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This paper addresses the design problem of the discrete-time stable unknown input estimator (UIE) based on parameter optimization using the artificial bee colony (ABC) algorithm. First, a stability-guaranteed design method for UIEs is presented, and a sufficient condition for the applicability of the design is provided. Next, to design UIEs with good disturbance rejection properties, a new objective function is developed that incorporates both waveform-based and norm-based performance criteria to allow direct evaluation of the adverse effects of disturbances on system performance. Finally, the proposed design method is compared with the previous one using an objective function based on the estimated disturbance to confirm the improvement of the disturbance rejection properties at the plant output. Furthermore, as another approach to the design of stable UIEs, the original UIE design method is combined with a constrained ABC algorithm, and the approach is compared with the proposed one in terms of disturbance rejection properties. • A design of the discrete-time stable unknown input estimator is addressed. • A new objective function is developed that incorporates both waveform-based and norm-based performance criteria. • The artificial bee colony algorithm is used to efficiently optimize the design parameters in the unknown input estimator. • A comparison with the constrained optimization approach is made. [ABSTRACT FROM AUTHOR]

An optimization spiking neural P (OSN P) system is a discrete optimization model without the aid of evolutionary operators of evolutionary algorithms or swarm intelligence algorithms. However, since the processing object of OSN P systems is a spike, where information is encoded by the timing of spikes or the number of spikes in neurons, OSN P systems are limited for solving continuous optimization problems. To break this limitation, an extended numerical spiking neural (ENSN P) system is proposed based on numerical spiking neural P (NSN P) systems and multiple (ENSN P) systems, called optimization numerical spiking neural P systems (ONSN P systems or ONSNPS), are designed to solve continuous constrained optimization problems. More specifically, in ENSN P systems, the production functions are selected by probability to achieve updated parameters. In OSN P systems, a guider algorithm is introduced to finish individuals' crossover and selection. The extensively experimental results in five benchmarks, thirty-two optimization problems including five benchmark problems, seventeen manufacturing design optimization problems and ten benchmarks from CEC show that ONSN P systems in this paper outperform or are competitive to twenty-eight optimization algorithms. Finally, algorithm complexity and Holm-Bonferroni procedure based on statistical results is used to test the complexity changing when we use different dimensionality of the search space and the difference in terms of statistical performance. The testing results indicate that the time complexity of ONSN P systems grows linearly with problem dimensions and ONSN P systems are better performance than the most algorithms. [ABSTRACT FROM AUTHOR]

Most metaheuristic optimizers rely heavily on precisely setting their control parameters and search operators to perform well. Considering the complexity of real-world problems, it is always preferable to adjust control parameter values automatically rather than clamping them to a fixed value. In recent years, Spherical Search (SS) has emerged as a population-based stochastic optimization method that exploits the concepts of random projection matrices in linear algebra. As a result of the success of SS in solving non-convex, real-parameter optimization problems of various complexity, we have significantly extended SS in this paper by introducing a set of new algorithms, collectively known as Self Adaptive Spherical Search (SASS). Our proposal aims to enhance the performance of SS by using different projection matrix schemes in conjunction with improved search-direction calculations and an adaptive modification of parameter values. In our proposed adaptation scheme, parameters are modified to relevant values by applying a self-adaptive process that does not rely upon prior knowledge of the correlation between the parameter values and characteristics of the problem space. Consequently, we may apply the algorithms to bound and nonlinearly constrained optimization problems. For the benchmark suites derived from the most recent IEEE Congress on Evolutionary Computation (CEC) competitions, simulation results indicate that the SASS family of algorithms performs better than or is comparable to state-of-the-art algorithms from the other paradigms concerning robustness and convergence. [ABSTRACT FROM AUTHOR]

In this paper, we correct some errors in the extended first and second Gordan's theorems in a recent paper—Information Sciences 504 (2019) 276–292. [ABSTRACT FROM AUTHOR]

Space Surveillance Network (SSN) task scheduling plays a crucial role in maintaining the catalog of Resident Space Objects (RSO). However, various emergencies, such as RSO maneuvering, collisions, or rocket launch, may disrupt the original scheduled scheme. Therefore, it is essential to rapidly regenerating emergency schemes while minimizing disturbance to the initial scheduling scheme. This paper introduces an Emergency Task Scheduling model, referred to as MM-ETS, which aims to Maximize observation profits and Minimize disturbance. This model incorporates constraints related to observability, tasks, and resources, which are derived from practical applications. Additionally, a Hierarchical Distributed Dynamic Emergency Scheduling algorithm, encompassing Task assignment, Conflict resolution, Resource negotiation, and Center collaboration (HD-TCRC-DES), is proposed. The presented algorithm is activated by emergencies and a Rolling Horizon Strategy (RHS) is employed to break down long-term, large-scale problems into short-term, small-scale problems, thus improving feasibility and emergency response capabilities. At each layer of the proposed algorithm, heuristic rules are utilized to solve the new scheme, which helps allocate the computational load to resource nodes, and quickly adjust the initial scheduling scheme. Experimental scenarios involving 15 ground observation resources and 1000 emergency tasks are constructed, and the simulation results demonstrate that the proposed method can enhance Comprehensive Benefits Indicators (CBI) by approximately 24.65%, 24.7%, 24.91%, and 30.5% compared to the baselines. Consequently, it is suitable for SSN emergency task scheduling. [ABSTRACT FROM AUTHOR]

