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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]

Node elimination is a numerical approach for obtaining cubature rules for the approximation of multivariate integrals. Beginning with a known cubature rule, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. This paper introduces a new criterion for selecting which nodes to eliminate that is based on a linearization of the moment equation. In addition, a penalized iterative solver is introduced, that ensures that weights are positive and nodes are inside the integration domain. A strategy for constructing an initial cubature rule for various polytopes in several space dimensions is described. High efficiency rules are presented for two, three and four dimensional polytopes. The new rules are compared with rules that are obtained by combining tensor products of one dimensional quadrature rules and domain transformations, as well as with known analytically constructed cubature rules. [ABSTRACT FROM AUTHOR]

Process monitoring based on neural networks is getting more and more attention. Compared with classical neural networks, high-order neural networks have natural advantages in dealing with heteroscedastic data. However, high-order neural networks might bring the risk of overfitting, which learning both the key information from original data and noises or anomalies. Orthogonal constraints can greatly reduce correlations between extracted features, thereby reducing the overfitting risk. This paper proposes a novel fault detection method called second-order component analysis (SCA). SCA rules out the heteroscedasticity of process data by optimizing a second-order autoencoder with orthogonal constraints. In order to deal with this constrained optimization problem, a geometric conjugate gradient algorithm is adopted in this paper, which performs geometric optimization on the combination of Stiefel manifold and Euclidean manifold. Extensive experiments on the Tennessee-Eastman benchmark process show that SCA outperforms the compared state-of-the-art methods with missed detection rate (MDR) and false alarm rate (FAR). • Second-order component analysis (SCA) is proposed for fault detection. • SCA uses the structure of autoencoder and adds second-order terms to improve nonlinear mapping capabilities. • SCA adopts orthogonal constraints to reduce the overfitting problem. • SCA adopts a geometric conjugate gradient (GCG) algorithm to deal with constrained optimization problem. [ABSTRACT FROM AUTHOR]

The challenges of classic rate-independent crystal plasticity models regarding the determination of active slip systems and computation of solutions due to linear dependent slip systems are still a field of active research. In that regard, interior-point methods are promising approaches because a logarithmic barrier term naturally avoids the combinatorial active set search, and these methods are applicable even when the gradient of inequality constraints is linearly dependent. In this paper, a new interior-point algorithm suitable for rate-independent crystal plasticity at finite strains is developed. For that purpose, the postulate of maximum dissipation is recast as a constrained optimization problem whose optimality conditions are derived by utilizing interior-point approaches. This optimization problem is discretized in time by means of an exponential time integration of the flow rule, and the time-discrete equations are solved by a Newton scheme. The focus of this paper is the efficiency and robustness of the implementation of this approach. In particular, the effect of different line search procedures, favorable residual forms, preconditioning methods, barrier parameter updates and the consistent algorithmic tangent modulus are discussed and further elaborated. In addition, aspects regarding uniqueness and well-posedness of the algorithm are analyzed in a geometrically linearized setting. Efficiency and robustness of the developed algorithm are shown by numerical examples of an FCC crystal including finite element simulations without stabilizing hardening or rate-dependent effects. Furthermore, the results are compared to the well-established augmented Lagrangian formulation. [ABSTRACT FROM AUTHOR]

The number of research works on dynamic constrained optimization problems has been increasing rapidly over the past two decades. In this domain, many real-life decision problems need to be solved repeatedly with changing data and parameters. However, no research on dynamic problems with changes in the coefficients of the constraint functions has been reported. In this paper, to deal with such problems, a new evolutionary framework with multiple novel mechanisms is proposed. The new mechanisms are for (1) dealing with both linear and non-linear components in the constraint functions, (2) identifying the rate of change in the coefficients of the variables and (3) updating the population efficiently after every change occurs in the problem. To evaluate the performance of the proposed algorithm, we designed a new set of 13 dynamic benchmark problems, each of which consists of 20 dynamic changes and 3 different scenarios. The results demonstrate that the proposed algorithm significantly contributes in achieving good quality solutions, high feasibility rates and fast convergence in rapidly changing environments. In addition, the framework shows its capability of using different meta-heuristics to solve dynamic problems. [ABSTRACT FROM AUTHOR]

