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To solve the constrained optimization problem, a new algorithm WDFSO is obtained by combining the exterior penalty function method and an improved snake optimization algorithm. Firstly, the constrained optimization problem is transformed into a series of bound-constrained optimization problems by the exterior penalty function method. Then, the improved snake optimization algorithm based on the oppositional learning of the centroid variation strategy and the population classification strategy is used to solve the bound-constrained optimization problem, and obtain the solution of the constrained optimization problem. In order to verify the effectiveness of WDFSO algorithm, 19 benchmark constrained optimization problems in CEC2006 are selected for numerical experiments, and the Wilcoxon rank sum test is used to prove the algorithm significance. The experimental results show that WDFSO algorithm has higher convergence accuracy and better stability than the comparison algorithms. Finally, WDFSO algorithm is applied to solve two engineering constraint optimization problems, and the results show that WDFSO algorithm has better performance. [ABSTRACT FROM AUTHOR]

In the last few decades, the particle swarm optimization (PSO) algorithm has been demonstrated to be an effective approach for solving real-world optimization problems. To improve the effectiveness of the PSO algorithm in finding the global best solution for constrained optimization problems, we proposed an improved composite particle swarm optimization algorithm (ICPSO). Based on the optimization principles of the PSO algorithm, in the ICPSO algorithm, we constructed an evolutionary update mechanism for the personal best position population. This mechanism incorporated composite concepts, specifically the integration of the e-constraint, differential evolution (DE) strategy, and feasibility rule. This approach could effectively balance the objective function and constraints, and could improve the ability of local exploitation and global exploration. Experiments on the CEC2006 and CEC2017 benchmark functions and real-world constraint optimization problems from the CEC2020 dataset showed that the ICPSO algorithm could effectively solve complex constrained optimization problems. [ABSTRACT FROM AUTHOR]

Under Type-II progressively censored data, joint confidence regions are proposed for the parameters of a general class of exponential distributions. The constrained optimization problem based on such censoring data can be adopted to obtain confidence regions for the unknown parameters of this general class with minimized size and a predetermined confidence level. The area of confidence sets are minimized by solving simultaneous non-linear equations. Two real data sets representing the duration of remission of leukemia patients and water level exceedances by River Nidd at Hunsingore located in New York, are analyzed by fitting appropriate well-known models. Further, numerical simulation study is performed to explain our procedures and findings here. [ABSTRACT FROM AUTHOR]

Motion planning and controller design are challenging tasks for highly coupled and nonlinear dynamical systems such as autonomous vehicles and robotic applications. Nonlinear model predictive control (NMPC) is an emerging technique in which sampling-based methods are used to synthesize the control and trajectories for complex systems. In this study, we have developed the sampling-based motion planning algorithm with NMPC through Bayesian estimation to solve the online nonlinear constrained optimization problem. In the literature, different filtration techniques have been applied to extract knowledge of states in the presence of noise. Due to the detrimental effects of linearization, the Kalman filter with NMPC only achieves modest effectiveness. Moving horizon estimation (MHE), on the other hand, frequently relies on simplifying assumptions and lacks an effective recursive construction. Additionally, it adds another optimization challenge to the regulation problem that has to be solved online. To address this problem, particle filtering is implemented for Bayesian filtering in nonlinear and highly coupled dynamical systems. It is a sequential Monte Carlo method that involves representing the posterior distribution of the state of the system using a set of weighted particles that are propagated through time using a recursive algorithm. For nonlinear and strongly coupled dynamical systems, the novel sampling-based NMPC technique is effective and simple to use. The efficiency of the suggested method has been assessed using simulated studies.

In a structural system, the connections (i.e., between the structural elements and the structure to the ground) play an important role in the integrity and stability of the system. So, using the certain pre-defined conventional properties for these systems can stand far away from the expected optimal condition. In this regard, the current study deals with optimal design (i.e., cost and geometry parameters under different loading conditions) of the footing systems applied in the precast industrial buildings and the concrete bracket system as the privilege connection type in the RC frames. To provide a broad perspective about the optimal design of these systems, several distinct optimization models are generated and solved. For solving the proposed optimization problems, a recently developed self-adaptive and non-gradient-based method, so-called Fuzzy Differential Evolution Incorporated Virtual Mutant (FDEVM), is utilized. In the developed models, effect of different loading conditions on the optimum geometry and cost parameters of the proposed systems are investigated. For this aim, sixty three different probable situations are considered and solved, and the attained outcomes are reported through illustrative tables and diagrams. The outcomes indicate that the vertical load and bracket width play important role in the total cost of the system. In addition, provided behavioral diagrams indicate that the FDEVM method shows a dynamic adaptive behavior on during the optimization process. [ABSTRACT FROM AUTHOR]