For data analysis, learning treatment rules in stratified medicine require the optimization of multiple responses. A common approach is to use a multi-objective function to find the optimal setting of the controllable factors. For patients, the optimal setting is a treatment regimen that yields the optimal value of potential responses. However, subclasses of patients are often stratified by their covariates. Thus, this paper proposes a new model called constrained optimization for stratified treatment rules (COSTAR) with multiple responses. This model incorporates covariates to build separate models for optimal responses and stratifies the patients with the balancing score from covariates. The optimal solution enables us to choose the optimal treatment for each subclass of patients. Theoretical results guarantee the identifiability of the solutions with conditional optimal values of multiple responses from survival probabilities. Examples of experiments with factorial designs and survival data validate the efficacy of the proposed method. The results suggest that this method improves the significance of the parameters and the adjusted R 2 in fitting on the primary response, while the unsupervised clustering method (i.e., k -means) does not. This method, with the fitting model, is more interpretable than the conventional method and provides optimal treatment rules for stratified patients. [ABSTRACT FROM AUTHOR]

Distributed optimization algorithms have the advantages of privacy protection and parallel computing. However, the distributed nature of these algorithms makes the system vulnerable to external attacks. This paper presents two penalty function based resilient algorithms for constrained distributed optimization under static and dynamic attacks. The objective function of the optimization problem is extended to nonsmooth ones and the convergence of the proposed algorithms in this case are proved under some mild conditions. Simulation experiments are performed and compared with some existing resilient primal-dual optimization algorithms using median-based mean estimator. For static attack, the proposed algorithm has better performance and faster convergence rate in the simulation experiments. For dynamic attack, the proposed algorithm has better performance and robustness in the simulation experiments, which illustrate that the proposed algorithms are more effective. [ABSTRACT FROM AUTHOR]

• A novel completely stealthy attack model is proposed. • The remote estimation error is analyzed which is more complicated. • The optimal policy is derived by solving the transformed optimization problem. This paper investigates the problem of designing the optimal completely stealthy attacks in cyber-physical systems. Different from the strictly stealthy attacks in the existing results which still have the possibilities to trigger the alarm and be invalid, a completely stealthy attack model is proposed such that the attack signals are able to bypass the detector successfully without being detected. Under the framework of the attacks, the remote estimation error is analyzed by deriving the recursion of the error covariance matrix, based on which the problem of attack design is transformed into a constrained optimization problem. By employing the Lagrange multiplier method, the optimal attack policy is derived which maximizes the remote estimation error and guarantees the complete stealthiness to the detector concurrently. Finally, simulation examples are provided to illustrate the effectiveness of this work. [ABSTRACT FROM AUTHOR]

In the constrained multi-objective optimization problems, the pursuit of feasibility could improve convergence but will lead to the loss of diversity. For optimization algorithm, balancing the weight between convergence and diversity dynamically is a challenge, especially in problems with low proportion of feasible regions. In this paper, a constrained multi-objective optimization algorithm is proposed based on a hybrid driven strategy to enhance both the feasibility and diversity performance of the approximate Pareto solutions. The proposed algorithm contains two archives, that one is driven by feasibility information and the other is driven by diversity information. A self-adaptive archive selection mechanism and a conditional tournament selection strategy are proposed to provide mating parent solutions according to the evolutionary stage. Moreover, in the update of the feasibility archive, an evolutionary direction prediction mechanism is proposed and adopted to improve the evolutionary efficiency. Compared to four other multi-objective algorithms on three benchmark suits of different types, the performance of the proposed algorithm is better than the peer algorithms, especially in large-infeasible-regions multi-objective optimization problems. [ABSTRACT FROM AUTHOR]

This paper presents an online-learning ensemble framework for nonstationary time series prediction. Optimal granular fuzzy rule-based models with different objective functions and constraints are evolved from data streams. Evolving optimal granular systems (eOGS) consider multiobjective optimization, the specificity of information, model compactness, and variability and coverage of the data within the process of modeling data streams. Forecasts of individual base eOGS models are combined using averaging aggregation functions: ordered weighted averaging (OWA), weighted arithmetic mean, median, and linear non-inclusive centered OWA. Some aggregation functions use specific weights for the relevance of the base models and exclude extreme values and outliers. The weights of other aggregation functions are adapted over time based on a quadratic programming problem and the data within a sliding window. This paper investigates whether an online-learning ensemble can outperform individual eOGS models, and which aggregation function provides the most accurate forecasts. Real multivariate weather time series, particularly time series of daily mean temperature, air humidity, and wind speed from different weather stations, such as Paris–Orly, Frankfurt–Main, Reykjavik, and Oslo–Blindern, are used for evaluation. The results show that ensemble schemes outperform individual models. The proposed linear non-inclusive centered OWA function provided the most accurate numerical predictions. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) require a delicate balance between satisfying constraints and optimizing objectives. Existing constrained multi-objective evolutionary algorithms (CMOEAs) often struggle to balance convergence, diversity, and feasibility, especially when dealing with CMOPs that have complex feasible regions. This paper proposes a multi-task-based self-organizing mapping evolutionary algorithm (MTSOM) to tackle this challenge, which includes a main and auxiliary task. Two populations independently optimize two tasks without considering constraints in the early stage. Subsequently, in the middle stage, both tasks explore the distribution structure of the population in parallel by employing a novel constraint-to-constraint self-organizing mapping (SOM) approach. In the late stage, the main task fully considers feasibility, while the auxiliary task focuses solely on the highest priority constraints. This approach enables rapid convergence toward feasible regions. To evaluate MTSOM's effectiveness, we conducted a series of experiments on five benchmark suites. Results indicate that MTSOM is competitive when compared to other state-of-the-art CMOEAs. Additionally, our proposed constraint-to-constraint SOM is superior in handling complex CMOPs. [ABSTRACT FROM AUTHOR]