• Stock management in a supply chain integrated inventory model. • A solution procedure is developed to find optimal policy for the problems under vendors warehouse capacity constraint. • Algorithms for solutions of unconstrained and constrained optimization problems. Coordination between a single manufacturer (vendor) and a buyer (retailer), via the delivery schedule in joint economic lot–sizing problem for a two stage supply chain, is investigated. To satisfy the buyer's demands, the product is delivered in discrete equal size sub-batches from the vendor's stock to the buyer's stock. Under stock management (SM) policy, the vendor delivers each sub-batch as soon as the buyer's inventory reduces to zero. For consignment stock (CS) policy, in the case of buyer's warehouse space limitation, the maximum level of the buyer's, consequently of the vendor's, inventory position can be controlled by the vendor's just in time or delayed deliveries (CS-k policies). If a space limitation is attached to vendor's warehouse, then the maximum level of the vendor's, consequently of the buyer's, inventory position can be controlled by just in time, or advanced for the buyer deliveries (in our notation SM-v-policies). Relatively optimal SM-v-policies can be obtained as solutions of adequate constrained problems. A comparative study, done in this paper, shows that the SM-v-policies can perform better than policies obtained as solutions of the sharply constrained problem where the maximal vendor's inventory level is equal to the maximum attainable space limit. Numerical examples are presented with appropriate comments to the solutions obtained by the proposed algorithm [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the problem of expertise matching with various constraints. Expertise matching, which aims to find the alignment between experts and queries, is a common problem in many applications such as conference paper–reviewer assignment, product–reviewer alignment, and product-endorser matching. Most existing methods formalize this problem as an information-retrieval problem and focus on finding a set of experts for each query independently. However, in real-world systems, various constraints are often needed to be considered. For example, in order to review a paper, it is desirable that there is at least one senior reviewer to guide the reviewing process. An important question is: “Can we design a framework to efficiently find the optimal solution for expertise matching under various constraints?” This paper explores such an approach by formulating the expertise matching problem in a constraint-based optimization framework. In the proposed framework, the problem of expertise matching is linked to a convex cost flow problem, which guarantees an optimal solution under various constraints. We also present an online matching algorithm to support incorporating user feedbacks in real time. The proposed approach has been evaluated on two different genres of expertise matching problems, namely conference paper–reviewer assignment and teacher–course assignment. Experimental results validate the effectiveness of the proposed approach. Based on the proposed method, we have also developed an online system for paper–reviewer suggestions, which has been used for paper–reviewer assignment in a top conference and feedbacks from the conference organizers are very positive. [Copyright &y& Elsevier]

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

Consider that the constrained convex optimization problems have emerged in a variety of scientific and engineering applications that often require efficient and fast solutions. Inspired by the Nesterov's accelerated method for solving unconstrained convex and strongly convex optimization problems, in this paper we propose two novel accelerated projection neurodynamic approaches for constrained smooth convex and strongly convex optimization based on the variational approach. First, for smooth, and convex optimization problems, a non-autonomous accelerated projection neurodynamic approach (NAAPNA) is presented and the existence, uniqueness and feasibility of the solution to it are analyzed rigorously. We provide that the NAAPNA has a convergence rate which is inversely proportional to the square of the running time. In addition, we present a novel autonomous accelerated projection neurodynamic approach (AAPNA) for addressing the constrained, smooth, strongly convex optimization problems and prove the existence, uniqueness to the strong global solution of AAPNA based on the Cauchy–Lipschitz–Picard theorem. Furthermore, we also prove the global convergence of AAPNA with different exponential convergence rates for different parameters. Compared with existing projection neurodynamic approaches based on the Brouwer's fixed point theorem, both NAAPNA and AAPNA use the projection operators of the auxiliary variable to map the primal variables to the constrained feasible region, thus our proposed neurodynamic approaches are easier to realize algorithm's acceleration. Finally, the effectiveness of NAAPNA and AAPNA is illustrated with several numerical examples. [ABSTRACT FROM AUTHOR]

The meta-heuristic algorithms have aroused great attention for controller optimization. However, most of them are inseparable from the explicit system models when addressing a constrained optimization problem (COP). In this paper, we propose a data-driven constrained bat algorithm via a gradient-based depth-first search (GDFS) strategy. In the proposed scheme, the GDFS strategy can predetermine a search space that satisfies some strict constraints (e.g., stability requirements) of the optimized system. Meanwhile, an improved boundary constraint handling method is proposed to limit the exploration process to the predetermined space. In this way, the proposed algorithm can solve the COP by utilizing experimental data from real scenes, thereby relieving the dependence on precisely modeling the complex system. Together with an ɛ -constraint-handling method, the bat algorithm is employed to seek the global optimum of the COP. The search performance is enhanced by the designed linear-varying elite layer-based local search and a social learning-based walk mechanism to dynamically balance exploration and exploitation. The convergence is ensured based on the criteria of the stochastic optimization algorithm. Experimental results on a servo drive system and benchmark test functions verify the effectiveness of the proposed algorithm. • Design a data-driven optimization method for the constrained controller tuning. • Design a gradient-based depth-first search strategy for strict constraints. • BA integrates a novel search mechanism to prevent premature convergence. • An improved boundary constraint handling scheme is proposed. [ABSTRACT FROM AUTHOR]

