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In this work, an improved moth-flame optimization algorithm is proposed to alleviate the problems of premature convergence and convergence to local minima. From the perspective of diversity, an inertia weight of diversity feedback control is introduced in the moth-flame optimization to balance the algorithm's exploitation and global search abilities. Furthermore, a small probability mutation after the position update stage is added to improve the optimization performance. The performance of the proposed algorithm is extensively evaluated on a suite of CEC'2014 series benchmark functions and four constrained engineering optimization problems. The results of the proposed algorithm are compared with the ones of other improved algorithms presented in literatures. It is observed that the proposed method has a superior performance to improve the convergence ability of the algorithm. In addition, the proposed algorithm assists in escaping the local minima. [ABSTRACT FROM AUTHOR]

Short-step methods are an important class of algorithms for solving convex constrained optimization problems. In this short paper, we show that under very mild assumptions on the self-concordant barrier and the width of the ℓ 2 -neighbourhood, any short-step interior-point method is not strongly polynomial-time. [ABSTRACT FROM AUTHOR]

Background: CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner‐up team. Purpose: This paper reports details of our PROSPECT algorithm (Prior‐based Restricted‐variable Optimization for SPEctral CT) and follow‐up studies regarding the algorithm's accuracy and enhancement of its convergence speed. Methods: We formulated the reconstruction task as an optimization problem. PROSPECT employed a one‐step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam‐hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projection data. Results: Prior knowledge allowed a reduction of the number of unknown variables by 85.9%$85.9\%$. PROSPECT algorithm achieved the average root of mean square error (RMSE) of 3.3×10−6$3.3\,\times \,10^{-6}$ in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double‐precision projection data reduced RMSE to 1.2×10−11$1.2\,\times \,10^{-11}$. Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computation time. Conclusions: PROSPECT algorithm achieved a high degree of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

In recent years, distributed optimization problem have a wide range of applications in various fields. This paper considers the prescribed-time distributed optimization problem with/without constraints. Firstly, we assume the state of each agent is constrained, and the prescribed-time distributed optimization algorithm with constraints is designed on the basis of gradient projection algorithm and consensus algorithm. Secondly, the constrained distributed optimization problem is transformed into the unconstrained distributed optimization problem, and according to the gradient descent algorithm and consensus algorithm, we also propose the prescribed-time distributed optimization algorithm without constraints. By designing the appropriate objective functions, we prove the multi-agent system can converge to the optimal solution within any prescribed-time, and the convergence time is fully independent of the initial conditions and system parameters. Finally, three simulation examples are provided to verify the validity of the designed algorithms. • For distributed optimization problem with convex constraints, we design an effective prescribed-time distributed algorithm which can guarantee the multi-agent system converge to the optimal solution. • The designed algorithm in this paper can achieve convergence within any prescribed-time, and the convergence time is fully independent of the initial conditions and system parameters. • In this paper, we not only consider the condition that the agents' states are constrained, but also ensure that the multi-agent system can reach the optimal solution within any prescribed-time, which is more practical. [ABSTRACT FROM AUTHOR]

This paper proposes a novel nature-inspired meta-heuristic algorithm, named Snow Geese Algorithm. It is inspired by the migratory behavior of snow geese and emulates the distinctive "Herringbone" and "Straight Line" shaped flight patterns observed during their migration. The algorithm is structured into three main phases for benchmark testing. In the first phase, the Snow Geese Algorithm's numerical results are compared with those of several classical meta-heuristic algorithms using the same test functions and original data from these algorithms. In the second phase, in order to minimize potential variations during the comparison, all algorithms undergo evaluation on a standardized testing platform. In the third phase, this paper applies the Snow Geese Algorithm to solve four widely recognized engineering optimization problems: the tubular column design, piston lever optimization design, reinforced concrete beam design and car side impact design. These real-world engineering problems serve as test cases to assess Snow Geese Algorithm problem-solving capabilities. The primary objective of the Snow Geese Algorithm is to provide an alternative perspective for tackling complex optimization problems. Please note that the complete source code for the Snow Geese Algorithm is publicly available at https://github.com/stones3421/SGA-project. • Snow Geese Algorithm: A novel meta-heuristic approach inspired by snow geese flight behavior, tackling optimization problems. • Two-stage Strategy: Mimics snow geese exploration and exploitation patterns, setting it apart from traditional methods. • Performance Evaluation: Multiple algorithms are assessed on different problems. • Algorithm Features: Experimental results validate the effectiveness of the Snow Geese Algorithm. • Practical Applications: Snow Geese Algorithm shows potential in engineering optimization, aiding accurate decision-making. [ABSTRACT FROM AUTHOR]

This paper reviews recent studies on the Particle Swarm Optimization (PSO) algorithm. The review has been focused on high impact recent articles that have analyzed and/or modified PSO algorithms. This paper also presents some potential areas for future study. [ABSTRACT FROM AUTHOR]