Network pruning has been a hot topic in recent years, and many popular pruning methods rely on network design expertise. However, the pruning process usually involves manual intervention and can be difficult for users who lack prior knowledge. Automatic pruning using evolutionary algorithms shows great promise, but it must address the challenge of performing time-consuming model evaluations and searching through a large solution space. Dataset distillation is a technique that compresses the original dataset to decrease the cost of fine-tuning models. In this paper, we explore the potential of using the distilled dataset to exhibit a similar role as the real dataset in network pruning, and proposed the evolutionary pruning framework using distilled dataset. Specifically, the network pruning pipeline is carried out on the distilled dataset to significantly reduce the model evaluation cost, and the number of filters in the convolutional layer is directly coded to narrow the search space. In addition, a tailored evolutionary algorithm is proposed that takes the form of constrained optimization to search the most suitable pruned network. The experiments conducted on VGG16, VGG19, ResNet56, and ResNet110 demonstrate that the proposed method reduces at least 41.56% of the flops and achieves competitive results with little compromising accuracy. • Distillation dataset is first applied to network pruning. • A constrained evolutionary algorithm with double-balanced multi-branch is proposed. • Deep convolutional neural network pruning is performed using the constrained evolutionary algorithm. [ABSTRACT FROM AUTHOR]

Many domination-based multi-objective evolutionary algorithms (MOEAs) are designed for constrained multi-objective optimization problems (CMOPs). However, they still face the challenge of balancing the feasibility, convergence and distribution. This paper tackles this issue by proposing a multi-objective differential evolution algorithm based on domination and a mechanism of constraint-handling switching (MODE-CHS). In constraint-handling switching, if there are no feasible solutions in the population, the population evolves by constraint-handling; otherwise, the population evolves without handling constraints. This mechanism enhances the rate of population convergence to the maximum while obtaining the feasible solutions. Furthermore, in MODE-CHS, the feasible solutions are saved to an external archive and evolve together with the population to explore the feasible region. Meanwhile, to enhance the distribution, the offspring of the external archive also participates in the individual-update procedure of the population. 27 bench-mark test problems and two real-world problems are used for the performance comparison of the proposed algorithm with other five state-of-the-art algorithms. In the experiment, the proposed algorithm, MODE-CHS, is shown to produce satisfactory solutions for most of the tested functions, where other five MOEAs perform relatively worse. The experiment results demonstrate MODE-CHS is very competitive for solving CMOPs. [ABSTRACT FROM AUTHOR]

A key issue in evolutionary constrained optimization is how to achieve a balance between feasible and infeasible solutions. The quality of generated solutions in decomposition-based multi-objective evolutionary algorithms (MOEAs) depends strongly on the weights' setting. To fully utilize both the promising feasible and infeasible solutions, this paper proposes two-type weight adjustments based on MOEA/D for solving highly constrained many-objective optimization problems (CMaOPs). During the course of the search, the number of infeasible weights is dynamically reduced, to guide infeasible solutions with better convergence to cross the infeasible barrier, and also to lead infeasible solutions with better diversity to locate multiple feasible subregions. Feasible weights are evenly distributed and keep unchanged throughout the evolution process, which aims to guide the population to search Pareto optimal solutions. The effectiveness of the proposed algorithm is verified by comparing it against six state-of-the-art CMaOEAs on three sets of benchmark problems. Experimental results show that the proposed algorithm outperforms compared algorithms on majority problems, especially on highly constrained optimization problems. Besides, the effectiveness of the proposed algorithm has also been verified on an antenna array synthesis problem. [ABSTRACT FROM AUTHOR]

Hybridization in context to Evolutionary Computation (EC) strives to combine operators, components, and the best merits of different EC paradigms, to form a new evolutionary algorithm that enjoys a statistically superior performance, compared to its ancestors, over a wide range of application-specific optimization problems. In this paper, we propose a simple yet powerful amalgam composed of a modified Cultural Algorithm (CA) that is supported with an Enhanced Levy Flight Search (ELFS) to guide the search and further promote the harmony between the explorative and exploitative capacities of the conventional techniques. The novel amalgam, denoted by q-a CA + m IS, utilizes a balanced search scheme where it employs an adapted Influence Function (IF) with a novel quality function that establishes a harmony between the Knowledge Sources (KSs) in the Belief Space (BS), and between the BS and other components in the hybrid to produce the most suitable knowledge needed for a certain search mode. The CA framework is reinforced with an updated Selection Function (SF) that employs a successful selection strategy that uses the extended situational knowledge for the future selection of individuals. The proposed algorithm is tested using more than 50 benchmark functions that are taken from the IEEE CEC'06, and the IEEE CEC'19 competitions on constrained real-parameter optimization. Moreover, three well-known engineering design problems are used to test the validity of the algorithm for the solution of complex real-life problems. The comparative study indicates that the q-a CA + m IS algorithm was able to obtain a statistically superior performance and scalability behavior over most of the considered functions in comparison with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• The niche-based density estimation and angle-based selection strategy are devised. • Individuals with poor diversity are identified by niche-based density estimation. • Individuals with worse convergence are removed via angle-based selection. • NAEA can be easily extended to constrained many-objective optimization problems. It is well known that balancing population diversity and convergence plays a crucial role in evolutionary many-objective optimization. However, most existing multiobjective evolutionary algorithms encounter difficulties in solving many-objective optimization problems. Thus, this paper suggests niche-based and angle-based selection strategies for many-objective evolutionary optimization. In the proposed algorithm, two strategies are included: niche-based density estimation strategy and angle-based selection strategy. Both strategies are employed in the environmental selection to eliminate the worst individual from the population in an iterative way. To be specific, the former estimates the diversity of each individual and finds the most crowded area in the population. The latter removes individuals with weak convergence in the same niche. Experimental studies on several well-known benchmark problems show that the proposed algorithm is competitive compared with six state-of-the-art many-objective algorithms. Moreover, the proposed algorithm has also been verified to be scalable to deal with constrained many-objective optimization problems. [ABSTRACT FROM AUTHOR]