This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Firstly, a constrained generalized policy iteration (CGPI) framework is developed to handle state constraints by transforming the traditional policy improvement process into a constrained policy optimization problem. Next, we propose an actor-critic variant of CGPI, called CADP, in which both policy and value functions are approximated by multi-layer neural networks to directly map the system states to control inputs and value function, respectively. CADP linearizes the constrained optimization problem locally into a quadratically constrained linear programming problem, and then obtains the optimal update of the policy network by solving its dual problem. A trust region constraint is added to prevent excessive policy update, thus ensuring linearization accuracy. We determine the feasibility of the policy optimization problem by calculating the minimum trust region boundary and update the policy using two recovery rules when infeasible. The vehicle control problem in the path-tracking task is used to demonstrate the effectiveness of this proposed method. [ABSTRACT FROM AUTHOR]

Selection of the satellite equipment layout with performance constraints is a complex task which can be viewed as a constrained multi-objective optimization and a multiple criteria decision making problem. The layout design of a satellite cabin involves the process of locating the required equipment in a limited space, thereby satisfying various behavioral constraints of the interior and exterior environments. The layout optimization of satellite cabin in this paper includes the C.G. offset, the moments of inertia and the space debris impact risk of the system, of which the impact risk index is developed to quantify the risk to a satellite cabin of coming into contact with space debris. In this paper an optimization tool for the integration of CAD software as well as the optimization algorithms is presented, which is developed to automatically find solutions for a three-dimensional layout of equipment in satellite. The effectiveness of the tool is also demonstrated by applying to the layout optimization of a satellite platform. [ABSTRACT FROM AUTHOR]

Box-constrained optimization problems in the real m × n matrix space have been widely applied in big data mining. However, efficient solution of them is still a challenge. In this paper, a new nonmonotone line search rule is first proposed by extending the well-known ones and inheriting their advantages. Then, by analyzing and exploiting properties of this rule, a new nonmonotone spectral projected gradient algorithm is developed to solve the box-constrained optimization problems in the matrix space. Global convergence of the developed algorithm is also established. Numerical tests are conducted on a series of randomly generated test problems and those in the set of benchmark test problems. Compared with other existing nonmonotone line search rules, our rule shows its advantages in terms of the significantly reduced number of function evaluations and significantly reduced number of iterations. To further validate applicability of this research, we apply the studied optimization problem and the developed algorithm to solve the problems of image clustering. Numerical results demonstrate that the proposed method can generate better clustering results and is more robust than the similar ones available in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved version of Twin SVM using a non-smooth optimization method. Twin SVM generally consists in determining two non-parallel planes by alternately solving two constrained optimization models. Solving this problem using the classical Lagrangian method has many limitations, notably: its only limited to handle Gaussian noise, generally exaggerates the influence of outliers and cannot handle unbalanced data, this due to the differentiability of the model. To circumvent these issues, we transform two-constraint optimization models using the penalty method into an unconstrained non-smooth optimization one. The non-smoothness nature of the problem has many advantages, but it requires special treatment, which is why we use the primal dual method to solve it, since it is the most appropriate and it is robust in terms of stability, convergence and speed (Lyaqini, Nachaoui and Hadri, 2022). To demonstrate the effectiveness of the proposed approach, several experiments were carried out on numerous UCI benchmarks, medical image and HandPD datasets. These experiments demonstrated the effectiveness and applicability of the proposed approach, with satisfactory results compared to the state of the art. [ABSTRACT FROM AUTHOR]

