Decision-making processes involving fixed charges arise in various real-world applications and can often be modeled as mixed-integer nonlinear programs (MINLPs) with semicontinuous variables. Perspective reformulation, a technique leveraging perspective functions, offers tight formulations for such MINLPs. In this article, we address the challenge of solving such reformulations by introducing perspective Benders cuts, a family of generalized Benders optimality cuts, and compare them with the classic generalized Benders cuts and the perspective cuts. We focus on their applications to two fixed-charge nonlinear resource allocation problems: a generalized sensor placement problem and a generalized uncapacitated facility location problem. The original quadratic allocation cost functions in these problems are extended to a class of reducible convex functions. By leveraging the reducible property of nonlinear resource allocation problems, we develop an ad-hoc procedure of solving the reduced quadratic subproblems to efficiently separate perspective Benders cuts. These features contribute to a highly efficient branch-and-Benders-cut approach, as demonstrated through extensive computational experiments on various sets of benchmark instances. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: K. Yang acknowledges financial support from China Scholarship Council [Grant 202406110031]. This work was also supported by the National Science Fund for Outstanding Young Scholars [Grant 62122093], the National Natural Science Foundation of China [Grants 72101264, 72431011, and 72421002], the Science and Technology Innovation Program of Hunan Province [Grant 2023RC3008], Open Project of Xiangjiang Laboratory [Grant 22XJ02003], and the University Fundamental Research Fund [Grant 23-ZZCX-JDZ-28]. H. Yang’s work is funded by National Natural Science Foundation of China [Grant 72201232 and 72231008], Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence [Grant 2023B1212010001], and Shenzhen Key Laboratory of Crowd Intelligence Empowered Low-Carbon Energy Network [Grant ZDSYS20220606100601002]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0984 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0984 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

With the rapid advancement of large language models (LLMs) in both academia and industry, their growing size and complexity have introduced significant challenges in terms of computational cost and deployment efficiency. To address these issues, a wide range of inference optimization techniques-including but not limited to model compression-have been proposed to accelerate LLM inference while preserving model performance. This survey provides a comprehensive overview of LLM inference acceleration strategies, analyzing them from multiple perspectives, including foundational principles, algorithmic techniques, real-world applications, and open research challenges. We begin by introducing core concepts underlying inference optimization and propose a new taxonomy that categorizes existing approaches, including quantization, pruning, distillation, efficient architectures, compilation, and hardware-aware methods. Following the lifecycle of LLM development and deployment, we examine how these techniques interact with model training, fine-tuning, and serving. Furthermore, we highlight key applications of efficient LLMs and discuss emerging trends and unresolved issues in the field. By synthesizing recent advances, this survey aims to provide actionable insights and practical guidance for researchers and practitioners working with scalable and efficient LLM systems.

The coordinated operation of modern air defense systems represents a highly complex engineering challenge, necessitating intelligent decision-making to maximize defensive performance. Central to this framework, air defense resource assignment problems (ADRAPs) require the flexible and coordinated management of radar and missile resources. However, solving ADRAPs is highly challenging due to their sparse decision spaces, complex system constraints, and strict computational requirements. To address these challenges, we formulate a mathematical model tailored to realistic battlefield scenarios and develop a novel evolutionary algorithm that leverages Q-learning to balance global and local search strategies. Specifically, the proposed algorithm incorporates an adaptive mechanism that dynamically selects the optimal local search strategy based on the current population state. Furthermore, we design and integrate a knowledge-guided search method to enhance the efficiency of the local search process. Experimental results across diverse air defense scenarios demonstrate that the proposed algorithm significantly outperforms six state-of-the-art algorithms, effectively improving the coordinated defensive capabilities of intelligent air defense systems.

The Reentrant Flexible Flow Shop Scheduling Problem (RFFSP) involves multiple repetitions of job processing in the production system, which leads to higher scheduling complexity. To solve the RFFSP, this paper proposes a Reinforcement Learning- enhanced Genetic Algorithm (RL-GA). First, a model for the RFFSP is established with the goal of minimizing the total delay time. Then, based on the characteristics of the RFFSP, a machine selection and operation selection (MSOS) encoding scheme is designed. Finally, to address the issue of genetic algorithms getting stuck in local optima and having poor local search capabilities, a reinforcement learning-based method for selecting crossover and mutation strategies is proposed. This allows the algorithm to adaptively choose more suitable crossover and mutation strategies during the iteration process. The proposed method is validated by comparing it with five other scheduling algorithms, demonstrating an improvement in the algorithm's performance

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 78% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this limitation, we propose Safe Diffusion Models for PDE Control (SafeDiffCon), which introduce the uncertainty quantile as model uncertainty quantification to achieve optimal control under safety constraints through both post-training and inference phases. Firstly, our approach post-trains a pre-trained diffusion model to generate control sequences that better satisfy safety constraints while achieving improved control objectives via a reweighted diffusion loss, which incorporates the uncertainty quantile estimated using conformal prediction. Secondly, during inference, the diffusion model dynamically adjusts both its generation process and parameters through iterative guidance and fine-tuning, conditioned on control targets while simultaneously integrating the estimated uncertainty quantile. We evaluate SafeDiffCon on three control tasks: 1D Burgers’ equation, 2D incompressible fluid, and controlled nuclear fusion problem. Results demonstrate that SafeDiffCon is the only method that satisfies all safety constraints, whereas other classical and deep learning baselines fail. Furthermore, while adhering to safety constraints, SafeDiffCon achieves the best control performance. The code can be found at https://github.com/AI4Science-WestlakeU/safediffcon.