Penalty function is well-known for constrained evolutionary optimization. An open question in the penalty function is how to tune the penalty coefficient. This paper proposes an adaptive fuzzy penalty method to address this issue, where the coefficient is adjusted at both the individual level and the population level. At the individual level, each individual chooses a penalty coefficient from a predefined domain according to some fuzzy rules. At the population level, the domain of the crisp output is adjusted adaptively by using population information. To enhance the population diversity, an effective mutation scheme is developed. Due to its numerous merits, differential evolution is used to design a search algorithm. By the above processes, a constrained optimization evolutionary algorithm called AFPDE is proposed. Since the objective function value and the degree of constraint violation are normalized, AFPDE is less problem-dependent than the seminal work of the fuzzy penalty method. AFPDE introduces a lower penalty value in the early stage of AFPDE while a higher one in the later stage. Thus, it can escape local optima in the infeasible region. Experiments on three well-known benchmark test sets and two mechanical design problems validate that AFPDE is competitive. [ABSTRACT FROM AUTHOR]

To solve constrained optimization problems (COPs), it is crucial to guide the infeasible solution to a feasible region. Gradient-based repair (GR) is a successful repair strategy, where the forward difference is often used to estimate the gradient. However, GR has major deficiencies. First, it is difficult to deal with individuals falling into the local optima. Second, large amounts of fitness evaluations are required to estimate the gradient. In this paper, we proposed a new repair strategy, random direction repair (RDR). RDR generates a set of random directions, and calculates the repair direction and the repair step size of infeasible individual to reduce its constraint violation. Since the introduction of randomness, RDR could deal with individuals falling into the local optima. Furthermore, RDR only requires a few number of fitness evaluation. To demonstrate the performance of RDR, RDR was embedded into two state-of-the-art evolutionary continuous constrained optimization algorithms, tested on the Congress on Evolutionary Computation 2017 constrained real-parameter optimization benchmark. Experimental results demonstrated that RDR combined with evolutionary algorithms are highly competitive. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) are difficult to handle because objectives and constraints need to be considered simultaneously, especially when the constraints are extremely complex. Some recent algorithms work well when dealing with CMOPs with a simple feasible region; however, the effectiveness of most algorithms degrades considerably for CMOPs with complex feasible regions. To address this issue, this paper proposes a multi-stage evolutionary algorithm, where constraints are added one after the other and handled in different stages of evolution. Specifically, in the early stages, the algorithm only considers a small number of constraints, which can make the population efficiently converge to the potential feasible region with good diversity. As the algorithm moves to the later stages, more constraints are considered to search the optimal solutions based on the solutions obtained in the previous stages. Furthermore, a strategy for sorting the constraint-handling priority according to the impact on the unconstrained Pareto front is proposed, which can accelerate the convergence of the algorithm. Experimental results on five benchmark suites and three real-world applications showed that the proposed algorithm outperforms several state-of-the-art constraint multi-objective evolutionary algorithms when dealing with CMOPs, especially for problems with complex constraints. [ABSTRACT FROM AUTHOR]

• A novel Kriging-assisted two-phase optimization framework is proposed based on TLBO's unique structure. • A data management approach is proposed to collect and organize the dynamically updated expensive samples. • Two prescreening operators are proposed in Kriging-assisted Teaching and Learning Phases to select elite individuals. • KTLBO performs efficient on 18 benchmark cases and can successfully solve actual engineering applications. In this paper, a novel algorithm KTLBO is presented to achieve computationally expensive constrained optimization. In KTLBO, Kriging is adopted to develop dynamically updated surrogate models for costly objective and inequality constraints. A data managing method aiming at solving expensive constrained problems is developed to archive, classify and update expensive samples, where a penalty function is set to adaptively select elite individuals. Moreover, based on the Teaching-Learning-based Optimization (TLBO), a Kriging-assisted two-phase optimization framework is presented to alternately conduct local and global searches. In Kriging-assisted Teaching and Learning Phases, two different prescreening operators considering the probability of feasibility are respectively proposed to select the high-quality samples around the present best solution and the samples exhibiting better space-filling performance, as an attempt to balance exploitation of surrogates and exploration of unknown area. In brief, KTLBO retains the meta -heuristic search mechanism of TLBO while adopting Kriging to accelerate its search, thereby acting as a novel idea for surrogate-assisted constrained optimization. Lastly, KTLBO is compared with 6 well-known methods on 27 benchmark cases, and then its significant advantages in expensive constrained optimization are verified. Furthermore, KTLBO is adopted to design the structure of a Blended-Wing-Body underwater glider, and the satisfactory solution is yielded. [ABSTRACT FROM AUTHOR]