In this study, a novel meta-heuristic search (MHS) algorithm for constrained global optimization problems is proposed. Since many algorithms aim to achieve well-balanced exploitation–exploration stages with often unsatisfactory results, in the approach introduced in this paper, Attraction–Repulsion Optimization Algorithm (AROA), the balance associated with attraction–repulsion phenomena that occur in nature is mimicked. AROA introduces a search strategy in which a candidate solution is moved in the search space depending on the quality of solutions in its neighborhood, as well as the best candidate. The candidates are managed by local search operators based on modified Brownian motion, trigonometric functions, randomly selected solutions, and a form of memory. Consequently, AROA exhibits a satisfactory exploitation–exploration balance exhibited by highly competitive performance. The introduced algorithm is experimentally compared with the state-of-the-art meta-heuristics on the CEC 2014, 2017, and 2020 test suites. The obtained results reveal the advantages of AROA over related algorithms and its suitability in solving complex real-world problems. • A novel attraction–repulsion search scheme is introduced. • Proposed meta-heuristic is governed by balanced search operators. • Algorithm is validated on three demanding CEC benchmarks. [ABSTRACT FROM AUTHOR]

A significant number of the planned on-orbit servicing and active debris removal missions will be performed by a spacecraft equipped with a robotic arm. In this paper we propose a new method for the path planning of the robotic arm mounted on the free-floating unmanned spacecraft. In the proposed approach the path of the arm is described in the joint space by a spline function. The coordinates of spline knots form the vector of decision variables. The constrained nonlinear optimization problem is formulated and solved with an active-set algorithm. The proposed method generates a collision-free path of the arm that results in the desired position and orientation of the gripper and the desired attitude of the spacecraft. The possibility of achieving all these goals at the same time is the major advantage of the proposed approach. The practical applicability of the presented method is demonstrated in experiments performed on the planar air-bearing microgravity simulator (for a planar case) and using numerical simulations performed with the Monte Carlo method (for a spatial case). In the planar case the optimal path is compared with the path obtained using the bi-directional Rapidly-exploring Random Trees (RRT) algorithm. It is shown that the path obtained using the proposed method is shorter and smoother than the RRT path. • A new method for path planning of a robotic arm mounted on a spacecraft is proposed. • The desired configuration of the gripper and attitude of the spacecraft is obtained. • The practical applicability is demonstrated in simulations and in experiments. • Experiments are performed on a planar air-bearing microgravity simulator. • The proposed approach is compared with the bi-directional RRT algorithm. [ABSTRACT FROM AUTHOR]

• This paper proposes an enhanced SCA algorithm variant, called ARSCA. • ARSCA improves the convergence accuracy and avoids premature convergence. • This paper compares ARSCA with classical algorithms, variations of other algorithms. • ARSCA is applied to six engineering design problems and its results are satisfactory. The sine cosine algorithm (SCA) is a well-known meta-heuristic optimization algorithm. SCA has received much attention in various optimization fields due to its simple structure and excellent optimization capabilities. However, the dimension of objective function also increases with the increasing complexity of optimization tasks. This makes the original SCA appear to have insufficient optimization capability and likely to fall into premature convergence. A multi-mechanism acting variant of SCA, called ARSCA, is proposed to address the above deficiencies. ARSCA is an enhanced SCA algorithm based on the adaptive quadratic interpolation mechanism (AQIM) and Rounding mechanism (RM). RM enables a more balanced state between exploration and exploitation of the ARSCA. AQIM enhances local exploitation capabilities. To verify the performance of ARSCA, we compared ARSCA with some advanced traditional optimization algorithms and variants of algorithms for 30 consecutive benchmark functions of IEEE CEC2014. In addition, ARSCA was applied to 6 constrained engineering optimization problems. These six algorithms include the tension–compression spring design problem, the welded beam design problem, the pressure vessel design problem, the I-beam design problem, the speed reducer design problem, and the three-bar design problem. Experimental results show that ARSCA outperforms its competitors in both the solution quality and the ability to jump out of the local optimum. The relevant codes for the paper are publicly available at https://github.com/YangXiao9799/paper_ARSCA. [ABSTRACT FROM AUTHOR]

• Transform the max-bisection problem to a linearly constrained optimization problem. • Propose a deterministic annealing neural network algorithm by introducing a barrier function in square-root form. • Prove the existence of the integral minimum solution of the max-bisection problem in theory and the proof is simpler than other algorithms. • Experimental results show that the proposed method outperforms other methods. The max-bisection problem has extensive applications in network engineering, making it imperative to develop effective methods to solve this problem. However, the efficient computation on this problem remains challenging due to its NP-hard computational complexity. To address this question, in this paper, we transform the max-bisection problem to an artificial linearly constrained optimization problem and develop a modified deterministic annealing neural network algorithm by introducing a barrier function. The barrier parameter of this function acts as the temperature in the annealing process and decreases from a large positive number to zero. The initial value of the barrier parameter promises that the artificial problem is convex and can be easily solved at the beginning of the descending process. The solution to the original max-bisection problem is finally obtained through a descent algorithm, in which the bound limit of the solution is always satisfied as long as the iteration step length is less than one. We have proved the theoretical convergence of the proposed algorithm. Numerical results demonstrate that the proposed algorithm has several advantages over both the approximation algorithms and metaheuristic methods. [ABSTRACT FROM AUTHOR]