The coordination of distributed energy resources (DERs) within virtual power plants (VPPs) is expected to generate significant economic benefits and enhance the operational stability of modern power systems. However, achieving massive coordination of heterogeneous and uncertain DERs remains a challenge in current research. To address this issue, this article proposes a novel bi-level optimization approach based on mean-field reinforcement learning (MFRL) to enable the coordination of massive DERs in VPPs. The problem is decomposed into multiple subproblems: the upper-level subproblem models power dispatch among integrated energy systems (IESs) in response to coordinated demand, while a series of lower-level subproblems determine the operational schemes of DERs within individual IESs. Considering the large decision space, an MFRL algorithm with fast Shapley credit allocation is developed to efficiently solve the upper-level optimization. Meanwhile, the lower-level subproblems are formulated as small-scale mixed-integer linear programming (MILP) problems, addressing the difficulties caused by IES heterogeneity in applying mean-field approximation. Simulation results show that the proposed approach significantly improves convergence speed and reduces the global cost of VPP operation, especially in massive-scale scenarios. In test scenarios ranging from 10 to 500 agents, the proposed bi-level optimization approach improves the objective by 4.8%-26.6%, compared to the advanced baseline method.

In recent years, prediction-based algorithms have attracted much attention for solving dynamic multiobjective optimization (DMO) problems in the evolutionary computing community. However, this class of algorithms still has potential for further improvements by enhancing the historical information extraction approach to balance convergence and diversity. In this article, we propose a DMO algorithm based on a recurrent neural network (RNN) to balance the population’s convergence and diversity in dynamic environments. The RNN model in the proposed algorithm employs online learning in order to constantly improve according to the increasing evolutionary information. Meanwhile, differing from most existing prediction-based algorithms, the learning machine is not limited by assumptions, such as linear or nonlinear correlation, when it predicts new solutions for future evolutionary environments. Besides, an auxiliary strategy is performed, which adaptively introduces the random or mutated solutions according to the error losses between the prediction solutions and the optimal solutions in the whole optimization process. The experimental results show that the proposed algorithm is more effective for handling DMO problems than several recent algorithms.

Traditional multiobjective evolutionary algorithms (MOEAs) face challenges when addressing sparse large-scale multiobjective optimization problems (SLSMOPs) with many zero decision variables. The “large-scale” refers to the high dimensionality of the decision space, making it difficult for traditional MOEAs to traverse vast expanses efficiently with limited computational resources. Furthermore, In sparse contexts, most variables in Pareto optimal solutions are zero. It is difficult for traditional MOEAs to identify nonzero variables’ positions efficiently. In reinforcement learning, Thompson sampling employs a probability distribution to estimate each item’s value or success probability. Drawing inspiration from this concept, we propose a Thompson sampling-based sparse evolutionary operator (TSSEO). TSSEO maintains a probability distribution for each variable and utilizes this distribution to recommend for the variable, assisting MOEAs in transitioning from high-dimensionality dense to sparse spaces. Experimental results show that when integrated with representative MOEAs, TSSEO performs competitively in three real-world problems and eight benchmark problems involving up to 10041 decision variables, compared to algorithms designed explicitly for SLSMOPs.

Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs. On the other hand, recent deep learning and reinforcement learning-based approaches often struggle to optimize long-term control sequences under the constraints of system dynamics. In this work, we introduce Diffusion Physical systems Control (DiffPhyCon), a new class of method to address the physical systems control problem. DiffPhyCon excels by simultaneously minimizing both the learned generative energy function and the predefined control objectives across the entire trajectory and control sequence. Thus, it can explore globally and plan near-optimal control sequences. Moreover, we enhance DiffPhyCon with prior reweighting, enabling the discovery of control sequences that significantly deviate from the training distribution. We test our method on three tasks: 1D Burgers' equation, 2D jellyfish movement control, and 2D high-dimensional smoke control, where our generated jellyfish dataset is released as a benchmark for complex physical system control research. Our method outperforms widely applied classical approaches and state-of-the-art deep learning and reinforcement learning methods. Notably, DiffPhyCon unveils an intriguing fast-close-slow-open pattern observed in the jellyfish, aligning with established findings in the field of fluid dynamics. The project website, jellyfish dataset, and code can be found at https://github.com/AI4Science-WestlakeU/diffphycon.

In recent years, researchers have made significant progress in handling dynamic multiobjective optimization problems (DMOPs), particularly for environmental changes with predictable characteristics. However, little attention has been paid to DMOPs with stochastic changes. It may be difficult for existing dynamic multiobjective evolutionary algorithms (DMOEAs) to effectively handle this kind of DMOPs because most DMOEAs assume that environmental changes follow regular patterns and consecutive environments are similar. This article presents a Mahalanobis distance-based approach (MDA) to deal with DMOPs with stochastic changes. Specifically, we make an all-sided assessment of search environments via Mahalanobis distance on saved information to learn the relationship between the new environment and historical ones. Afterward, a change response strategy applies the learning to the new environment to accelerate the convergence and maintain the diversity of the population. Besides, the change degree is considered for all decision variables to alleviate the impact of stochastic changes on the evolving population. An MDA has been tested on stochastic DMOPs with two to four objectives. The results show that MDA performs significantly better than the other latest algorithms in this article, suggesting that MDA is effective for DMOPs with stochastic changes.

