobjective optimization problems (MOPs) using deep reinforcement learning (DRL), that we call DRL-based multiobjective optimization algorithm (DRL-MOA). The idea of decomposition is adopted to decompose the MOP into a set of scalar optimization subproblems. Then, each subproblem is modeled as a neural network. Model parameters of all the subproblems are optimized collaboratively according to a neighborhood-based parameter-transfer strategy and the DRL training algorithm. Pareto-optimal solutions can be directly obtained through the trained neural-network models. Specifically, the multiobjective traveling salesman problem (MOTSP) is solved in this article using the DRL-MOA method by modeling the subproblem as a Pointer Network. Extensive experiments have been conducted to study the DRL-MOA and various benchmark methods are compared with it. It is found that once the trained model is available, it can scale to newly encountered problems with no need for retraining the model. The solutions can be directly obtained by a simple forward calculation of the neural network; thereby, no iteration is required and the MOP can be always solved in a reasonable time. The proposed method provides a new way of solving the MOP by means of DRL. It has shown a set of new characteristics, for example, strong generalization ability and fast solving speed in comparison with the existing methods for multiobjective optimizations. The experimental results show the effectiveness and competitiveness of the proposed method in terms of model performance and running time.

Multi-objective optimization and multi-criteria decision-making methods for optimal design of standalone photovoltaic system: A comprehensive review

Abstract: Standalone photovoltaic (SAPV) systems have been considered as promising and fast development renewable energy sources due to free-noise, easy availability, and low-cost, especially for remote areas. However, the main disadvantages of these systems are low energy conversion and high capital cost. Therefore, many factors should be considered before installing the SAPV systems such as types of PV panels and configurations, mathematical models of PV module, storage battery, environmental criteria, sizing method based on techno-economic objectives, and selection the final optimum configuration. The goals of this paper are to presents a comprehensive review of the recent development in designing SAPV systems based on multi-objective optimization (MOO) and multi-criteria decision-making (MCDM) methodologies, including the mathematical models used in estimating the output power of the PV module and storage battery are also presented. Finally, the techno-economic criteria for assessing the performance of the SAPV system are considered. This will help the designers and customers to choose the most suitable design before installing the SAPV system. For supplementary resources and further discussions, please refer to the devoted homepage at http://aliasgharheidari.com .

A Two-Stage Cooperative Evolutionary Algorithm With Problem-Specific Knowledge for Energy-Efficient Scheduling of No-Wait Flow-Shop Problem

Abstract: Green scheduling in the manufacturing industry has attracted increasing attention in academic research and industrial applications with a focus on energy saving. As a typical scheduling problem, the no-wait flow-shop scheduling has been extensively studied due to its wide industrial applications. However, energy consumption is usually ignored in the study of typical scheduling problems. In this article, a two-stage cooperative evolutionary algorithm with problem-specific knowledge called TS-CEA is proposed to address energy-efficient scheduling of the no-wait flow-shop problem (EENWFSP) with the criteria of minimizing both makespan and total energy consumption. In TS-CEA, two constructive heuristics are designed to generate a desirable initial solution after analyzing the properties of the problem. In the first stage of TS-CEA, an iterative local search strategy (ILS) is employed to explore potential extreme solutions. Moreover, a hybrid neighborhood structure is designed to improve the quality of the solution. In the second stage of TS-CEA, a mutation strategy based on critical path knowledge is proposed to extend the extreme solutions to the Pareto front. Moreover, a co-evolutionary closed-loop system is generated with ILS and mutation strategies in the iteration process. Numerical results demonstrate the effectiveness and efficiency of TS-CEA in solving the EENWFSP.

MOSMA: Multi-Objective Slime Mould Algorithm Based on Elitist Non-Dominated Sorting