This paper studies a smoothing norm objective penalty function for two-cardinality sparse constrained optimization problems. Good properties are proved for the smoothing norm objective penalty functions in solving two-cardinality sparse constrained optimization problems, after which an algorithm is presented. Furthermore, its convergence is also proved under some conditions. The proposed algorithm can solve a satisfactory approximate optimal solution in a numerical example. [ABSTRACT FROM AUTHOR]

When solving constrained optimization problems in real industrial processes, both optimality and computational efficiency need to be considered. However, most existing meta-heuristic algorithms are slow to find the global optimum. The first reason is that the way to generate and select candidate solutions is time-consuming. The low probability to generate and select potential solutions in assisting the computational efficiency is another reason. In this paper, a simplified state transition algorithm (STA) and a novel constraint-handling technique are proposed to address the above issues for small size constrained optimization problems. Firstly, three out of four operators in basic STA to produce candidate solutions are selected and two operators are modified with adaptive parameter tuning, which have a large probability to generate potential solutions, but consumes less time. Secondly, the constraint-handling technique considers not only the objective function value and the constraint violation but also the difference among candidate solutions. Thirdly, the sequential quadratic programming embedded into the simplified STA can further speed up the convergence. Experiments are conducted on 22 well-known test functions from IEEE CEC2006 and 4 engineering constrained optimization problems, in comparison with state-of-the-art algorithms. The experimental results show that the proposed method is competitive in finding the optimum faster. [ABSTRACT FROM AUTHOR]

In this paper, the inverse problem of the determination of an unknown discontinuous parameter in elliptic equations is considered. A constrained optimization problem is formulated using the TV regularization and a specified selection term, in order to absorb the effect of noise and singularities. The discretization scheme used in this work is a combined finite element/volume method, then we establish the discrete version of optimization problem. The convergence and stability analysis are performed in term of noise level and diameter of singular set. We have considered the projected Wolfe algorithm to design our proposed minimization method. At the end we show some numerical experiments to prove the validity of theoretical results and the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a new hybrid algorithm of Harris hawks' optimization with sequential quadratic programming (HHO-SQP) for optimal coordination of directional overcurrent relays to find optimal relays settings. The SQP procedure is employed in the hybrid algorism as a local search mechanism to enhance the performance of the original HHO method. The optimization problem is described based on a developed objective function as a non-linear and highly constrained optimization problem to minimize the total operating time for primary relays at the same time of maximizing the backup relays operating time. The developed objective function is subject to some constraints related to the coordination process including the absence of any miss coordination between primary and backup relays. The performance of the proposed algorithm based on the new objective function is implemented for two different test systems. The results of the proposed algorithm is compared with those obtained from other recent meta-heuristic techniques. The results show that the new hybrid algorithm outperforms the recently published meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

As an indicator of the stability of spectral clustering of an undirected weighted graph into k clusters, the k th spectral gap of the graph Laplacian is often considered. The k th spectral gap is characterized in this paper as an unstructured distance to ambiguity, namely as the minimal distance of the Laplacian to arbitrary symmetric matrices with vanishing k th spectral gap. As a conceptually more appropriate measure of stability, the structured distance to ambiguity of the k -clustering is introduced as the minimal distance of the Laplacian to Laplacians of graphs with the same vertices and edges but with weights that are perturbed such that the k th spectral gap vanishes. To compute a solution to this matrix nearness problem, a two-level iterative algorithm is proposed that uses a constrained gradient system of matrix differential equations in the inner iteration and a one-dimensional optimization of the perturbation size in the outer iteration. The structured and unstructured distances to ambiguity are compared on some example graphs. The numerical experiments show, in particular, that selecting the number k of clusters according to the criterion of maximal stability can lead to different results for the structured and unstructured stability indicators. [ABSTRACT FROM AUTHOR]