The multimicrogrid network structure design problem (MNSDP) represents a binary matrix optimization challenge, targeting the minimization of the cumulative length of power supply circuits within a multimicrogrid system, subject to specific constraints. The optimization of this problem is pivotal for augmenting the stability and resilience of power systems, particularly in remote locales harnessing renewable energy sources. Given its inherent large-scale, sparse, and multimodal nature, the pursuit of the global optimal solution for MNSDP is inherently complex. In this research, we introduce a sophisticated mathematical model of the MNSDP, accommodating three distinct node types, each having disparate reliability prerequisites. We further unveil a benchmark test suite based on real-world scenarios, dubbed MNSDP-LIB. To further our innovations, we present the large-scale binary matrix-based differential evolution (LBMDE) algorithm. This novel algorithm adopts a binary-matrix-centric DE operator with an enhanced feasibility-centric environmental selection strategy. Empirical experiments accentuate the proficiency of LBMDE in addressing large-scale binary matrix optimization challenges. When juxtaposed with extant evolutionary algorithms and a renowned commercial solver, LBMDE demonstrates commendable competitiveness.

Universal lesion detection using computerised tomography (CT) scans is a critical computer-aided diagnosis measure in clinical diagnosis. One of the key issues during the diagnosis is to identify the correlations between sequential slices to improve the feature representation of CT scans. In the process of fusing slice features containing temporal correlations, the correlation between the contextual slices in the channel dimension and the target slices is closely related to the spatial distance in practice. However, convolutional fusion approaches commonly ignore that features of different distances have unequal weights. To tackle this issue, we present a temporal correlation weighted fusion lesion detection network, called TCW-Net. Specifically, for the slices in the channel dimension, we develop a weighted feature fusion module to adjust the more discriminative features using learned weights. Then, we adapt a spatial offset attention mechanism that allows the detection network to pay more attention to the lesion’s slight spatial offset and thus improve the model’s capacity for distinguishing between different lesion features. Extensive experiments carried out on the DeepLesion dataset show that the proposed algorithm has superior performance over the state-of-the-art methods.

Multimodal multiobjective problems (MMOPs) commonly arise in real-world situations where distant solutions in decision space share a very similar objective value. Traditional multimodal multiobjective evolutionary algorithms (MMEAs) prefer to pursue multiple Pareto solutions that have the same objective values. However, a more practical situation in engineering problems is that one solution is slightly worse than another in terms of objective values, while the solutions are far away in the decision space. In other words, such problems have global and local Pareto fronts (PFs). In this study, we proposed several benchmark problems with several local PFs. Then, we proposed an evolutionary algorithm with a hierarchy ranking method (HREA) to find both the global and the local PFs based on the decision maker’s preference. Regarding HREA, we proposed a local convergence quality evaluation method to better maintain diversity in the decision space. Moreover, a hierarchy ranking method was introduced to update the convergence archive. The experimental results show that HREA is competitive compared with other state-of-the-art MMEAs for solving the chosen benchmark problems.

Multiobjective orienteering problems (MO-OPs) are classical multiobjective routing problems and have received much attention in recent decades. This study seeks to solve MO-OPs through a problem-decomposition framework, that is, an MO-OP is decomposed into a multiobjective knapsack problem (MOKP) and a traveling salesman problem (TSP). The MOKP and TSP are then solved by a multiobjective evolutionary algorithm (MOEA) and a deep reinforcement learning (DRL) method, respectively. While the MOEA module is for selecting cities, the DRL module is for planning a Hamiltonian path for these cities. An iterative use of these two modules drives the population toward the Pareto front of MO-OPs. The effectiveness of the proposed method is compared against NSGA-II and NSGA-III on various types of MO-OP instances. Experimental results show that our method performs best on almost all the test instances and has shown strong generalization ability.

This paper proposes a multi-source references (MSR) based face super-resolution (FSR) model. More specifically, to enhance the low-quality large-scale reconstruction of faces without the involvement of face prior knowledge, we propose a multi-source references based FSR framework exploiting a constructed reference library of nonidentity faces and an information mining module for external and internal references. Experimental results show that the proposed model can provide more satisfactory and reliable face super-resolution results than the-state-of-the-art methods.

There is an increasing interest in enhancing the quality of low-resolution (LR) facial images for various social life applications. Existing methods often use domain-specific prior knowledge, which is effective in improving the face super-resolution model's performance. However, it is challenging to obtain rich and accurate prior information from LR inputs in real-world scenarios, which can limit the robustness and generalization ability of the developed face super-resolution model. In this paper, a multisource reference-based face super-resolution Network, namely MSRNet, is proposed. Without considering the prior knowledge of faces, the network can reconstruct a LR face image with a magnitude factor of 8 under the guidance of multiple reference face images of different identities. By constructing an “appearance-alike” reference data set Face_Ref, the designed MSRNet aims to fully exploit the local and spatially similar high frequency information between the distinct references and the current face. More specifically, to effectively combine the information from multiple references, a cross-scale and cross-space feature fusion mechanism is introduced for external and internal references, and then the enhanced local semantics are finally incorporated into the high-resolution face reconstruction. The robustness of face image super-resolution is increased compared to current correlation approaches, since it not only eliminates the need for face prior knowledge but also avoids performing alignment operations on reference faces with multiple expressions and different poses. Experimental results show that the proposed model is able to produce results for face super-resolution that are satisfying and dependable and outperforms the state-of-the-art methods in terms of visual perceptual quality and quantity evaluation.