This paper considers the constrained consensus problem over multi-cluster networks. It is assumed that the agents’ states are constrained by different sets, where each constraint set is privately known by the corresponding agent. Within this framework, a hierarchical projection-based consensus algorithm is presented to solve the considered problem. Technically, the consensus analysis of the proposed algorithm consists of the following three aspects: First, by using the property of the projection operator, the limiting behaviors of the agents’ states generated by the algorithm are investigated. Then, based on the limiting behaviors, it is proven that the agents’ states in the whole network achieve a constrained consensus. Furthermore, by introducing an important auxiliary variable that relates to the agents’ states, the linear convergence of the proposed algorithm is proved. Compared with the existing results, this paper generalizes the constrained consensus methods under single-cluster networks to the multi-cluster ones. Finally, simulations are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Integrative multi-view subspace clustering aims to partition observed samples into underlying clusters through fusing representative subspace information from different views into a latent space. The clustering performance relies on the accuracy of sample affinity measurement. However, existing approaches leverage the subspace representation of each view and overlook the learning of appropriate sample affinities. This paper proposes to learn a consensus affinity directly by merging subspace representations of different views on a Grassmann manifold while maintaining their geometric structures across these views. The proposed method not only preserves the structure of the most informative individual view, but also discovers a latent common structure across all views. The associated constrained optimization problem is solved using the alternating direction method of multipliers. Extensive experiments on synthetic and real-world datasets show that the proposed method outperforms several state-of-the-art multi-view subspace clustering methods. The affinity matrix obtained by our method can extract highly representative and latent common information to enhance the clustering performance. [ABSTRACT FROM AUTHOR]

Balancing multiple objectives and various constraints is crucial for effectively solving constrained multi-objective optimization problems (CMOPs). Excessive focus on either convergence or feasibility may not result in favorable outcomes of the algorithm. To confront this challenge, this paper proposes a cooperative evolutionary algorithm named SaE-CMO, which aims to achieve a harmonious balance between convergence and feasibility by extracting valuable information from both feasible and infeasible regions. To achieve this, SaE-CMO employs a dual-population approach to enhance search progress, consisting of a main population, Population1, and an auxiliary population, Population2. These two populations complement each other to achieve optimal results. A newly proposed self-adaptive epsilon method is employed in both Population1 and Population2, using different comparison criteria to select next population from mating pools, respectively. Population2 can retain some solutions that are well-constrained but poorly converged, thereby preserving information about both the constrained and the unconstrained Pareto front. This property enables Population2 to assist Population1 in maintaining diversity in certain complex CMOPs. To verify the effectiveness of SaE-CMO, we conduct experiments on three benchmark test instances and four real-world CMOPs with some related state-of-the-art constrained multi-objective optimization algorithms, experimental results prove that the proposed algorithm outperforms the compared algorithms. [ABSTRACT FROM AUTHOR]

It is of necessity to select appropriate optimization algorithms from an algorithm library due to the universality of constrained multi-objective optimization problems and the suitability of intelligent optimization algorithms, which requires a rich optimization algorithm library. This paper proposes a migration-based method of enriching the algorithm library for constrained multi-objective optimization problems. After calculating the similarity between problems based on their landscape features, the proposed method calculates the migration probabilities of intelligent optimization algorithms solving similar problems based on the performance of each algorithm and the similarity between problems. According to the redundancy and compatibility of components, the algorithms with large migration probabilities enrich the algorithm library for solving the current problem. Based on the enhanced algorithm library, a Softmax regression model is trained to generate an optimal intelligent algorithm to solve the current problem. The proposed method is applied to solve a series of constrained multi-objective optimization benchmark problems and the operation optimization problems of an integrated coal mine energy system, and the experimental results verify its effectiveness and feasibility. • A method based on landscape features is proposed to determine similar problems. • A method is given to select migrated algorithms based on similarity and performance. • A method based on redundancy and compatibility is presented to enrich an IOAL. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) are challenging due to the complexity of feasible regions caused by constraints, especially when facing small feasible ranges, multiple feasible regions, and complex distribution of feasible regions. Existing algorithms struggle to balance population convergence, diversity, and feasibility. This paper proposes a constrained multi-objective evolutionary algorithm framework based on global and local feasible solutions search to address this issue. The proposed framework is divided into three stages, and an adaptive method is proposed to decide when to switch the search state. In the first two stages, the evolution of the population is relatively free and not subject to constraint restrictions. Feasible solutions in the population are saved in the FeasiblePool for environmental selection during these two stages. The FeasiblePool does not affect the evolving population during these stages. In the first stage, the framework uses global search operator to fully explore the decision space and determine the rough range of feasible solutions in the decision space. In the second stage, the framework uses local search operator to enhance the diversity of FeasiblePool within this determined range. In the last stage, the framework reuses these excellent feasible solutions information to guide population evolution while considering constraints. The proposed framework has been compared with four state-of-the-art constrained multi-objective algorithms on four benchmark suites and three real-world applications. The complete experimental results show that the proposed framework has high competitiveness for solving CMOPs. [ABSTRACT FROM AUTHOR]

• A novel CHT is proposed based on Pareto dominance-based ranking and CDP-based ranking. • A search algorithm based on four mutation operators is proposed. • A new constrained multiobjective differential evolution algorithm is proposed. The tradeoff between objective functions and constraints is a key issue that needs to be addressed by constrained multiobjective optimization algorithms, and constraint handling techniques (CHTs) are an important technique for balancing objective functions and constraints. In this paper, a novel CHT that fuses two rankings is proposed. Specifically, each individual is assigned two rankings: one ranking calculated based on Pareto dominance (regardless of constraints) and another calculated based on the constrained dominance principle (CDP). The fitness value of an individual is the weighted sum of these two rankings, and the weight is related to the generation number and the proportion of feasible solutions in the current generation. Based on the proposed CHT, a constrained multiobjective differential evolution algorithm is proposed. To generate high-quality offspring, the proposed constrained multiobjective differential evolution algorithm combines four mutation operations as core components of the search algorithm. The proposed algorithm is compared with eight state-of-the-art algorithms in experiments with five test suites, and the experimental results show that the proposed algorithm performs significantly better than the eight state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the problem of designing the worst-case ϵ-stealthy false data injection attacks in cyber-physical systems is investigated. The attacker attempts to degrade the remote state estimation performance by modifying the transmitted sensor measurements. Different from the existing ϵ-stealthy actuator attacks where the effect of the attacks is characterized by the information theoretic analysis, the remote estimation error is calculated with the statistical characteristics of the innovations and the problem is transformed into a constrained optimization problem with multiple decision variables. By utilizing the properties of the K-L divergence and mutual information, the problem is solved with the Lagrange multiplier method and the worst-case attack strategy is derived, which maximizes the estimation error and guarantees the stealthiness. Finally, simulation examples are provided to demonstrate the results. [ABSTRACT FROM AUTHOR]