In this paper, we consider the continuous relaxation reformulation of cardinality-constrained optimization problems that has become more popular in recent years and propose a new sequential optimality condition (approximate stationarity) for cardinality-constrained optimization problems, which is proved to be a genuine necessary optimality condition that does not require any constraint qualification to hold. We compare this condition with the rest of the sequential optimality conditions and prove that our condition is stronger and closer to the local minimizer. A problem-tailored regularity condition is proposed, and we show that this regularity condition ensures that the approximate stationary point proposed in this paper is the exact stationary point and is the weakest constraint qualification with this property. Finally, we apply the results of this paper to safeguarded augmented Lagrangian method and prove that the algorithm converges to the approximate stationary point proposed in this paper under mild assumptions, the existing theoretical results of this algorithm are further enhanced. [ABSTRACT FROM AUTHOR]

This paper proposes a path-based approach for the minimization of a continuously differentiable function over sparse symmetric sets, which is a hard problem that exhibits a restrictiveness-hierarchy of necessary optimality conditions. To achieve the more restrictive conditions in the hierarchy, state-of-the-art algorithms require a support optimization oracle that must exactly solve the problem in smaller dimensions. The path-based approach developed in this study produces a path-based optimality condition, which is placed well in the restrictiveness-hierarchy, and a method to achieve it that does not require a support optimization oracle and, moreover, is projection-free. In the development process, new results are derived for the regularized linear minimization problem over sparse symmetric sets, which give additional means to identify optimal solutions for convex and concave objective functions. We complement our results with numerical examples. [ABSTRACT FROM AUTHOR]

Modern 5G wireless cellular networks use massive multiple-input multiple-output (MIMO) technology. This concept entails using an antenna array at a base station to concurrently service many mobile devices that have several antennas on their side. In this field, a significant role is played by the precoding (beamforming) problem. During downlink, an important part of precoding is the power allocation problem that distributes power between transmitted symbols. In this paper, we consider the power allocation problem for a class of precodings that asymptotically work as regularized zero-forcing. Under some realistic assumptions, we simplify the spectral efficiency functional and obtain tractable expressions for it. We prove that equal power allocation provides optimum for the simplified functional with total power constraint (TPC). We propose low-complexity Intersection methods (IM) that improve equal power allocation in the case of per-antenna power constraints (PAPC). On simulations using Quadriga, the proposed IM method in combination with widely-studied water filling (WF) shows a significant gain in spectral efficiency while using a similar computing time as the reference equal power (EP) solution. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to present an improved neural network algorithm (INNA) for solving the reliability-redundancy allocation problem (RRAP) with nonlinear resource constraints. In this RRAP, both the component reliability and the redundancy allocation are to be considered simultaneously. Neural network algorithm (NNA) is one of the newest and efficient swarm optimization algorithms having a strong global search ability that is very adequate in solving different kinds of complex optimization problems. Despite its efficiency, NNA experiences poor exploitation, which causes slow convergence and also restricts its practical application of solving optimization problems. Considering this deficiency and to obtain a better balance between exploration and exploitation, searching procedure for NNA is reconstructed by implementing a new logarithmic spiral search operator and the searching strategy of the learner phase of teaching–learning-based optimization (TLBO) and an improved NNA has been developed in this paper. To demonstrate the performance of INNA, it is evaluated against seven well-known reliability optimization problems and finally compared with other existing meta-heuristics algorithms. Additionally, the INNA results are statistically investigated with the Wilcoxon sign-rank test and Multiple comparison test to show the significance of the results. Experimental results reveal that the proposed algorithm is highly competitive and performs better than previously developed algorithms in the literature. [ABSTRACT FROM AUTHOR]

Motivation Understanding causal effects is a fundamental goal of science and underpins our ability to make accurate predictions in unseen settings and conditions. While direct experimentation is the gold standard for measuring and validating causal effects, the field of causal graph theory offers a tantalizing alternative: extracting causal insights from observational data. Theoretical analysis has shown that this is indeed possible, given a large dataset and if certain conditions are met. However, biological datasets, frequently, do not meet such requirements but evaluation of causal discovery algorithms is typically performed on synthetic datasets, which they meet all requirements. Thus, real-life datasets are needed, in which the causal truth is reasonably known. In this work we first construct such a large-scale real-life dataset and then we perform on it a comprehensive benchmarking of various causal discovery methods. Results We find that the PC algorithm is particularly accurate at estimating causal structure, including the causal direction which is critical for biological applicability. However, PC does only produces cause-effect directionality, but not estimates of causal effects. We propose PC-NOTEARS (PCnt), a hybrid solution, which includes the PC output as an additional constraint inside the NOTEARS optimization. This approach combines PC algorithm's strengths in graph structure prediction with the NOTEARS continuous optimization to estimate causal effects accurately. PCnt achieved best aggregate performance across all structural and effect size metrics. Availability and implementation https://github.com/zhu-yh1/PC-NOTEARS. [ABSTRACT FROM AUTHOR]