Abstract: This paper proposes a multi-objective Slime Mould Algorithm (MOSMA), a multi-objective variant of the recently-developed Slime Mould Algorithm (SMA) for handling the multi-objective optimization problems in industries. Recently, for handling optimization problems, several meta-heuristic and evolutionary optimization techniques have been suggested for the optimization community. These methods tend to suffer from low-quality solutions when evaluating multi-objective optimization (MOO) problems than addressing the objective functions of identifying Pareto optimal solutions’ accurate estimation and increasing the distribution throughout all objectives. The SMA method follows the logic gained from the oscillation behaviors of slime mould in the laboratory experiments. The SMA algorithm shows a powerful performance compared to other well-established methods, and it is designed by incorporating the optimal food path using the positive-negative feedback system. The proposed MOSMA algorithm employs the same underlying SMA mechanisms for convergence combined with an elitist non-dominated sorting approach to estimate Pareto optimal solutions. As a posteriori method, the multi-objective formulation is maintained in the MOSMA, and a crowding distance operator is utilized to ensure increasing the coverage of optimal solutions across all objectives. To verify and validate the performance of MOSMA, 41 different case studies, including unconstrained, constrained, and real-world engineering design problems are considered. The performance of the MOSMA is compared with Multiobjective Symbiotic-Organism Search (MOSOS), Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), and Multiobjective Water-Cycle Algorithm (MOWCA) in terms of different performance metrics, such as Generational Distance (GD), Inverted Generational Distance (IGD), Maximum Spread (MS), Spacing, and Run-time. The simulation results demonstrated the superiority of the proposed algorithm in realizing high-quality solutions to all multi-objective problems, including linear, nonlinear, continuous, and discrete Pareto optimal front. The results indicate the effectiveness of the proposed algorithm in solving complicated multi-objective problems. This research will be backed up with extra online service and guidance for the paper’s source code at https://premkumarmanoharan.wixsite.com/mysite and https://aliasgharheidari.com/SMA.html . Also, the source code of SMA is shared with the public at https://aliasgharheidari.com/SMA.html .

Evolutionary Large-Scale Multi-Objective Optimization: A Survey

Abstract: Multi-objective evolutionary algorithms (MOEAs) have shown promising performance in solving various optimization problems, but their performance may deteriorate drastically when tackling problems containing a large number of decision variables. In recent years, much effort been devoted to addressing the challenges brought by large-scale multi-objective optimization problems. This article presents a comprehensive survey of stat-of-the-art MOEAs for solving large-scale multi-objective optimization problems. We start with a categorization of these MOEAs into decision variable grouping based, decision space reduction based, and novel search strategy based MOEAs, discussing their strengths and weaknesses. Then, we review the benchmark problems for performance assessment and a few important and emerging applications of MOEAs for large-scale multi-objective optimization. Last, we discuss some remaining challenges and future research directions of evolutionary large-scale multi-objective optimization.

EMoSOA: a new evolutionary multi-objective seagull optimization algorithm for global optimization

Abstract: This study introduces the evolutionary multi-objective version of seagull optimization algorithm (SOA), entitled Evolutionary Multi-objective Seagull Optimization Algorithm (EMoSOA). In this algorithm, a dynamic archive concept, grid mechanism, leader selection, and genetic operators are employed with the capability to cache the solutions from the non-dominated Pareto. The roulette-wheel method is employed to find the appropriate archived solutions. The proposed algorithm is tested and compared with state-of-the-art metaheuristic algorithms over twenty-four standard benchmark test functions. Four real-world engineering design problems are validated using proposed EMoSOA algorithm to determine its adequacy. The findings of empirical research indicate that the proposed algorithm is better than other algorithms. It also takes into account those optimal solutions from the Pareto which shows high convergence.

Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)

Abstract: Recently, increasing works have been proposed to drive evolutionary algorithms using machine-learning models. Usually, the performance of such model-based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e., the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales due to the curse of dimensionality. To address this issue, we propose a multiobjective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on ten benchmark problems with up to 200 decision variables. The experimental results on these test problems demonstrate the effectiveness of the proposed algorithm.

Cognizant Multitasking in Multiobjective Multifactorial Evolution: MO-MFEA-II

Abstract: Humans have the ability to identify recurring patterns in diverse situations encountered over a lifetime, constantly understanding relationships between tasks and efficiently solving them through knowledge reuse. The capacity of artificial intelligence systems to mimic such cognitive behaviors for effective problem solving is deemed invaluable, particularly when tackling real-world problems where speed and accuracy are critical. Recently, the notion of evolutionary multitasking has been explored as a means of solving multiple optimization tasks simultaneously using a single population of evolving individuals. In the presence of similarities (or even partial overlaps) between high-quality solutions of related optimization problems, the resulting scope for intertask genetic transfer often leads to significant performance speedup—as the cost of re-exploring overlapping regions of the search space is reduced. While multitasking solvers have led to recent success stories, a known shortcoming of existing methods is their inability to adapt the extent of transfer in a principled manner. Thus, in the absence of any prior knowledge about the relationships between optimization functions, a threat of predominantly negative (harmful) transfer prevails. With this in mind, this article presents a realization of a cognizant evolutionary multitasking engine within the domain of multiobjective optimization. Our proposed algorithm learns intertask relationships based on overlaps in the probabilistic search distributions derived from data generated during the course of multitasking—and accordingly adapts the extent of genetic transfers online . The efficacy of the method is substantiated on multiobjective benchmark problems as well as a practical case study of knowledge transfers from low-fidelity optimization tasks to substantially reduce the cost of high-fidelity optimization.