This article introduces a new deep learning approach to approximately solve the covering salesman problem (CSP). In this approach, given the city locations of a CSP as input, a deep neural network model is designed to directly output the solution. It is trained using the deep reinforcement learning without supervision. Specifically, in the model, we apply the multihead attention (MHA) to capture the structural patterns, and design a dynamic embedding to handle the dynamic patterns of the problem. Once the model is trained, it can generalize to various types of CSP tasks (different sizes and topologies) without the need of retraining. Through controlled experiments, the proposed approach shows desirable time complexity: it runs more than 20 times faster than the traditional heuristic solvers with a tiny gap of optimality. Moreover, it significantly outperforms the current state-of-the-art deep learning approaches for combinatorial optimization in the aspect of both training and inference. In comparison with traditional solvers, this approach is highly desirable for most of the challenging tasks in practice that are usually large scale and require quick decisions.

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.

Classic portfolio selection problems mainly focus on high-risk financial markets with tradeoffs between returns and risk. However, more risk-averse investors pursue long-term portfolio planning with the objectives of maximizing final returns and maximizing flexibility. This article addresses a new type of the portfolio problem, called periodic investment portfolio selection problems (PIPSPs), in which investors periodically allocate resources to financial products with different periods. A multiobjective model for PIPSPs is first presented. With a mechanism for utilizing the data generated during the implementation of multiobjective evolutionary algorithms (MOEAs), a data-assisted MOEA (DA-MOEA) is proposed to solve PIPSPs. The main idea of a DA-MOEA is to combine a MOEA with a data-assisted process that consists of three components: 1) feature construction; 2) data fusion model development; and 3) obtained information utilization. To solve the addressed PIPSPs, two versions of DA-MOEAs with baselines of nondominated sorting and decomposition-based mechanisms are implemented, namely, the data-assisted NSGA-II (DA-NSGA-II) and data-assisted MOEA/D (DA-MOEA/D). In the developed DA-MOEAs for PIPSPs, a feature construction process and a data fusion model are well designed for mining data with different formats. To validate the algorithms, two sets of test instances are generated. The experimental results demonstrate the efficacy of the data-assisted process. Furthermore, the effects of the algorithm components, such as the data source sizes, information types, and information utilization strategies, are investigated.

Due to the high variability and uncertainty of the wind speed, an interval forecast can provide more information for decision makers to achieve a better energy management compared to the traditional point forecast. In this article, a knee-based lower upper bound estimation method (K-LUBE) is proposed to construct wind speed prediction intervals (PIs). First, we analyze the underlying limitations of traditional direct interval forecast methods, i.e., their obtained PIs often fail to achieve a good balance between the interval width and the coverage probability. K-LUBE resolves the difficulty based on a multiobjective optimization framework in conjunction with a knee selection criterion. Specifically, a PI-NSGA-II multiobjective optimization algorithm is designed to obtain a set of Pareto-optimal solutions. A parameter transfer and a sample training strategies are developed to significantly improve the convergence speed of the optimization procedure. Then, the knee selection criterion is introduced to select the best tradeoff solution among the obtained solutions. In comparison with traditional methods, this method can always provide a reliable PI for decision makers. The procedure is automatic and requires no parameter to be specified in advance, making it more practical for use. The effectiveness of the proposed K-LUBE method is demonstrated through extensive comparisons with four traditional direct interval forecast methods and four classical benchmark models.

In addition to the search for feasible solutions, the utilization of informative infeasible solutions is important for solving constrained multiobjective optimization problems (CMOPs). However, most of the existing constrained multiobjective evolutionary algorithms (CMOEAs) cannot effectively explore and exploit those solutions and, therefore, exhibit poor performance when facing problems with large infeasible regions. To address the issue, this article proposes a novel method, called DD-CMOEA, which features dual stages (i.e., exploration and exploitation) and dual populations. Specifically, the two populations, called mainPop and auxPop, first individually evolve with and without considering the constraints, responsible for exploring feasible and infeasible solutions, respectively. Then, in the exploitation stage, mainPop provides information about the location of feasible regions, which facilitates auxPop to find and exploit surrounding infeasible solutions. The promising infeasible solutions obtained by auxPop in turn help mainPop converge better toward the Pareto-optimal front. Extensive experiments on three well-known test suites and a real-world case study fully demonstrate that DD-CMOEA is more competitive than five state-of-the-art CMOEAs.

This study contributes to the treatment of numerous constraints in evolutionary many-constraint optimization through consideration of the relationships between pair-wise constraints. In a conflicting relationship, the functional value of one constraint increases as the value in another constraint decreases. In a harmonious relationship, the improvement in one constraint is rewarded with simultaneous improvement in the other constraint. In an independent relationship, the adjustment to one constraint never affects the adjustment to the other. Based on the different features, methods for identifying constraint relationships are investigated, helping to simplify many-constraint optimization problems (MCOPs). Additionally, the transitivity of the relationships is further discussed, facilitating the determination of the relationship in a new pair of constraints.