This contribution discusses the influence of different barrier update strategies on the performance and robustness of an interior point algorithm for single-crystal plasticity at small strains. To this end, single-crystal plasticity is first briefly presented in the framework of a primal-dual interior point algorithm to outline the general algorithmic structure. The manner in which the barrier parameter is modified within the interior point method, steering the penalization of constraints, plays a crucial role for the robustness and efficiency of the overall algorithm. In this paper, we compare and analyze different strategies in the framework of crystal plasticity. In a thorough analysis of a numerical example covering a broad range of settings in monocrystals, we investigate robust hyperparameter ranges and identify the most efficient and robust barrier parameter update strategies. [ABSTRACT FROM AUTHOR]

The use of evolutionary algorithms to solve constrained multi-objective optimization problems (CMOPs) with various characteristics and difficulties obtains considerable attention. Most of existing methods tend to introduce an alternate formulation to simplify the original problem and facilitate the solving, which corresponds to the methodology of multiform optimization. Inspired by multiform optimization, this paper proposes a multi-stage multiform optimization framework to solve CMOPs. To prevent the population from falling into local optima in the early stages of evolution, we construct an alternate formulation that ignores all constraints. Meanwhile, in order to utilize high-quality infeasible solutions to explore more feasible regions, we construct another alternate formulation by using a constraint relaxation technique that analyzes the relationships between constraints, evaluating important constraints, and ignoring unimportant constraints. The two formulations provide exclusive and complementary searches in the objective space with the help of knowledge transfer. As both alternate formulations are designed to find the unconstrained Pareto front in the early stages and the final goal must be finding the constrained Pareto front, a multi-stage strategy is devised. Different numbers of alternate formulations are used at different stages to allocate computational resources more effectively. In addition, we propose a hybrid operator strategy to improve the performance of the algorithm by combining the advantages of different operators. Then, 33 instances and 18 real-world CMOPs are selected to evaluate the performance of the algorithm. Experimental results demonstrate the superiority or competitiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

Deploying unmanned aerial vehicle base stations (UAV-BSs) to provide wireless access for terrestrial users is an alternative solution in emergency scenarios. Due to the dynamic nature of UAV-BSs and strong line-of-sight (LoS) transmission, co-frequency networking worsens the interference suffered by edge users, while the use of fully orthogonal channels for all UAV-BSs also faces the problem of frequency resource constraints. This paper develops a new deployment scheme by combining multiple UAV-BS locations, limited frequency reuse and power optimization. Thus, the nonlinear constrained optimization model is proposed to maximize user coverage. To reduce the computational complexity, the basic multi-UAV-BS network layout is first determined by polycentric clustering and connectivity adjustment based on user location distribution. Then, a genetic algorithm is used to optimize the multi-UAV-BS frequency arrangement and power adjustment to obtain the model solution. Simulations verify the effectiveness of the proposed scheme and evaluate the impact of co-channel interference. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) exist widely in the real world, which simultaneously contain multiple constraints to be satisfied and multiple conflicting objectives to be optimized. Therefore, the challage in addressing CMOPs is how to better balance constraints and objectives. To remedy this issue, this paper proposes a novel dual-population based constrained multi-objective evolutionary algorithm to solve CMOPs, in which two populations with different functions are employed. Specifically, the main population considers both objectives and constraints for solving the original CMOPs, while the auxiliary population is used only for optimization of objectives without considering constraints. In addition, a dynamic population size reducing mechanism is proposed, which is used to adjust the size of the auxiliary population, so as to reduce the consumption of computing resoruces in the later stage. Moreover, an independent external archive is set to store feasible solutions found by the auxiliary population, so as to provide high-quality feasible solutions for the main population. The experimental results on 55 benchmark functions show that the proposed algorithm exhibits superior or at least competitive performance compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis‐Hastings warm‐starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis‐Hastings warm‐starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1‐depth QAOA. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem to be solved inexactly in such way that a relative approximate criterion is satisfied. In terms of the iteration number k, we establish global O (1 / k) pointwise and O (1 / k) ergodic convergence rates of the method for a domain of the acceleration parameters, which is consistent with the largest known one in the exact case. Since the symmetric proximal ADMM can be seen as a class of ADMM variants, the new algorithm as well as its convergence rates generalize, in particular, many others in the literature. Numerical experiments illustrating the practical advantages of the method are reported. To the best of our knowledge, this work is the first one to study an inexact version of the symmetric proximal ADMM. [ABSTRACT FROM AUTHOR]

In this paper, we propose a filter sequential adaptive regularization algorithm using cubics (ARC) for solving nonlinear equality constrained optimization. Similar to sequential quadratic programming methods, an ARC subproblem with linearized constraints is considered to obtain a trial step in each iteration. Composite step methods and reduced Hessian methods are employed to tackle the linearized constraints. As a result, a trial step is decomposed into the sum of a normal step and a tangential step which is computed by a standard ARC subproblem. Then, the new iteration is determined by filter methods and ARC framework. The global convergence of the algorithm is proved under some reasonable assumptions. Preliminary numerical experiments and comparison results are reported. [ABSTRACT FROM AUTHOR]