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The appearance and disappearance of the optimal solution for the change of system parameters in optimization theory is a fundamental problem. This paper aims to address this issue by transforming the solutions of a constrained optimization problem into equilibrium points (EPs) of a dynamical system. The bifurcation of EPs is then used to describe the appearance and disappearance of the optimal solution and saddle point through two classes of bifurcation, namely the pseudo bifurcation and saddle-node bifurcation. Moreover, a new class of pseudo-bifurcation phenomena is introduced to describe the transformation of regular and degenerate EPs, which sheds light on the relationship between the optimal solution and a class of infeasible points. This development also promotes the proposal of a tool for predicting optimal solutions based on this phenomenon. The study finds that the bifurcation of the optimal solution is closely related to the bifurcation of the feasible region, as demonstrated by the 5-bus and 9-bus optimal power flow problems.

Source localization is a critical issue in various wireless sensor network applications. However, communication and concealment constraints often restrict sensor placement, resulting in non-arbitrary sensor deployment regions. To further enhance localization accuracy, this paper presents an optimality analysis of range sensor placement under constrained deployment regions, focusing on optimal geometries rather than specific localization algorithms. The optimality analysis is formulated as a constrained optimisation problem that maximizes the determinant of the Fisher information matrix, also known as D-optimality, while taking into account the constraints imposed by the deployment region. To simplify the analysis, we introduce the concepts of maximum feasible angle and separation angle, which are used to express the objective function and constraints in equivalent forms. By comparing the maximum feasible angle with the optimal separation angles in unconstrained cases, our method will be applicable to both circular constrained regions and general irregular regions. The conclusions we have reached are comprehensive and intuitive, and they differ significantly from the conventional uniform angular geometry. The proposed range sensor-source geometries are verified through theoretical analysis and simulations. [ABSTRACT FROM AUTHOR]

The mathematical form of many optimization problems in engineering is constrained optimization problems. In this paper, an improved genetic algorithm based on two-direction crossover and grouped mutation is proposed to solve constrained optimization problems. In addition to making full use of the direction information of the parent individual, the two-direction crossover adds an additional search direction and finally searches in the better direction of the two directions, which improves the search efficiency. The grouped mutation divides the population into two groups and uses mutation operators with different properties for each group to give full play to the characteristics of these mutation operators and improve the search efficiency. In experiments on the IEEE CEC 2017 competition on constrained real-parameter optimization and ten real-world constrained optimization problems, the proposed algorithm outperforms other state-of-the-art algorithms. Finally, the proposed algorithm is used to optimize a single-stage cylindrical gear reducer.

An improved hybrid firefly algorithm with probability attraction model (IHFAPA) is proposed to solve the problems of low computational efficiency and low computational accuracy in solving complex optimization problems. First, the method of square-root sequence was used to generate the initial population, so that the initial population had better population diversity. Second, an adaptive probabilistic attraction model is proposed to attract fireflies according to the brightness level of fireflies, which can minimize the brightness comparison times of the algorithm and moderate the attraction times of the algorithm. Thirdly, a new location update method is proposed, which not only overcomes the deficiency in that the relative attraction of two fireflies is close to 0 when the distance is long but also overcomes the deficiency that the relative attraction of two fireflies is close to infinity when the distance is small. In addition, a combinatorial variational operator based on selection probability is proposed to improve the exploration and exploitation ability of the firefly algorithm (FA). Later, a similarity removal operation is added to maintain the diversity of the population. Finally, experiments using CEC 2017 constrained optimization problems and four practical problems in engineering show that IHFAPA can effectively improve the quality of solutions. [ABSTRACT FROM AUTHOR]

In this paper, by applying the Fan-KKM Theorem, we prove the existence of solutions to a constrained optimization problem. As applications, we solve some constrained optimal taxation problems. That is, we demonstrate the existence of tax rate functions that maximizes the utilities of taxpayers subjected to some government tax revenue plans. [ABSTRACT FROM AUTHOR]