Evolutionary algorithms (EAs) are often applied to deal with UAV route planning. The solution encoding is one of important factor in designing effective EAs. In a traditional encoding mechanism, each individual represents one route. The whole population then consists of a number of routes. We argue that such an encoding is less effective in route planning, and then proposed an alternative encoding mechanism in which one individual represents only one navigation point. The whole population then represents one route. This implicitly turns EAs into single-point based search with high exploitation ability. To further improve the exploration ability of algorithms using this new encoding, a slightly modified differential evolution operator is applied. Combining the modified DE operator and the new encoding mechanism, the performance of the derived algorithm is significantly improved, obtaining much better route planning results than DE with the traditional encoding mechanism.

Evolutionary algorithms (EAs) have been widely applied in various optimization problems. However, EAs are found as less effective on multi-modal optimization due to their multiple local optima. Inspired by the idea of self-paced learning, that is, problems can be solved step by step, from easy to difficult. In this study, we propose to design a helper objective function to assist the optimization of multi-modal problems via multitask optimization framework. In principle the helper objective function shares common features with the original function but is easier to solve. Thus, the information gained by solving the helper objective can be utilized to tackle the multi-modal problems. Specifically, the Gaussian process is applied to build the helper objective function. The multi-factorial evolutionary algorithm is applied to optimize the helper and original objective functions simultaneously. Experimental results show that the idea is effective on a set of multi-modal optimization benchmarks.

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.

Multimodal multiobjective problems (MMOPs) arise frequently in the real world, in which multiple Pareto-optimal solution (PS) sets correspond to the same point on the Pareto front. Traditional multiobjective evolutionary algorithms (MOEAs) show poor performance in solving MMOPs due to a lack of diversity maintenance in the decision space. Thus, recently, many multimodal MOEAs (MMEAs) have been proposed. However, for most existing MMEAs, the convergence performance in the objective space does not meet expectations. In addition, many of them cannot always obtain all equivalent Pareto solution sets. To address these issues, this study proposes an MMEA based on a weighted indicator, termed MMEA-WI. The algorithm integrates the diversity information of solutions in the decision space into an objective space performance indicator to maintain the diversity in the decision space and introduces a convergence archive to ensure a more effective approximation of the Pareto-optimal front (PF). These strategies can readily be applied to other indicator-based MOEAs. The experimental results show that MMEA-WI outperforms some state-of-the-art MMEAs on the chosen benchmark problems in terms of the inverted generational distance (IGD) and IGD in the decision space (IGDX) metrics.

The main challenge in constrained multiobjective optimization problems (CMOPs) is to appropriately balance convergence, diversity and feasibility. Their imbalance can easily cause the failure of a constrained multiobjective evolutionary algorithm (CMOEA) in converging to the Pareto-optimal front with diverse feasible solutions. To address this challenge, we propose a dual-population-based evolutionary algorithm, named c-DPEA, for CMOPs. c-DPEA is a cooperative coevolutionary algorithm which maintains two collaborative and complementary populations, termedPopulation1andPopulation2. In c-DPEA, a novel self-adaptive penalty function, termedsaPF, is designed to preserve competitive infeasible solutions inPopulation1. On the other hand, infeasible solutions inPopulation2are handled using a feasibility-oriented approach. To maintain an appropriate balance between convergence and diversity in c-DPEA, a new adaptive fitness function, namedbCAD, is developed. Extensive experiments on three popular test suites comprehensively validate the design components of c-DPEA. Comparison against six state-of-the-art CMOEAs demonstrates that c-DPEA is significantly superior or comparable to the contender algorithms on most of the test problems.

Task scheduling of multiple UAVs has become a highly active area of research in recent years. Previous research has generally solved the problem in a whole manner, which makes it hard to efficiently generate high-quality task scheduling schemes due to prohibitive computational complexity. By contrast, the paper constructs a novel divide and conquer framework for multi-UAV task scheduling (DCF), which partitions the original multi-UAV scheduling problem into multiple scheduling sub-problems for all the UAVs. To be specific, DCF includes two phases: one is the task allocation phase which produces multiple scheduling sub-problems and the other is the single UAV scheduling phase which generates the scheduling scheme with sequential tasks for each single UAV considering constraints involving UAV capabilities and task demands. Two phases are iteratively performed until the predefined stopping criteria are met. In the task allocation phase, we propose a tabu-list-based simulated annealing (SATL) algorithm to realize task allocation among multiple UAVs. After obtaining the task allocation scheme, a satisfactory scheduling scheme of each single UAV is generated by variable neighborhood descent (VND) algorithm. Extensive experiments and comparative studies are conducted, demonstrating the efficiency of DCF and the proposed SATL-VND algorithm.

Constraint handling techniques are of great significance in efficiently solving constrained optimization problems. This paper proposes a novel ensemble framework for constraint handling techniques based on voting-mechanism, in which four popular constraint handling techniques are included. Each of the constituent constraint handling techniques votes for the solutions at each generation based on its own rules. Solutions getting more votes are regarded as promising individuals and survive to the next generation. This ensemble framework based on voting-mechanism reflects the collective wisdom in decision-making of human beings. In addition, a differential evolution (DE) variant is designed as the search engine, in which four search strategies are combined to generate new individuals and maintain the balance between diversity and convergence of the population. The proposed algorithm has been tested on 57 real world single-objective constraint optimization problems and 7 problems are selected using variable reduction strategy (VRS). The experiment shows that the proposed algorithm achieves competitive performance, indicating that the voting-mechanism ensemble constraint handling technique combine DE algorithm together can effectively deal with constrained optimization problems.