The ideal gas molecular movement (IGMM) as a metaheuristic optimization method is a prominent option for solving optimization problems. However, in some complex cases, IGMM may possess premature convergence or get trapped in local optima. Therefore, to tackle these issues, this paper indicates a new modified IGMM algorithm named opposition‐based IGMM, which has been incorporated with opposition based learning (OBL), Cauchy mutation (CM), velocity clamping (VC), and mirror operator (MO) to enhance its performance. OBL, VC, and MO improve the convergence of IGMM, whereas CM assists IGMM to escape local optima. The effect of each strategy, OBL, CM, VC, and MO, on IGMM, is confirmed through 30 low and high‐dimensional benchmarks, including 23 well‐known mathematical problems and CEC2017 as complex test functions and three engineering problems. Analysis results represent that integration IGMM with OBL, CM, VC, and MO has the best performance among other IGMM variants and eventually improved IGMM in exploration, exploitation, accelerating convergence, and local optima avoidance. [ABSTRACT FROM AUTHOR]

Recent papers indicate that some algorithms for constrained optimization may exhibit worst-case complexity bounds that are very similar to those of unconstrained optimization algorithms. A natural question is whether well-established practical algorithms, perhaps with small variations, may enjoy analogous complexity results. In the present paper we show that the answer is positive with respect to inexact restoration algorithms in which first-order approximations are employed for defining the subproblems. [ABSTRACT FROM AUTHOR]

In this paper, a numerical approximation method is developed to find approximate solutions to a class of constrained multi-objective optimization problems. All the functions of the problem are not necessarily convex functions. At each iteration of the method, a particular type of subproblem is solved using the trust region technique, and the step is evaluated using the notions of actual reduction and predicted reduction. A non-differentiable $ l_{\infty } $ l∞ penalty function restricts the constraint violations. An adaptive BFGS update formula is introduced. Global convergence of the proposed algorithm is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. Furthermore, it is justified that the proposed algorithm displays a super-linear convergence rate. Numerical results are provided to show the efficiency of the algorithm in the quality of the approximated Pareto front. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an away-step Frank–Wolfe algorithm designed for solving multiobjective optimization problems over polytopes. We prove that each limit point of the sequence generated by the algorithm is a weak Pareto optimal solution. Furthermore, under additional conditions, we show linear convergence of the whole sequence to a Pareto optimal solution. Numerical examples illustrate a promising performance of the proposed algorithm in problems where the multiobjective Frank–Wolfe convergence rate is only sublinear. [ABSTRACT FROM AUTHOR]

In this paper, we discuss how to use the Dantzig–Wolfe (DW) decomposition method to solve a class of constrained variational inequality (VI) problems. These problems include multi-regional energy equilibrium models with linking constraints or nonlinear multicommodity network flow problems with asymmetric cost functions and side constraints. The decomposed VI problem has a subproblem which is a constrained optimisation problem consisting of all structural constraints. The resulting master problem is a VI problem with dummy linking constraints. The size of the master problem is much smaller than that of the original constrained VI problem. If the subproblem comprises the constraint set with a special structure, such as block-angular structure, it can be further decomposed by the DW decomposition method (nested DW). We find that by performing an iteration of the nested DW decomposition on the subproblem (truncated DW), we can obtain an equilibrium solution. The efficiency of this truncated DW may depend on the VI problems. Theoretical analysis indicated that the algorithm is guaranteed to converge under some assumptions. Illustrative examples are given. From the results of the examples, we find that moving the linking constraints of the structural constraints back from the subproblem to the master problem may worsen the computational performance. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to test the performance of the recently proposed weighted superposition attraction-repulsion algorithms (WSA and WSAR) on unconstrained continuous optimization test problems and constrained optimization problems. WSAR is a successor of weighted superposition attraction algorithm (WSA). WSAR is established upon the superposition principle from physics and mimics attractive and repulsive movements of solution agents (vectors). Differently from the WSA, WSAR also considers repulsive movements with updated solution move equations. WSAR requires very few algorithm-specific parameters to be set and has good convergence and searching capability. Through extensive computational tests on many benchmark problems including CEC’2015 and CEC’2020 performance of the WSAR is compared against WSA and other metaheuristic algorithms. It is statistically shown that the WSAR algorithm is able to produce good and competitive results in comparison to its predecessor WSA and other metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

Tree–seed algorithm is a stochastic search algorithm with superior performance suitable for solving continuous optimization problems. However, it is also prone to fall into local optimum and slow in convergence. Therefore, this paper proposes an improved tree–seed algorithm based on pattern search, dimension permutation, and elimination update mechanism (PDSTSA). Firstly, a global optimization strategy based on pattern search is used to promote detection ability. Secondly, in order to maintain the diversity of the population, a random mutation strategy of individual dimension replacement is introduced. Finally, the elimination and update mechanism based on inferior trees is introduced in the middle and later stages of the iteration. Subsequently, PDSTSA is compared with seven representative algorithms on the IEEE CEC2015 test function for simulation experiments and convergence curve analysis. The experimental results indicate that PDSTSA has better optimization accuracy and convergence speed than other comparison algorithms. Then, the Wilcoxon rank sum test demonstrates that there is a significant difference between the optimization results of PDSTSA and each comparison algorithm. In addition, the results of eight algorithms for solving engineering constrained optimization problems further prove the feasibility, practicability, and superiority of PDSTSA. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential optimal hyper-rectangles. A key contribution lies in applying a new mapping technique to eliminate the infeasible region efficiently. This allows calculations to be performed only within the feasible region defined by linear constraints. We perform extensive tests using a diverse set of benchmark problems to evaluate the effectiveness and performance of the proposed algorithm compared to existing DIRECT solvers. Statistical analyses using Friedman and Wilcoxon tests demonstrate the superiority of a new algorithm in solving such problems. [ABSTRACT FROM AUTHOR]