This paper presents an extended Karush-Kuhn-Tucker condition to characterize efficient solutions to constrained interval optimization problems. We develop the theory from the geometrical fact that at an optimal solution the cone of feasible directions and the set of descent directions have an empty intersection. With the help of this fact, we derive a set of first-order optimality conditions for unconstrained interval optimization problems. In the sequel, we extend Gordan's theorems of the alternative for the existence of a solution to a system of interval linear inequalities. Using Gordan's theorem, we derive Fritz John and Karush-Kuhn-Tucker necessary optimality conditions for constrained interval optimization problems. It is observed that these optimality conditions appear with inclusion relations instead of equations. The derived Karush-Kuhn-Tucker condition is applied to the binary classification problem with interval-valued data using support vector machines. [ABSTRACT FROM AUTHOR]

Privacy-preserving methods play an indispensable role in protecting agents' cost functions from being disclosed during the dispatch process. In this paper, we aim at resolving Economic Dispatch Problems (EDPs) over multi-agent systems in a fully decentralized and privacy-preserving manner. Based on both row- and column-stochastic weight matrices, we first design a fully decentralized algorithm without any privacy-masking techniques, namely F-Deed, to resolve a class of structured EDPs over directed networks. We further consider an adverse case that potential attackers including both internal honest-but-curious adversaries and external eavesdroppers try to infer or steal the local cost functions of all agents to achieve their malicious goals. To protect agents' local cost functions against differential attacks, a differentially private algorithm, dubbed DPF-Deed, is developed via enhancing F-Deed with local differential privacy (LDP). To attain LDP, DPF-Deed decomposes the gradient tracker of F-Deed into two sub-trackers, with one of them invisible to any other agents, and masks a decomposed gradient with Laplace noise. Under standard assumptions, theoretical analysis validates that DPF-Deed can achieve linear convergence and an explicit trade-off between LDP and convergence accuracy, which are derived by analyzing the contraction relationships among the network consensus error, the optimal gap, and the gradient-tracking error. Theoretical results are validated by case studies for (dynamical) EDPs based on modified IEEE-14 and IEEE-118 bus systems. [ABSTRACT FROM AUTHOR]

To improve the utilization of infrastructure resources and reduce the cost of operators in the future 6G network construction, a 6G shared base stations optimization model is proposed in this paper, which is a bi-level multiobjective optimization problem (BLMOP). In such a BLMOP, the tower company is responsible for the construction of base stations at the upper level, while operators share the base station resources of the tower company at the lower level. In addition, we also propose two strategies to solve the optimization efficiently. First, we use surrogate models to fit lower-level Pareto fronts (PF), then the degree of lower-level optimality constraint violation is converted to distance between the candidate solutions and the approximate lower level PF. So the BLMOP is transformed to a single-level constrained multi-objective optimization problem. Second, to accelerate the current lower-level optimization, we migrate the modified population from the adjacent lower-level optimization tasks. These two strategies effectively reduce the computational overhead. Compared with three existing works, the proposed method has achieved the best or comparable results on 7 benchmark problems and 5 generated test instances with less computation overhead, whose efficiency has been confirmed. [ABSTRACT FROM AUTHOR]

• A RBF-assisted MOEA/D framework is designed to achieve adaptive search. • Different optimization states of subproblems are effectively identified by OSDM. • Optimization state-driven search strategies are used for targeted suboptimization. • The RBF accuracies are gradually improved by emphasizing specific points. • The performance difference of two classical decompositions has been well studied. In this paper, an adaptive surrogate-assisted MOEA/D framework (ASA-MOEA/D) is proposed for solving computationally expensive constrained multi-objective optimization problems, in which three specific search strategies are adaptively implemented based on the optimization states of subproblems to achieve targeted searches for different subproblems. To maintain feasibility, the RBF-based local search models are constructed by comprehensively considering the orthogonal distance difference and constraint satisfaction information for guiding infeasible solutions of the infeasible subproblems into feasible regions. To maintain convergence, the RBF surrogates of the aggregated objective and constraints are employed to construct local search models for locating better feasible solutions. To maintain diversity, the subregions of unexplored subproblems are effectively explored by utilizing the valuable information of their neighboring elite solutions. Moreover, the solution with the maximum overall uncertainty of RBF surrogates is selected for progressively increasing the prediction accuracies of surrogates. Therefore, ASA-MOEA/D strikes an adaptive balance among diversity, feasibility and convergence with the assistance of RBF surrogates as the optimization progresses. Empirical studies on three classical test suites demonstrate that ASA-MOEA/D with tchebycheff approach achieves highly competitive performance over other four state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In constrained optimisation, the augmented Lagrangian method is considered as one of the most effective and efficient methods. This paper studies the behaviour of augmented Lagrangian function (ALF) in the solution space and then proposes an improved augmented Lagrangian method. We have shown that our proposed method can overcome some of the drawbacks of the conventional augmented Lagrangian method. With the improved augmented Lagrangian approach, this paper then proposes a cooperative coevolutionary differential evolution algorithm for solving constrained optimisation problems. The proposed algorithm is evaluated on a set of 24 well-known benchmark functions and five practical engineering problems. Experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art algorithms with respect to solution quality as well as efficiency. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a new hybrid GSA-GA algorithm is presented for the constraint nonlinear optimization problems with mixed variables. In it, firstly the solution of the algorithm is tuned up with the gravitational search algorithm and then each solution is upgraded with the genetic operators such as selection, crossover, mutation. The performance of the algorithm is tested on the several benchmark design problems with different nature of the objectives, constraints and the decision variables. The obtained results from the proposed approach are compared with the several existing approaches result and found to be very profitable. Finally, obtained results are verified with some statistical testing. [ABSTRACT FROM AUTHOR]