Local Linear Embedding (LLE) is a nonlinear manifold learning method for dimensionality reduction in high-dimensional data. However, when the data is distorted by noise, efficiency of LLE significantly diminishes. This paper proposes a robust locally nonlinear embedding (RLNE) method to alleviate the impact of noise. This is achieved by constructing nonlinear functions between data neighbors in high-dimensional space, and then mapping the relationships to low manifolds. The constrained least squares method is used to obtain more uniform weights to ensure that the neighborhood is approximately located on the local nonlinear patches of the manifold. Theoretical analysis is conducted on the reasons underlying RLNE's robustness to noise. Experimental results on synthetic and real-world data highlight RLNE's ability to preserve the intrinsic structure of data, showcasing robustness across various types data with various levels of noise, as well as with a larger number of nearest neighbors. [ABSTRACT FROM AUTHOR]

In order to solve the problems of low convergence accuracy and easy convergence to local optimum of traditional flower pollination algorithms, a flower pollination algorithm combining dynamic convergence factor and golden sine (DGSFPA) was proposed. The dynamic convergence factor was introduced to cross-pollination to improve the convergence precision of the algorithm. The golden sine optimization was performed in self-pollination to enhance the ability to jump out of the local optimum. Compared with the other three algorithms on the test function, the improved algorithm had higher convergence accuracy and faster convergence speed. DGSFPA was applied to solve the problem of design optimization of pressure vessels. The results show that the values of the four design variables obtained by the improved algorithm are all smaller than those obtained by the other three algorithms. Moreover, the total cost of the improved algorithm is 5 270.82 yuan less than that obtained by the flower pollination algorithm algorithm, and 876.72 yuan less than that obtained by the artificial bee colony algorithm, which proves the effectiveness and feasibility of the DGSFPA algorithm. [ABSTRACT FROM AUTHOR]

Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly. [ABSTRACT FROM AUTHOR]

Considering some communication or security requirements, the sensors cannot be deployed randomly. In order to improve the localization accuracy, we discuss the optimal geometry problem with some constraints: 1) the source and the sensors are restricted to be deployed inside a circular region; 2) the relative sensor-source distance must be greater than the minimum safety distance. The optimal geometry problem can be summarized as a constrained optimization problem, with D-optimality as its objective function, the deployment feasible region as constraints. To avoid complicated mathematical calculations, our primary idea is to establish equivalent and more intuitive constraints by using the introduced maximum feasible angle and optimal separation angle. [ABSTRACT FROM AUTHOR]

Canonical duality theory (CDT) is presented by its creator DY Gao as a theory which can be used for solving a large class of challenging real-world problems. It is the aim of this paper to study rigorously constrained optimization problems in finite dimensional spaces using the method suggested by CDT and to discuss several results published in the last ten years. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The ${\varepsilon }$ -constrained method is a very effective one. In the literature, the ${\varepsilon }$ value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive ${\varepsilon }$ control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of ${\varepsilon }$ through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive ${\varepsilon }$ -constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive ${\varepsilon }$ control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer Engineering & Applications is the property of Beijing Journal of Computer Engineering & Applications Journal Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper deals with the Frank–Wolfe algorithm to solve a special class of non-compact constrained optimization problems. The notion of asymptotic cone is one the main concept used to introduce the class of problems considered as well as to establish the well definition of the algorithm. This class of optimization problems, with closed and convex constraint set, are characterized by two conditions on the gradient of the objective function. The first one establishes that the gradient of the objective function is Lipschitz continuous, which is quite usual in the analysis of this algorithm. The second one, which is new in this subject, establishes that the gradient belongs to the interior of dual asymptotic cone of the constraint set. Classical results on asymptotic behaviour and iteration complexity bounds for the sequence generated by Frank–Wolfe algorithm are extended to this new class of problems. Some examples of problems with non-compact constraints and objective functions satisfying the aforementioned conditions are provided. [ABSTRACT FROM AUTHOR]