In the scenario of device-free localization under multiple effects, the accuracy of localization based on compressed sensing theory is severely affected. Most existing localization techniques directly ignore multiple path effects. However, it is not practical to ignore the multiple path effect due to its high signal strength, which can provide localization information. In this paper, we formulate the sensing matrix optimization problem in compressed sensing for device-free localization scenarios based on multiple reflections. To solve this problem, we model it as a constrained combinatorial optimization problem and propose a hybrid meta-heuristic algorithm. First, smart reflection surfaces and virtual node models are used to construct the desired communication links. Second, we iteratively improve the properties of the measurement matrix by using K-means clustering to obtain reasonable thresholds, and use a meta-heuristic algorithm to optimize the sensing matrix. Finally, the simulation results show that the proposed method efficiently optimizes the sensing matrix and achieves fast and high-precision localization while conserving communication resources. [ABSTRACT FROM AUTHOR]

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The adaptive regularisation algorithm using cubics (ARC) is initially proposed for unconstrained optimization. ARC has excellent convergence properties and complexity. In this paper, we extend ARC to solve nonlinear equality constrained optimization and propose a sequential adaptive regularisation using cubics algorithm inspired by sequential quadratic programming (SQP) methods. In each iteration of our method, the trial step is computed via composite-step approach, i.e., it is decomposed into the sum of normal step and tangential step. By means of reduced-Hessian approach, a new ARC subproblem for nonlinear equality constrained optimization is constructed to compute the tangential step, which can supply sufficient decrease required in the proposed algorithm. Once the trial step is obtained, the ratio of the penalty function reduction to the model function reduction is calculated to determine whether the trial point is accepted. The global convergence of the algorithm is investigated under some mild assumptions. Preliminary numerical experiments are reported to show the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a population-based evolutionary computation model for solving continuous constrained nonlinear optimization problems. The primary goal is achieving better solutions in a specific problem type, regardless of metaphors and similarities. The proposed algorithm assumes that candidate solutions interact with each other to have better fitness values. The interaction between candidate solutions is limited with the closest neighbors by considering the Euclidean distance. Furthermore, Tabu Search Algorithm and Elitism selection approach inspire the memory usage of the proposed algorithm. Besides, this algorithm is structured on the principle of the multiplicative penalty approach that considers satisfaction rates, the total deviations of constraints, and the objective function value to handle continuous constrained problems very well. The performance of the algorithm is evaluated with real-world engineering design optimization benchmark problems that belong to the most used cases by evolutionary optimization researchers. Experimental results show that the proposed algorithm produces satisfactory results compared to the other algorithms published in the literature. The primary purpose of this study is to provide an algorithm that reaches the best-known solution values rather than duplicating existing algorithms through a new metaphor. We constructed the proposed algorithm with the best combination of features to achieve better solutions. Different from similar algorithms, constrained engineering problems are handled in this study. Thus, it aims to prove that the proposed algorithm gives better results than similar algorithms and other algorithms developed in the literature. [ABSTRACT FROM AUTHOR]

Dynamic constrained optimization is a challenging research topic in which the objective function and/or constraints change over time. In such problems, it is commonly assumed that all problem instances are feasible. In reality some instances can be infeasible due to various practical issues, such as a sudden change in resource requirements or a big change in the availability of resources. Decision-makers have to determine whether a particular instance is feasible or not, as infeasible instances cannot be solved as there are no solutions to implement. In this case, locating the nearest feasible solution would be valuable information for the decision-makers. In this paper, a differential evolution algorithm is proposed for solving dynamic constrained problems that learns from past environments and transfers important knowledge from them to use in solving the current instance and includes a mechanism for suggesting a good feasible solution when an instance is infeasible. To judge the performance of the proposed algorithm, 13 well-known dynamic test problems were solved. The results indicate that the proposed algorithm outperforms existing recent algorithms with a margin of 79.40% over all the environments and it can also find a good, but infeasible solution, when an instance is infeasible. [ABSTRACT FROM AUTHOR]