Knee Point-Based Imbalanced Transfer Learning for Dynamic Multiobjective Optimization

Abstract: Dynamic multiobjective optimization problems (DMOPs) are optimization problems with multiple conflicting optimization objectives, and these objectives change over time Transfer learning-based approaches have been proven to be promising; however, a slow solving speed is one of the main obstacles preventing such methods from solving real-world problems One of the reasons for the slow running speed is that low-quality individuals occupy a large amount of computing resources, and these individuals may lead to negative transfer Combining high-quality individuals, such as knee points, with transfer learning is a feasible solution to this problem However, the problem with this idea is that the number of high-quality individuals is often very small, so it is difficult to acquire substantial improvements using conventional transfer learning methods In this article, we propose a knee point-based transfer learning method, called KT-DMOEA, for solving DMOPs In the proposed method, a trend prediction model (TPM) is developed for producing the estimated knee points Then, an imbalance transfer learning method is proposed to generate a high-quality initial population by using these estimated knee points The advantage of this approach is that the seamless integration of a small number of high-quality individuals and the imbalance transfer learning technique can greatly improve the computational efficiency while maintaining the quality of the solution The experimental results and performance comparisons with some chosen state-of-the-art algorithms demonstrate that the proposed design is capable of significantly improving the performance of dynamic optimization

A New Arithmetic Optimization Algorithm for Solving Real-World Multiobjective CEC-2021 Constrained Optimization Problems: Diversity Analysis and Validations

Abstract: In this paper, a new Multi-Objective Arithmetic Optimization Algorithm (MOAOA) is proposed for solving Real-World constrained Multi-objective Optimization Problems (RWMOPs). Such problems can be found in different fields, including mechanical engineering, chemical engineering, process and synthesis, and power electronics systems. MOAOA is inspired by the distribution behavior of the main arithmetic operators in mathematics. The proposed multi-objective version is formulated and developed from the recently introduced single-objective Arithmetic Optimization Algorithm (AOA) through an elitist non-dominance sorting and crowding distance-based mechanism. For the performance evaluation of MOAOA, a set of 35 constrained RWMOPs and five ZDT unconstrained problems are considered. For the fitness and efficiency evaluation of the proposed MOAOA, the results obtained from the MOAOA are compared with four other state-of-the-art multi-objective algorithms. In addition, five performance indicators, such as Hyper-Volume (HV), Spread (SD), Inverted Generational Distance (IGD), Runtime (RT), and Generational Distance (GD), are calculated for the rigorous evaluation of the performance and feasibility study of the MOAOA. The findings demonstrate the superiority of the MOAOA over other algorithms with high accuracy and coverage across all objectives. This paper also considers the Wilcoxon signed-rank test (WSRT) for the statistical investigation of the experimental study. The coverage, diversity, computational cost, and convergence behavior achieved by MOAOA show its high efficiency in solving ZDT and RWMOPs problems.

A multi-objective optimization algorithm for feature selection problems

Abstract: Feature selection (FS) is a critical step in data mining, and machine learning algorithms play a crucial role in algorithms performance. It reduces the processing time and accuracy of the categories. In this paper, three different solutions are proposed to FS. In the first solution, the Harris Hawks Optimization (HHO) algorithm has been multiplied, and in the second solution, the Fruitfly Optimization Algorithm (FOA) has been multiplied, and in the third solution, these two solutions are hydride and are named MOHHOFOA. The results were tested with MOPSO, NSGA-II, BGWOPSOFS and B-MOABC algorithms for FS on 15 standard data sets with mean, best, worst, standard deviation (STD) criteria. The Wilcoxon statistical test was also used with a significance level of 5% and the Bonferroni–Holm method to control the family-wise error rate. The results are shown in the Pareto front charts, indicating that the proposed solutions' performance on the data set is promising.

Learning to Optimize: Reference Vector Reinforcement Learning Adaption to Constrained Many-Objective Optimization of Industrial Copper Burdening System.