Abstract Expected improvement (EI) is a popular infill criterion in Gaussian process assisted optimization of expensive problems for determining which candidate solution is to be assessed using the expensive evaluation method. An EI criterion for constrained expensive optimization (constrained EI) has also been suggested, which requires that feasible solutions exist in the candidate solutions. However, the constrained EI criterion will fail to work in case there are no feasible solutions. To address the above issue, this paper proposes a new EI criterion for highly constrained optimization that can work properly even when no feasible solution is available in the current population. The proposed constrained EI criterion can not only exploit local feasible regions, but also explore infeasible yet promising regions, making it a complete constrained EI criterion. The complete constrained EI is theoretically validated and empirically verified. Simulation results demonstrate that the proposed complete constrained EI is better than or comparable to five existing infill criteria. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a novel algorithm to solve real-world constrained optimization problems, which hybridizes multiobjective optimization techniques with an ϵ-constrained method. First, a constrained optimization problem at hand is transformed into a bi-objective optimization problem. By the transformation, the advantage of multiobjective optimization techniques can be utilized in the constrained optimization area to balance population diversity and convergence. Meanwhile, the ϵ-constrained method is applied, which keeps the population evolving toward feasible region of the constrained optimization problem. In our proposed algorithm, the differential evolution is employed as a search engine to create offspring at each generation. Further, different combinations of mutation operators have been developed to improve the search ability and the population convergence at different stages. The performance of our approach is evaluated on 64 benchmark test functions from three popular test suits. Experimental results demonstrate that our proposed approach is capable of obtaining high-quality solutions on the majority of benchmark test functions, when compared with some other state-of-the-art constrained optimization algorithms. [ABSTRACT FROM AUTHOR]

Constrained optimization problems (COPs) are common in many fields. To solve such problems effectively, in this paper, we propose a new constrained optimization evolutionary algorithm (COEA) named CACDE that combines an adaptive trial vector generation strategy-based differential evolution (DE) algorithm with a cluster-replacement-based feasibility rule. In CACDE, some potential mutation strategies, scale factors and crossover rates are stored in candidate pools, and each element in the pools is assigned a selection probability. During the trial vector generation stage, the mutation strategy, scale factor and crossover rate for each target vector are competitively determined based on these selection probabilities. Meanwhile, the selection probabilities are dynamically updated based on statistical information learned from previous searches in generating improved solutions. Moreover, to alleviate the greediness of the feasibility rule, the main population is divided into several clusters, and one vector in each cluster is conditionally replaced with an archived infeasible vector with a low objective value. The superior performance of CACDE is validated via comparisons with some state-of-the-art COEAs over 2 sets of artificial problems and 5 widely used mechanical design problems. The results show that CACDE is an effective approach for solving COPs, basically due to the use of adaptive DE and cluster-replacement-based feasibility rule. [ABSTRACT FROM AUTHOR]

Resource constrained project scheduling is critical in logistic and planning operations across a range of industries. Most businesses rely on priority rules to determine the order in which the activities required for the project should be executed. However, the design of such rules is non-trivial. Even with significant knowledge and experience, human experts are understandably limited in terms of the possibilities they can consider. This paper introduces a genetic programming based hyper-heuristic (GPHH) for producing efficient priority rules targeting the resource constrained project scheduling problem (RCPSP). For performance analysis of the proposed approach, a series of experiments are conducted on the standard PSPLib instances with up to 120 activities. The evolved priority rules are then compared against the existing state-of-the-art priority rules to demonstrate the efficacy of our approach. The experimental results indicate that our GPHH is capable of producing reusable priority rules which significantly out-perform the best human designed priority rules. [ABSTRACT FROM AUTHOR]

Least squares regression (LSR) is a widely used regression technique for multicategory classification. Conventional LSR model assumes that during the learning phase, the labeled samples can be exactly transformed into a discrete label matrix, which is too strict to learn a regression matrix for fitting the labels. To overcome this drawback, lots of LSR’s variants utilize the soft target label, which contains the continuous values, to replace this discrete label to improve the learning performance. Since the regression matrix can be learnt from these soft target labels, it is reasonable to assume that the samples in the same class have similar soft target labels. Nevertheless, most of existing LSR-based models don’t adequately consider this similarity assumption. In this paper, we propose a constrained least squares regression (CLSR) model for multicategory classification. The main motivation of CLSR is to force the samples in the same class to obtain the similar soft target labels. To effectively optimize CLSR, we propose a novel alternating algorithm, which can converge to the globally optimal solution. Extensive experiments results on face and digit data sets confirm the effectiveness of our proposed model. [ABSTRACT FROM AUTHOR]

The obnoxious p -median problem can be formulated as a constrained binary linear program. It is NP-hard, and has a lot of real world applications. In this paper, a hybrid binary particle swarm optimization is proposed to solve the obnoxious p -median problem. A new position updating rule is presented to inherit the good structure of previous high quality solutions. Furthermore, two tabu based mutation operators are used to avoid the premature convergence and guide the search to a promising area. A greedy repair procedure is developed to repair infeasible solutions. In addition, an iterated greedy local search procedure is utilized to enhance the exploitation ability. Extensive experiments are done on a set of 72 benchmark instances from the literature. Experimental results and comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm. In particular, the proposed algorithm finds new best solutions for 15 instances. Compared with existing algorithms, the proposed algorithm is able to find better average objective function value in a short average computing time. [ABSTRACT FROM AUTHOR]