This paper proposes a simple and effective optimization algorithm named as "Improved Rao (I-Rao) algorithm". The I-Rao algorithm consists of two phases: the local exploitation phase and the global exploration phase. The local exploitation phase improves the exploitation of the search process of Rao algorithms and enhances the algorithm's convergence speed. The global exploration phase helps the algorithm to get away from the local optimum solutions and enhances the exploration ability of the search process of the algorithm. Like Rao algorithms, the I-Rao algorithm also does not need algorithm-specific control parameters. The effectiveness of the I-Rao algorithm is tested on 25 unconstrained benchmark functions, 45 complex CEC test functions, and 19 real-world constrained mechanical design optimization problems of CEC2020. The comparison of results reveals the effectiveness of the I-Rao algorithm over many state-of-the-art advanced optimization algorithms such as GWO, SCA, PSO, WOA, Jaya, IJAYA, MJAYA, PGJAYA, EJAYA, IUDE, εMAgES, iLSHADEε, and COLSHADE. The Friedman test is also carried out to check the overall performance of the I-Rao algorithm as compared to other advanced optimization algorithms considered. The convergence plots illustrate the convergence speed of the I-Rao algorithm. [ABSTRACT FROM AUTHOR]

Community detection is a significant and challenging task in network research. Nowadays, many community detection methods have been developed. Among them, the classical Louvain algorithm is an excellent method aiming at optimizing an objective function. In this paper, we propose a modularity function F 2 as a new objective function. Our modularity function F 2 overcomes certain disadvantages of the modularity functions raised in previous literature, such as the resolution limit problem. It is desired as a competitive objective function. Then, the constrained Louvain algorithm is proposed by adding some constraints to the classical Louvain algorithm. Finally, through the comparison, we have found that the constrained Louvain algorithm with F 2 is better than the constrained Louvain algorithm with other objective functions on most considered networks. Moreover, the constrained Louvain algorithm with F 2 is superior to the classical Louvain algorithm and the Newman's fast method. [ABSTRACT FROM AUTHOR]

In this paper, we study swarm intelligence computation for constrained optimization problems and propose a new hybrid PSO-DE algorithm based on feasibility rules. Establishing individual feasibility rules as a way to determine whether the position of an individual satisfies the constraint or violates the degree of the constraint, which will determine the choice of the individual optimal position and the global optimal position in the particle population. First, particle swarm optimization (PSO) is used to act on the top 50% of individuals with higher degree of constraint violation to update their velocity and position. Second, Differential Evolution (DE) is applied to act on the individual optimal position of each individual to form a new population. The current individual optimal position and the global optimal position are updated using the feasibility rules, thus forming a hybrid PSO-DE intelligent algorithm. Analyzing the convergence and complexity of PSO-DE. Finally, the performance of the PSO-DE algorithm is tested with 12 benchmark functions of constrained optimization and 57 engineering optimization problems, the numerical results show that the proposed algorithm has good accuracy, effectiveness and robustness. [ABSTRACT FROM AUTHOR]

Existing discriminative correlation filters suffer from the defects of potential spatial distractors and the degradation of appearance model caused by hard-temporal correlation. Aiming at this issue, a robust tracker which combines the adaptive spatial regularization and the temporal consistent constraint is proposed in this paper. First, we propose to take the extracted saliency map of the background as a reference weight to construct the spatial regularization term, with which the perceived performance of the filter against distractors is enhanced by learning the spatial sparse constraint adaptively. Second, we further implement the temporal consistent regularization formed by capturing dynamic appearance information from multiple historical frames with a high-confidence strategy to mitigate the model degradation. Third, we employ the alternating direction method of multipliers to solve the constrained optimization problem efficiently, thereby the computational complexity can be reduced. The concrete experimental results on OTB-2013, OTB-2015, Temple-Color-128 and VOT2016 benchmarks demonstrate that our tracker outperforms several state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Nonnegative Matrix Factorization (NMF) has attracted a great deal of attention as an effective technique for dimensionality reduction of large-scale nonnegative data. Given a nonnegative matrix, NMF aims to obtain two low-rank nonnegative factor matrices by solving a constrained optimization problem. The Hierarchical Alternating Least Squares (HALS) algorithm is a well-known and widely-used iterative method for solving such optimization problems. However, the original update rule used in the HALS algorithm is not well defined. In this paper, we propose a novel well-defined update rule of the HALS algorithm, and prove its global convergence in the sense of Zangwill. Unlike conventional globally-convergent update rules, the proposed one allows variables to take the value of zero and hence can obtain sparse factor matrices. We also present two stopping conditions that guarantee the finite termination of the HALS algorithm. The practical usefulness of the proposed update rule is shown through experiments using real-world datasets. [ABSTRACT FROM AUTHOR]