Abstract: The performance of decomposition-based algorithms is sensitive to the Pareto front shapes since their reference vectors preset in advance are not always adaptable to various problem characteristics with no a priori knowledge. For this issue, this article proposes an adaptive reference vector reinforcement learning (RVRL) approach to decomposition-based algorithms for industrial copper burdening optimization. The proposed approach involves two main operations, that is: 1) a reinforcement learning (RL) operation and 2) a reference point sampling operation. Given the fact that the states of reference vectors interact with the landscape environment (quite often), the RL operation treats the reference vector adaption process as an RL task, where each reference vector learns from the environmental feedback and selects optimal actions for gradually fitting the problem characteristics. Accordingly, the reference point sampling operation uses estimation-of-distribution learning models to sample new reference points. Finally, the resultant algorithm is applied to handle the proposed industrial copper burdening problem. For this problem, an adaptive penalty function and a soft constraint-based relaxing approach are used to handle complex constraints. Experimental results on both benchmark problems and real-world instances verify the competitiveness and effectiveness of the proposed algorithm.

A Fast Dynamic Evolutionary Multiobjective Algorithm via Manifold Transfer Learning

Abstract: Many real-world optimization problems involve multiple objectives, constraints, and parameters that may change over time. These problems are often called dynamic multiobjective optimization problems (DMOPs). The difficulty in solving DMOPs is the need to track the changing Pareto-optimal front efficiently and accurately. It is known that transfer learning (TL)-based methods have the advantage of reusing experiences obtained from past computational processes to improve the quality of current solutions. However, existing TL-based methods are generally computationally intensive and thus time consuming. This article proposes a new memory-driven manifold TL-based evolutionary algorithm for dynamic multiobjective optimization (MMTL-DMOEA). The method combines the mechanism of memory to preserve the best individuals from the past with the feature of manifold TL to predict the optimal individuals at the new instance during the evolution. The elites of these individuals obtained from both past experience and future prediction will then constitute as the initial population in the optimization process. This strategy significantly improves the quality of solutions at the initial stage and reduces the computational cost required in existing methods. Different benchmark problems are used to validate the proposed algorithm and the simulation results are compared with state-of-the-art dynamic multiobjective optimization algorithms (DMOAs). The results show that our approach is capable of improving the computational speed by two orders of magnitude while achieving a better quality of solutions than existing methods.

Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization

Abstract: Pareto dominance-based multiobjective optimization has been successfully applied to constrained evolutionary optimization during the last two decades. However, as another famous multiobjective optimization framework, decomposition-based multiobjective optimization has not received sufficient attention from constrained evolutionary optimization. In this paper, we make use of decomposition-based multiobjective optimization to solve constrained optimization problems (COPs). In our method, first of all, a COP is transformed into a biobjective optimization problem (BOP). Afterward, the transformed BOP is decomposed into a number of scalar optimization subproblems. After generating an offspring for each subproblem by differential evolution, the weighted sum method is utilized for selection. In addition, to make decomposition-based multiobjective optimization suit the characteristics of constrained evolutionary optimization, weight vectors are elaborately adjusted. Moreover, for some extremely complicated COPs, a restart strategy is introduced to help the population jump out of a local optimum in the infeasible region. Extensive experiments on three sets of benchmark test functions, namely, 24 test functions from IEEE CEC2006, 36 test functions from IEEE CEC2010, and 56 test functions from IEEE CEC2017, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

An Effective Knowledge Transfer Approach for Multiobjective Multitasking Optimization

Abstract: Multiobjective multitasking optimization (MTO), which is an emerging research topic in the field of evolutionary computation, was recently proposed. MTO aims to solve related multiobjective optimization problems at the same time via evolutionary algorithms. The key to MTO is the knowledge transfer based on sharing solutions across tasks. Notably, positive knowledge transfer has been shown to facilitate superior performance characteristics. However, how to find more valuable transferred solutions for the positive transfer has been scarcely explored. Keeping this in mind, we propose a new algorithm to solve MTO problems. In this article, if a transferred solution is nondominated in its target task, the transfer is positive transfer. Furthermore, neighbors of this positive-transfer solution will be selected as the transferred solutions in the next generation, since they are more likely to achieve the positive transfer. Numerical studies have been conducted on benchmark problems of MTO to verify the effectiveness of the proposed approach. Experimental results indicate that our proposed framework achieves competitive results compared with the state-of-the-art MTO frameworks.