Bayesian optimization is a promising methodology for analog circuit synthesis. However, the sequential nature of the Bayesian optimization framework significantly limits its ability to fully utilize real-world computational resources. In this article, we propose an efficient parallelizable Bayesian optimization algorithm via multiobjective acquisition function ensemble (MACE) to further accelerate the optimization procedure. By sampling query points from the Pareto front of the probability of improvement (PI), expected improvement (EI), and lower confidence bound (LCB), we combine the benefits of state-of-the-art acquisition functions to achieve a delicate tradeoff between exploration and exploitation for the unconstrained optimization problem. Based on this batch design, we further adjust the algorithm for the constrained optimization problem. By dividing the optimization procedure into two stages and first focusing on finding an initial feasible point, we manage to gain more information about the valid region and can better avoid sampling around the infeasible area. After achieving the first feasible point, we favor the feasible region by adopting a specially designed penalization term to the acquisition function ensemble. The experimental results quantitatively demonstrate that our proposed algorithm can reduce the overall simulation time by up to $74\times $ compared to differential evolution (DE) for the unconstrained optimization problem when the batch size is 15. For the constrained optimization problem, our proposed algorithm can speed up the optimization process by up to $15\times $ compared to the weighted EI-based Bayesian optimization (WEIBO) approach, when the batch size is 15. [ABSTRACT FROM AUTHOR]

• Propose a linguistic information granulation model. • Develop a penalty function-based co-evolutionary PSO (PFCPSO) solution approach. • Present the whole algorithm framework for the PFCPSO solution approach. • Discuss how the granulation model and the PFCPSO solution approach work in practice. • Compare PFCPSO and co-evolutionary PSO in terms of the performance of the solution. This study focuses on linguistic information operational realization through information granulation in group decision-making (GDM) scenarios where the preference information offered by decision-makers over alternatives is described using distributed linguistic preference relations (DLPRs). First, an information granulation model is proposed to arrive at the operational realization of linguistic information in the GDM with DLPRs. The information granulation is formulated as a certain optimization problem where a combination of consistency degree of individual DLPRs and consensus degree among individuals is regarded as the underlying performance index. Then, considering that the proposed model is a constrained optimization problem (COP) with an adjustable parameter, which is difficult to be effectively solved using general optimization methods, we develop a novel approach towards achieving the optimal solution, referred to as penalty function-based co-evolutionary particle swarm optimization (PFCPSO). Within the PFCPSO setting, the designed penalty function is used to transform the COPs into unconstrained ones. Besides, the penalty factors and the adjustable parameter, as well as the decision variables of the optimization problems, are simultaneously optimized through the co-evolutionary mechanism of two populations in co-evolutionary particle swarm optimization (CPSO). Finally, a comprehensive evaluation problem about car brands is studied using the proposed model and the newly developed PFCPSO approach, which demonstrates their applicability. Two comparative studies are also conducted to show the effectiveness of the proposals. Overall, this study exhibits two facets of originality: the presentation of the linguistic information granulation model, and the development of the PFCPSO approach for solving the proposed model. [ABSTRACT FROM AUTHOR]

An improved hybrid firefly algorithm with probability attraction model (IHFAPA) is proposed to solve the problems of low computational efficiency and low computational accuracy in solving complex optimization problems. First, the method of square-root sequence was used to generate the initial population, so that the initial population had better population diversity. Second, an adaptive probabilistic attraction model is proposed to attract fireflies according to the brightness level of fireflies, which can minimize the brightness comparison times of the algorithm and moderate the attraction times of the algorithm. Thirdly, a new location update method is proposed, which not only overcomes the deficiency in that the relative attraction of two fireflies is close to 0 when the distance is long but also overcomes the deficiency that the relative attraction of two fireflies is close to infinity when the distance is small. In addition, a combinatorial variational operator based on selection probability is proposed to improve the exploration and exploitation ability of the firefly algorithm (FA). Later, a similarity removal operation is added to maintain the diversity of the population. Finally, experiments using CEC 2017 constrained optimization problems and four practical problems in engineering show that IHFAPA can effectively improve the quality of solutions.