In recent years, significant attentions have been devoted to design of metaheuristic optimization algorithms in order to solve optimization problems. Metaheuristic optimizers are methods which are inspired by observing the phenomena occurring in nature. In this paper, a comprehensive and exhaustive review has been carried out on water cycle algorithm (WCA) and its applications in a wide variety of study fields. The WCA is one of the novel metaheuristic optimization algorithms which is inspired by water cycle process in nature and how streams and rivers flow into the sea. Good exploitation and exploration capabilities have made the WCA a good alternative for solving large-scale optimization problems. Due to its capabilities and strengths, the WCA has been utilized in many and various majors including mechanical engineering, electrical and electronic engineering, civil engineering, industrial engineering, water resources and hydropower engineering, computer engineering, mathematics, and so forth. A variety of articles based on WCA have been published in different international journals such as Elsevier, Springer, IEEE Transactions, Wiley, Taylor & Francis, and in the proceedings of international conferences as well, since 2012 to the present. Thus, it is highly believed that this paper can be appropriate, beneficial and practical for students, academic researchers, professionals, and engineers. Also, it can be an innovative and comprehensive reference for subsequent academic papers and books relevant to the WCA, optimization methods, and metaheuristic optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces a new evolutionary computing method inspired by the seed transmission process of garden balsam. Garden balsam, a beautiful and attractive flower, randomly ejects the seeds within a certain range by virtue of mechanical force originating from cracking of mature seed pods, which is different from natural expansion of most species of plants. The seeds scattered to suitable growth area will have greater reproductive capacity in the next generation, followed by iteration until the most suitable point for growth in a particular space is eventually found. This phenomenon can more intuitively show the process of searching the problem solution space in the optimization problem. The garden balsam optimization algorithm proposed in this paper incorporates two different types of search processes and has a mechanism to maintain population diversity. Through the optimization experiment on 24 constrained optimization problems, the results obtained by using this algorithm are compared with those of some known meta-heuristic search algorithms. The statistical analysis of the experimental results has been implemented by Friedman rank test and Holm–Sidak test. The comparison results verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

The expected improvement (EI) algorithm is a very popular method for expensive optimization problems. In the past twenty years, the EI criterion has been extended to deal with a wide range of expensive optimization problems. This paper gives a comprehensive review of the EI extensions designed for parallel optimization, multiobjective optimization, constrained optimization, noisy optimization, multi-fidelity optimization and high-dimensional optimization. The main challenges of extending the EI approach to solve these complex optimization problems are pointed out, and the ideas proposed in literature to tackle these challenges are highlighted. For each reviewed algorithm, the surrogate modeling method, the computation of the infill criterion and the internal optimization of the infill criterion are carefully studied and compared. In addition, the monotonicity properties of the multiobjective EI criteria and constrained EI criteria are analyzed in detail. Through this review, we give an organized summary about the EI developments in the past twenty years and show a clear picture about how the EI approach has advanced. In the end of this paper, several interesting problems and future research topics about the EI developments are given. [ABSTRACT FROM AUTHOR]

The objective of a fixed-cost transportation problem (FCTP) is to minimize the total transportation cost (or to maximize the total profit). FCTPs become more complex due to the presence of uncertain factors like suppliers' capacity, customers' demand, fixed cost and amount of goods transported. In order to deal with its complexity, three mathematical models, namely the expected value, chance-constrained and measure chance models, are basically available in the literature. This paper aims to solve the crisp equivalent models of an uncertain two-echelon FCTP by employing a robust hybrid evolutionary algorithm. The framework of the designed algorithm comprises of parameter-free Jaya algorithm and the efficient quadratic approximation operator. Initially, its efficiency is validated on the 24 constrained benchmark functions from CEC 2006 (Liang et al. in Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization, 2006) and 30 unconstrained benchmark functions (Rao in Int J Ind Eng Comput 7:19–34, 2016). Friedman rank test and Iman–Davenport test are conducted for both constrained and unconstrained test instances. Additionally, five real-life engineering design problems are solved to further analyze the flexibility of the proposed algorithm. The computational results and convergence graphs justify the robustness of the designed algorithm over state-of-the-art algorithms. Finally, its application is demonstrated on chance-constrained and measure chance two-echelon FCTP models. Near-optimal results are contradicted by genetic algorithm and particle swarm optimization in solving both these models. Further, a few large-scale instances of FCTP are solved by the proposed algorithm. [ABSTRACT FROM AUTHOR]

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A novel optimization algorithm called hybrid salp swarm algorithm with teaching-learning based optimization (HSSATLBO) is proposed in this paper to solve reliability redundancy allocation problems (RRAP) with nonlinear resource constraints. Salp swarm algorithm (SSA) is one of the newest meta-heuristic algorithms which mimic the swarming behaviour of salps. It is an efficient swarm optimization technique that has been used to solve various kinds of complex optimization problems. However, SSA suffers a slow convergence rate due to its poor exploitation ability. In view of this inadequacy and resulting in a better balance between exploration and exploitation, the proposed hybrid method HSSATLBO has been developed where the searching procedures of SSA are renovated based on the TLBO algorithm. The good global search ability of SSA and fast convergence of TLBO help to maximize the system reliability through the choices of redundancy and component reliability. The performance of the proposed HSSATLBO algorithm has been demonstrated by seven well-known benchmark problems related to reliability optimization that includes series system, complex (bridge) system, series-parallel system, overspeed protection system, convex system, mixed series-parallel system, and large-scale system with dimensions 36, 38, 40, 42 and 50. After illustration, the outcomes of the proposed HSSATLBO are compared with several recently developed competitive meta-heuristic algorithms and also with three improved variants of SSA. Additionally, the HSSATLBO results are statistically investigated with the wilcoxon sign-rank test and multiple comparison test to show the significance of the results. The experimental results suggest that HSSATLBO significantly outperforms other algorithms and has become a remarkable and promising tool for solving RRAP. [ABSTRACT FROM AUTHOR]