Nature-inspired algorithms are a very important part of meta-heuristics. A novel nature inspired algorithm called the Dynamic Virtual Bats Algorithm (DVBA) is presented in this paper. DVBA is inspired by a bat’s ability to manipulate frequency and wavelength of the emitted sound waves when hunting. A role based search has been developed to improve the diversification and intensification capability of Bat Algorithm. In the DVBA, there are only two bats: explorer and exploiter bat. While the explorer bat explores the search space, the exploiter bat makes an intensive search of the local with the highest probability of locating the desired target. Depending on their location, bats exchange the roles dynamically. The performance of the DVBA is extensively evaluated on a suite of 30 bound-constrained optimization problems from CEC 2014 and compared favorably with other well-known meta-heuristics algorithms. The experimental results demonstrated that the proposed DVBA outperform, or is comparable to, its competitors in terms of the quality of final solution and its convergence rates. [ABSTRACT FROM AUTHOR]

This paper proposes an improved constrained teaching–learning-based optimization (ICTLBO) method to efficiently solve constrained optimization problems (COPs). In the teacher phase of ICTLBO, the population is partitioned into several subpopulations, and the direction information between the mean position of each subpopulation and the best position of population guide the corresponding subpopulation to the promising region promptly. Information exchange between different subpopulations is used to discourage premature convergence of each subpopulation. Furthermore, in the learner phase, a new learning strategy is introduced to improve the population diversity and enhance the global search ability. Three different constraint handling methods are adopted for three situations, which are infeasible, semi-feasible, and feasible situations, during the evolution process. To evaluate the performance of ICTLBO, 22 benchmark functions presented in CEC2006 and 18 benchmark functions introduced in CEC2010 are chosen as the test suite. Moreover, four widely used engineering design problems are selected to test the performance of ICTLBO for real-world problems. Experimental results indicate that ICTLBO can obtain a highly competitive performance compared with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a multi-cycled sequential memetic computing structure for constrained optimisation. The structure is composed of multiple evolutionary cycles. At each cycle, an evolutionary algorithm is considered as an operator, and connects with a local optimiser. This structure enables the learning of useful knowledge from previous cycles and the transfer of the knowledge to facilitate search in latter cycles. Specifically, we propose to apply an estimation of distribution algorithm (EDA) to explore the search space until convergence at each cycle. A local optimiser, called DONLP2, is then applied to improve the best solution found by the EDA. New cycle starts after the local improvement if the computation budget has not been exceeded. In the developed EDA, an adaptive fully-factorized multivariate probability model is proposed. A learning mechanism, implemented as the guided mutation operator, is adopted to learn useful knowledge from previous cycles. The developed algorithm was experimentally studied on the benchmark problems in the CEC 2006 and 2010 competition. Experimental studies have shown that the developed probability model exhibits excellent exploration capability and the learning mechanism can significantly improve the search efficiency under certain conditions. The comparison against some well-known algorithms showed the superiority of the developed algorithm in terms of the consumed fitness evaluations and the solution quality. [ABSTRACT FROM AUTHOR]

The knowledge of the similarity of two or more sequences is crucial in computational molecular biology. The longest common subsequence (LCS) is a well-known and widely used measure for sequence similarity. Constrained variants of the LCS problem have been studied in the literature where the knowledge of the functionalities or structures of the input sequences are provided in the form of inclusion/exclusion constraint patterns. In this paper we focus on different variants of the LCS problem involving multiple input sequences and constraint patterns. Given L input sequences and ℓ constraint patterns, the goal here is to construct an LCS of the given sequences such that each of the constraint patterns occurs/does not occur in the LCS as a subsequence/substring. We devise finite automata based efficient algorithms for all the variants of the problem that run in O ( | Σ | ( R + L ) + nL + | Σ | R n ℓ ) time, where R is the size of the resulting subsequence automaton, n is the length of each input sequence and Σ is the underlying alphabet. We also conduct an extensive experimental study to evaluate the practical performance of our algorithms. The experimental results suggest the superiority of our finite automata based algorithms. Therefore, we believe that our automata based algorithms will be useful in practical sequence analysis in computational biology and will replace the existing algorithms that are mostly based on memory intensive dynamic programming based methods. [ABSTRACT FROM AUTHOR]

Abstract: In recent years, many different variants of the particle swarm optimizer (PSO) for solving optimization problems have been proposed. However, PSO has an inherent drawback in handling constrained problems, mainly because of its complexity and dependency on parameters. Furthermore, one PSO variant may perform well for some test problems but not obtain good results for others. In this paper, our purpose is to develop a new PSO algorithm that can efficiently solve a variety of constrained optimization problems. It considers a mix of different PSO variants each of which evolves with a different number of individuals from the current population. In each generation, the algorithm assigns more individuals to the better-performing variants and fewer to the worse-performing ones. Also, a new PSO variant is developed for use in the proposed algorithm to maintain a better balance between its local and global PSO versions. A new methodology for adapting PSO parameters is presented and the proposed self-adaptive PSO algorithm tested and analyzed on two sets of test problems, namely the CEC2006 and CEC2010 constrained optimization problems. Based on the results, the proposed algorithm shows significantly better performance than the same global and local PSO variants as well as other-state-of-the-art algorithms. Although, based on our analysis, it cannot guarantee an optimal solution for any unknown problem, it is expected to be able to solve a wide variety of practical problems. [Copyright &y& Elsevier]