In many-objective optimization problems (MaOPs), forming sound tradeoffs between convergence and diversity for the environmental selection of evolutionary algorithms is a laborious task. In particular, strengthening the selection pressure of population toward the Pareto-optimal front becomes more challenging, since the proportion of nondominated solutions in the population scales up sharply with the increase of the number of objectives. To address these issues, this paper first defines the nondominated solutions exhibiting evident tendencies toward the Pareto-optimal front as prominent solutions, using the hyperplane formed by their neighboring solutions, to further distinguish among nondominated solutions. Then, a novel environmental selection strategy is proposed with two criteria in mind: 1) if the number of nondominated solutions is larger than the population size, all the prominent solutions are first identified to strengthen the selection pressure. Subsequently, a part of the other nondominated solutions are selected to balance convergence and diversity and 2) otherwise, all the nondominated solutions are selected; then a part of the dominated solutions are selected according to the predefined reference vectors. Moreover, based on the definition of prominent solutions and the new selection strategy, we propose a hyperplane assisted evolutionary algorithm, referred here as hpaEA, for solving MaOPs. To demonstrate the performance of hpaEA, extensive experiments are conducted to compare it with five state-of-the-art many-objective evolutionary algorithms on 36 many-objective benchmark instances. The experimental results show the superiority of hpaEA which significantly outperforms the compared algorithms on 20 out of 36 benchmark instances.

The evolutionary multi-objective optimization algorithm was used to optimize the clustering and splitting of nodes in the construction of inverted spatial objects index tree(ITSR) in this paper. Considering the objective factors including object's coverage, overlap, group center distance, directory rectangle perimeter and the word similarity between tree nodes, etc., a multi-objective optimization model for solving the optimal ITSR construction is established. To solve the model, this paper find a novel method of constructing high efficiency inverted text-spatial R-tree index. The experimental results show that the algorithm supports the multi-objective optimal clustering of ITSR with high efficiency and accuracy .

The brain storm optimization (BSO) algorithm is a new and promising swarm intelligence paradigm, based on the emerging intelligence of the human brain storming process. However, BSO is ineffective to deal with the large data sets because its clustering and idea updating operations are computationally expensive. Aiming at this issue, we propose a parallelized brain storm optimizer based on Spark framework called PLBSO. The basic idea is to parallelize the complex operations of population clustering and idea updating in BSO so as to reduce the computation cost. Especially, the generation process of new ideas is modified to make BSO more suitable for parallelism. In addition, a new parallelized algorithm called PBAR based on PLBSO is proposed for association rule mining. The performance of PLBSO is evaluated over serialized BSO on complex multimodal benchmarks. Results show that, compared with serialized BSO, PLBSO can acquire a 350% speedup approximately while keeping similar accuracy. Finally, PBAR is adopted to resolve the association rule mining problem on a transactional dataset taken from IBM SPSS modeler. The encouraging results prove the validity of our algorithms.

The brain storm optimization (BSO) algorithm is a new and promising swarm intellgience paradigm, inspired from the behaviors of the human process of brainstorming. The noverty of BSO lies in the clustering mechanism where the ideas are clustered into a set of groups and each idea learns from experiences of one inter-cluster or two intra-cluster neighbors. However, this mechanism is inefficient to deal with complex optimiaiton problems. In this paper, we propose an improved BSO algorithm called OSBSO using orthogonal experimental design (OED) strategy, which aims to discover useful search experiences for improving the convergence and solution accurancy. In OSBSO, two new clustering procedures are developed, i.e., orthogonal initialization and orthogonal clustering. The orthogonal initialization aims to improve the uniformity of the initial cluster centers in the objective space instead of the decision space, which can enhance the convergence performance. The orthogonal clustering uses the information between inter- cluster and intra-cluster indviduals to alleviate the evolution stagnation of clusters. Experiments are conducted on a set of the CEC2017 benchmark functions and the results verify the effectivenss and efficiency of OSBSO.

Chinese herbal medicine is an important part of traditional Chinese medicine (TCM). With developing of traditional Chinese medicine, the usage of Chinese herbal medicine is growing rapidly. It is essential to identify Chinese herbal medicine correctly since Chinese herbal medicine is used to treat disease. However, identifying Chinese herbal medicine is a hard task because lots of Chinese herbal medicine with different properties displays similar appearance, such as Radix StephaniaeTetrandrae and Radix Paeoniae Alba. Traditional methods of classifying Chinese herbal medicine are low-efficiency and rely on professional medical knowledge. Machine learning methods can reduce the need for professional knowledge in some fields due to its self-learning ability. In this study, a framework, called CNN & BLS, combining the convolutional neural network (CNN) with broad learning system (BLS) for identifying the Chinese herbal medicine, is proposed. Experimental results show the CNN & BLS displays the promising performance for identifying Chinese herbal medicine.