The existing parallel multiobjective evolutionary computation does not perform well for constrained multiobjective optimization problems with discontinuous Pareto fronts or narrow feasible regions. This study parallelizes the state-of-the-art cooperative multiobjective coevolutionary algorithm and proposes an effective parallel evolutionary algorithm for constrained multiobjective optimization problems that are difficult to optimize. Two parallelization methods are compared: a global parallel model in which solution evaluations are performed in parallel, and a hybrid model that treats the cooperative populations in a distributed manner while performing each solution evaluation in parallel. The first model is a straightforward parallelization, while the second one capitalizes on the characteristics of the coevolutionary framework. To investigate the efficacy of the proposed models, experiments are conducted on constrained multiobjective optimization problems, including complex characteristics, while varying the number of parallel cores up to 64. The experiments compare the two proposed methods from the viewpoint of search performance and execution time. The experimental results reveal that the latter hybrid model shows better computational efficiency and scalability against an increasing number of cores without adversely affecting the search performance compared to the former straightforward parallelization. • Parallel cooperative multiobjective coevolutionary algorithm is proposed. • Two parallelization proposals are compared. • Up to 64 parallel core scalability is analyzed. • The proposed method exhibits high computing efficiency and scalability. [ABSTRACT FROM AUTHOR]

Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly.

In the optimization of constrained type problems, the main difficulty is the elimination of the constraint violations in the evolutionary search process. Evolutionary algorithms are designed by default according to the requirements of unconstrained and continuous global optimization problems. Since there are no constraint functions in these type of problems, the constraint violations are not considered in the design of the guiding mechanism of evolutionary algorithms. In this study, two new methods were introduced to redesign the evolutionary algorithms in accordance with the requirements of constrained optimization problems. These were (i) constraint space-based, called Fitness-Distance-Constraint (FDC), selection method and (ii) dynamic guiding mechanism. Firstly, thanks to the FDC guide selection method, the constraint violation values of the individuals in the population were converted into score values and the individuals who increase the diversity in the search process were selected as guide. On the other hand, in dynamic guiding mechanism, the FDC method was applied in case of constraint violation, otherwise the default guide selection method was used The proposed methods were used to redesign the guiding mechanism of adaptive guided differential evolution (AGDE), a current evolutionary algorithm, and the FDC-AGDE algorithm was designed. The performance of the FDC-AGDE was tested on eleven different constrained real-world optimization problems. The results of the FDC-AGDE and AGDE were evaluated using the Friedman and Wilcoxon test methods. According to Wilcoxon pairwise results, the FDC-AGDE showed better performance than the AGDE in nine of the eleven problems and equal performance in two of the eleven problems. Moreover, the proposed algorithm was compared with the competitive and up-to-date MHS algorithms in terms of the results of Friedman test, Wilcoxon test, feasibility rate, and success rate. According to Friedman test results, the first three algorithms were the FDC-AGDE, LSHADE-SPACMA, and AGDE algorithms with the score of 2.69, 4.05, and 4.34, respectively. According to the mean values of the success rates obtained from the eleven problems, the FDC-AGDE, LSHADE-SPACMA, and AGDE algorithms ranked in the first three with the success rates of 67%, 48% and 28%, respectively. Consequently, the FDC-AGDE algorithm showed a superior performance comparing with the competing MHS algorithms. According to the results, it is expected that the proposed methods will be widely used in the constrained optimization problems in the future. [Display omitted] • Fitness-Distance-Constraint (FDC) method has been proposed. • FDC based dynamic guide selection mechanism has been introduced for MHS algorithms. • FDC-AGDE algorithm has been proposed for optimization of constrained problems. • The AGDE algorithm with FDC was 39% more successful than the version without FDC. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles are applied extensively in various fields due to their advantages of low-cost, high-maneuverability, and easy-operation. However, the path planning problem of unmanned aerial vehicles, which directly determines the flight safety and efficiency, still remains challenging when building and optimizing the path model. To further study the path planning problem, we firstly construct it as a constrained optimization problem. The objective function considers the costs of path length and threat, and the constraints involve the collision and turning angle. Additionally, we employ the theory of B-Spline curve to represent the planned paths to facilitate the optimization of established model. Then, aiming at the poor searchability and slow convergence speed of current optimization methods, we propose a reinforcement learning-based multi-strategy cuckoo search algorithm. Specifically, we establish an innovative reinforcement learning-based multi-strategy mechanism and a reinforced switch parameter based on the theory of reinforcement learning. To verify the effectiveness of the proposed algorithm, extensive experiments are carried out on the CEC'17 benchmark test and different three-dimensional path planning problems. Detailed statistical analysis of the experimental results confirm the superiority of our proposed algorithm to the other well-established algorithms. [ABSTRACT FROM AUTHOR]