In this paper, we study a joint placement, resource allocation, and user association problem for UAV-assisted wireless networks with constrained backhaul links, where multiple UAV-mounted base stations (UBSs) are deployed to provide wireless services for ground users. We propose a novel framework to maximize the user throughput within the flight-time of UBSs and provides fairness among the users. We first obtain the optimal resource allocation schemes based on different fronthaul and backhaul conditions, and an efficient iterative algorithm is then developed to jointly optimize user association and UBS placement. The optimal UBS placement can be achieved by solving an unconstrained optimization problem which is a simplification of the initial constrained optimization problem based on the optimal resource allocation. We develop a dual-domain coordinated descent and bipartite graph matching based sub-process to identify an optimal user association that prefers the nearby UBSs, as the user association under constrained backhaul links have non-unique optimal solutions. Extensive simulations are conducted to verify the effectiveness of the proposed algorithm, and results show that our proposed method under constrained backhaul can improve both the average throughput by 49% and the fairness among the users by 47% in comparison with the method under ideal backhaul. [ABSTRACT FROM AUTHOR]

Localization plays an important role in manufacturing the curved thin-walled parts, which can determine the distribution of machining allowance and has great influence on the manufacturing accuracy. The registration algorithm is the most efficient way to locate the billet in the machining coordinate system of the machine tool by computing a transformation matrix. However, the localization of the curved thin-walled parts is complicated and challenging since the billets are individual, the shape and location of which are unknown. This paper attempts to develop an adaptive localization approach with the constraints of the profile and thickness based on on-machine measured data. The framework for constrained adaptive localization approach is illustrated, in which on-machine measurement, registration, isometric mapping and allowance optimization are involved. The details of the on-machine measurement for both the profile inspection and the thickness measurement are presented. An isometric mapping method is employed to build the separate point pairs between the measured points and the nominal shape of the part. A constrained optimization algorithm for the machining allowance is performed iteratively until meeting the constraints of the profile and thickness tolerance ranges. Finally, a case study of constrained adaptive localization was carried out, the results of which confirm the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the constrained global optimization problems, in which the functions are of the "black-box" type and satisfy the Lipschitz condition. The algorithms for solving the problems of this class require the use of adequate estimates of the a priori unknown Lipschitz constants for the problem functions. A novel approach presented in this paper is based on a simultaneous use of two estimates of the Lipschitz constant: an overestimated and an underestimated one. The upper estimate provides the global convergence, whereas the lower one reduces the number of trials necessary to find the global optimizer with the required accuracy. The considered algorithm for solving the constrained problems does not use the ideas of the penalty function method; each constraint of the problem is accounted for separately. The convergence conditions of the proposed algorithm are formulated in the corresponding theorem. The results of the numerical experiments on a series of multiextremal problems with non-convex constraints demonstrating the efficiency of the proposed scheme of dual Lipschitz constant estimates are presented. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to outline a new approach to represent the randomness that we can find in different metaheuristics as a stochastic process which helps in the performance of the analyzed metaheuristic. This new way of viewing randomness is based on the behavior of sine waves that we can find in many situations in nature or in physics laws. In this paper, we evaluate this proposed randomness with three metaheuristics: the grey wolf optimizer, firefly algorithm and flower pollination algorithm, with the goal of studying the performance of the proposed randomness method in different types of metaheuristics. A set of standard benchmark functions were used to test the proposed randomness method, which are classified as unimodal and multimodal benchmark functions. In addition, the benchmark functions of the CEC 2015 Competition are used. Finally, we present tests with functions that were presented in the CEC 2017 competition for constrained real-parameter optimization. We also present a comparative study of the analyzed metaheuristics, and this comparison is between their original randomness method and the proposed randomness method for each algorithm. Finally, we present the performance and results of the methods with different number of dimensions to complete the study. [ABSTRACT FROM AUTHOR]

In this paper, a multi-objective bird swarm algorithm (MOBSA) is proposed to cope with multi-objective optimization problems. The algorithm is explored based on BSA which is an evolutionary algorithm suitable for single objective optimization. In this paper, non-dominated sorting approach is used to distinguish optimal solutions and parallel coordinates is applied to evaluate the distribution density of non-dominated solution and further update the external archive when it is full to overflowing, which ensure faster convergence and more widespread of Pareto front. Then, the MOBSA is adopted to optimize benchmark problems. The results demonstrate that MOBSA gets better performance compared with NSGA-II and MOPSO. Since a vehicle power train problem could be treated as a typical multi-objective optimization problem with constraints, with integration of constrained non-dominated solution, MOBSA is adopted to acquire optimal gear ratios and optimize vehicle power train. The results compared with other popular algorithm prove the proposed algorithm is more suitable for constrained multi-objective optimization problem in engineering field. [ABSTRACT FROM AUTHOR]