Decomposition via scalarization is a basic concept for multiobjective optimization. The weighted sum (WS) method, a frequently used scalarizing method in decomposition-based evolutionary multiobjective (EMO) algorithms, has good features such as computationally easy and high search efficiency, compared to other scalarizing methods. However, it is often criticized by the loss of effect on nonconvex problems. This paper seeks to utilize advantages of the WS method, without suffering from its disadvantage, to solve many-objective problems. A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner. That is, for each search direction, the optimal solution is selected only amongst its neighboring solutions. The neighborhood is defined using a hypercone. The apex angle of a hypervcone is determined automatically in a priori. The effectiveness of MOEA/D-LWS is demonstrated by comparing it against three variants of MOEA/D, i.e., MOEA/D using Chebyshev method, MOEA/D with an adaptive use of WS and Chebyshev method, MOEA/D with a simultaneous use of WS and Chebyshev method, and four state-of-the-art many-objective EMO algorithms, i.e., preference-inspired co-evolutionary algorithm, hypervolume-based evolutionary, θ-dominance-based algorithm, and SPEA2+SDE for the WFG benchmark problems with up to seven conflicting objectives. Experimental results show that MOEA/D-LWS outperforms the comparison algorithms for most of test problems, and is a competitive algorithm for many-objective optimization.

Wind speed prediction plays a crucial role in energy system planning and management. This study proposes to predict wind speed using a cooperative coevolution (CC) genetic algorithm based on back propagation (GABP) neural network. A decomposition method is provided to decompose decision variables into several subcomponents, simultaneously, independence among variables in different subcomponents are kept to a minimum. With neuron-based sub-population (NSP), the simulation results show that the proposed method CC-GABP achieves higher prediction precision.

Decomposition-based algorithms have become increasingly popular for evolutionary multiobjective optimization. However, the effect of scalarizing methods used in these algorithms is still far from being well understood. This paper analyzes a family of frequently used scalarizing methods, the Lpmethods, and shows that the p value is crucial to balance the selective pressure toward the Pareto optimal and the algorithm robustness to Pareto optimal front (PF) geometries. It demonstrates that an Lpmethod that can maximize the search ability of a decomposition-based algorithm exists and guarantees that, given some weight, any solution along the PF can be found. Moreover, a simple yet effective method called Pareto adaptive scalarizing (PaS) approximation is proposed to approximate the optimal p value. In order to demonstrate the effectiveness of PaS, we incorporate PaS into a state-of-the-art decomposition-based algorithm, i.e., multiobjective evolutionary algorithm based on decomposition (MOEA/D), and compare the resultant MOEA/D-PaS with some other MOEA/D variants on a set of problems with different PF geometries and up to seven conflicting objectives. Experimental results demonstrate that the PaS is effective.

For real-world problems, the task of decision-makers is to identify a solution that can satisfy a set of performance criteria, which are often in conflict with each other. Multi-objective evolutionary algorithms tend to focus on obtaining a family of solutions that represent the trade-offs between the criteria; however ultimately a single solution must be selected. This need has driven a requirement to incorporate decision-maker preference models into such algorithms - a technique that is very common in the wider field of multiple criteria decision making. This paper reviews techniques which have combined evolutionary multi-objective optimization and multiple criteria decision making. Three classes of hybrid techniques are presented: a posteriori, a priori, and interactive, including methods used to model the decision-makers preferences and example algorithms for each category. To encourage future research directions, a commentary on the remaining issues within this research area is also provided.

Bounded model checking (BMC, for short) is a successful application of SAT technique in model checking. In a broad sense, BMC encoding approaches could be categorised into the syntactic fashion and semantic fashion. In this paper, we present a new BMC encoding approach specially tailored for LTL model checking. The key observation is that syntactic encoding and semantic encoding respectively have the superiority in dealing with "next" operator and "until" operator in the specification. The proposed encoding could be implemented in an "on-the-fly" manner, and finally results in a linear scale blow-up. To justify it, the approach is experimentally evaluated by comparing with some of the best known existing encodings.

Preference-inspired co-evolutionary algorithms (PICEAs) are a novel class of population-based approaches for multi-objective optimization. PICEA-g is one realization of PICEAs in which goal vectors are taken as preferences and are co-evolved with the candidate solutions during the search. The performance of PICEA-g is affected by the distribution of the co-evolved goal vectors. In PICEA-g, new goal vectors are generated within pre-defined bounds determined by the ideal and anti-ideal points in each generation. Such bounds are often unknown or at least problem knowledge requires. In this paper, firstly, we analyse the influence of different initial bounds to the performance of PICEA-g. Then, we propose a method, called cutting plane, which adaptively sets proper bounds for the generation of goal vectors, adjusting the search effort toward different objective appropriately, and therefore guide the candidate solutions toward the Pareto optimal front efficiently. Experimental results show that this adaptive approach is effective.

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has become increasingly popular in solving multi-objective problems (MOPs). In MOEA/D, weight vectors are responsible for maintaining a nice distribution of Pareto optimal solutions. Often, we expect to obtain a set of uniformly distributed solutions by applying a set of uniformly distributed weight vectors in MOEA/D. In this paper, we argue that uniformly distributed weights do not produce uniformly distributed solutions, however, uniformly distributed search directions do. Moreover, we propose to perform a pre-organization procedure before running MOEA/D. The procedure matches each weight to its closet candidate solution. Experimental results show (i) MOEA/D with uniformly distributed search directions would exhibit a better diversity performance, and (ii) MOEA/D with the pre-organization procedure performs better, especially for the convergence performance.

Preference-inspired co-evolutionary algorithm (PICEA) is a novel class of multi-objective evolutionary algorithm. In PICEA, the usual candidate solutions are guided toward the Pareto optimal front by co-evolving a set of decision maker preferences during the search process. PICEA-g is one realization of PICEAs in which goal vectors are taken as preferences. This study points out one limitation of this method -the obtained solutions are distributed unevenly along the Pareto optimal front. To handle this limitation, an improved fitness assignment method is proposed in which the density information of the solutions is considered. Experimental results, in terms of the selected performance metrics, show this improved fitness assignment method is effective.

The simultaneous optimization of many objectives (in excess of 3), in order to obtain a full and satisfactory set of tradeoff solutions to support a posteriori decision making, remains a challenging problem. The concept of coevolving a family of decision-maker preferences together with a population of candidate solutions is studied here and demonstrated to have promising performance characteristics for such problems. After introducing the concept of the preference-inspired coevolutionary algorithm (PICEA), a realization of this concept, PICEA-g, is systematically compared with four of the best-in-class evolutionary algorithms (EAs); random search is also studied as a baseline approach. The four EAs used in the comparison are a Pareto-dominance relation-based algorithm (NSGA-II), an$\epsilon$-dominance relation-based algorithm [$\epsilon$-multiobjective evolutionary algorithm (MOEA)], a scalarizing function-based algorithm (MOEA/D), and an indicator-based algorithm [hypervolume-based algorithm (HypE)]. It is demonstrated that, for bi-objective problems, all of the multi-objective evolutionary algorithms perform competitively. As the number of objectives increases, PICEA-g and HypE, which have comparable performance, tend to outperform NSGA-II,$\epsilon$-MOEA, and MOEA/D. All the algorithms outperformed random search.

Preference-inspired co-evolutionary algorithms (PICEAs) are a new class of approaches which have been demonstrated to perform well on multi-objective problems (MOPs). The good performance of PICEAs is largely due to its clever fitness calculation method which is in a competitive co-evolutionary way. However, this fitness calculation method has a potential limitation. In this work, we analyze this limitation and propose to implement PICEAs within a local structure (LPICEAs). By using the local structure, the benefits of local operations are incorporated into PICEAs. Meanwhile, the limitation of the original fitness calculation method is solved. In details, the candidate solutions are firstly partitioned into several clusters according to a clustering technique. Then the evolutionary operations, i.e. selection-for-survival and genetic-variation are executed on each cluster, separately. To validate the performance of LPICEAs, LPICEAs are compared to PICEAs on some benchmarks functions. Experimental results indicate LPICEAs significantly outperform PICEAs on most of the benchmarks. Moreover, the influence of LPICEAs to the tuning of the parameter k, i.e. the number of clusters used in LPICEAs is studied. The results indicate that the performance of LPICEAs is sensitive to the parameter k.

The quality of an approximation set usually includes two aspects-- approaching distance and spreading diversity. This paper introduces a new technique for assessing the diversity of an approximation to an exact Pareto-optimal front. This diversity is assessed by using an ldquoexposure degreerdquo of the exact Pareto-optimal front against the approximation set. This new technique has three advantages: Firstly, The ldquoexposure degreerdquo combines the uniformity and the width of the spread into a direct physical sense. Secondly, it makes the approaching distance independent from the spreading diversity at the most. Thirdly, the new technique works well for problems with any number of objectives, while the widely used diversity metric proposed by Deb would work poor in problems with 3 objectives or over. Experimental computational results show that the new technique assesses the diversity well.

This paper proposes a new evolutionary algorithm with lower dimensional crossover and gradient-based mutation for real-valued optimization problems with constraints. The crossover operator of the new algorithm searches a lower dimensional neighbor of the parent points where the neighbor center is the barycenter of the parents, and therefore the new algorithm converges fast. The gradient-based mutation is used to converge fast for the problems with equality constraints and active inequality constraints. And the new algorithm is simple and easy to be implemented. We have used 24 constrained benchmark problems to test the new algorithm. The experimental results show it works better than or competitive to a known effective algorithm.

Since the emergence of peer-to-peer (P2P) networking in the last 90s, P2P traffic has become one of the most significant portions of the network traffic. Accurate identification of P2P traffic makes great sense for efficient network management and reasonable utility of network resources. Application level classification of P2P traffic, especially without payload feature detection, is still a challenging problem. This paper proposes a new method for P2P traffic identification and application level classification, which merely uses transport layer information. The method uses Support Vector Machines which have been optimized for performing large learning tasks, rendering that this method become more suitable for large network traffic. The experimental results show that this method achieved high efficiency and is suitable for real-time identification. And carefully tuning the parameters could make the method achieve high accuracy.

A robust dynamic evolutionary algorithm (labeled RODEA), where both the robust calculation and mutation operator are based on an orthogonal design, is proposed in this paper. Previous techniques calculate the mean effective objective (for robust) by using samples without much evenly distributing over the neighborhood. The samples by using orthogonal array distribute evenly. Therefore the calculation of mean effective objective more robust. The new technique is generalized from the ODEA algorithm [1]. An orthogonal design method is employed on the niches for the mutation operator to find a potentially good solution that may become the representative in the niche. The fitness of the offspring is therefore likely to be higher than that of its parent. We propose a complex benchmark, consisting of moving function peaks, to test our new approach. Numerical experiments show that the moving solutions of the algorithm are a little worse in objective value but robust.