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O 1 t . Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O 1 t 2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The cooperation of multi-agent systems (MAS) based on distributed model predictive control (DMPC) is a current research hotspot, and how to more effectively handle additive disturbances and reduce resource consumption are two difficult problems that need to be solved. In view of this, this paper aims to design a more effective DMPC strategy for MAS, so as to effectively deal with the above problems without loss of the control performance. Firstly, a finite-horizon constrained optimization problem is established for MAS, in which a robustness constraint is designed to effectively handle additive disturbances. Then, a new efficient event-triggering condition is designed, which is established by considering the mixed information of differential and integral of the state error. Furthermore, based on the dual-mode control, an event-triggered robust DMPC algorithm is proposed to further reduce the resource consumption of the system. In addition, theoretical results are provided through analysis and deduction to ensure the iterative feasibility of the algorithm, stability of the closed-loop system and Zeno-free behavior. Finally, the proposed algorithm is applied to two examples for simulation and comparison to verify its effectiveness. The simulation results show that compared to DMPC and classical event-triggered DMPC methods, the proposed algorithm can reduce the average resource consumption of MAS by more than 81% and 36%, respectively, which indicates that the proposed strategy can effectively reduce the computation and communication burden of MAS without affecting the control performance. [ABSTRACT FROM AUTHOR]

Over the past decade, surrogate-assisted evolutionary algorithms have demonstrated their effectiveness across various computationally expensive real-world domains. Nevertheless, the focus of surrogate-assisted multi-objective evolutionary algorithms has primarily centered on non-constrained optimization problems. There has been relatively limited exploration into addressing expensive constrained multi-objective optimization problems, which inherently require a delicate equilibrium between convergence, diversity, and feasibility. To bridge this gap, this paper concentrates on constrained multi-objective optimization problems where both objectives and constraints involve substantial computational costs. In response, a novel data-driven constrained multi-objective evolutionary algorithm is introduced, leveraging feasible region localization and performance-improvement exploration. For feasible region localization, a constraints-domain-search strategy is presented to locate the feasible region quickly. To enhance performance-improvement exploration, a progressive enhancement of convergence and diversity is achieved through the incorporation of constraint penalties. With the help of exploration and exploitation, the proposed algorithm can balance convergence, diversity, and feasibility while working within a limited number of function evaluations. By comparing the proposed algorithm with state-of-the-art algorithms on 66 mathematical problems and a resource-intensive black-box problem, its outstanding performance for solving multi-objective constrained black-box problems is validated. • A notably effective multi-objective constrained black-box optimization algorithm is proposed. • A constraints-domain-search strategy is designed to rapidly decrease the CV while avoiding a local minimum in the CV space. • A performance-improvement exploration strategy is presented through the integration of constraint penalties. • Comprehensive conclusions that can serve as valuable insights for future algorithm development are included. [ABSTRACT FROM AUTHOR]

In this paper a novel nature-inspired optimization paradigm is proposed called Moth-Flame Optimization (MFO) algorithm. The main inspiration of this optimizer is the navigation method of moths in nature called transverse orientation. Moths fly in night by maintaining a fixed angle with respect to the moon, a very effective mechanism for travelling in a straight line for long distances. However, these fancy insects are trapped in a useless/deadly spiral path around artificial lights. This paper mathematically models this behaviour to perform optimization. The MFO algorithm is compared with other well-known nature-inspired algorithms on 29 benchmark and 7 real engineering problems. The statistical results on the benchmark functions show that this algorithm is able to provide very promising and competitive results. Additionally, the results of the real problems demonstrate the merits of this algorithm in solving challenging problems with constrained and unknown search spaces. The paper also considers the application of the proposed algorithm in the field of marine propeller design to further investigate its effectiveness in practice. Note that the source codes of the MFO algorithm are publicly available at http://www.alimirjalili.com/MFO.html . [ABSTRACT FROM AUTHOR]

To enhance the machining efficiency, curved thin-walled parts in the aerospace and automobile industries are often formed to the near-net shapes and then subtractive manufactured to their design shapes. The billets for the manufacturing process may lack of the removal material in some regions due to low forming accuracy, which would increase the rejection rate of these parts. However, there is a chance that some rejected billets can be saved by using partial tolerance ranges to compensate the shape errors of the raw billets. Aiming to reduce the rejection rate and save the production cost, this paper attempts to develop a novel approach for constructing process shape of curved thin-walled part, in which its nominal shape was slightly changed within their tolerance ranges to avoid the undercut during the machining process. Firstly, a registration algorithm was used to find an optimal position between the design shape and the on-machine measurement points. Afterwards, a non-linear constrained optimization model was established to search for the feasible points in the tolerance ranges, in which the profile occupancy, thickness occupancy and non-uniformity of machining allowances were carefully considered. Finally, a new process shape was constructed based on these feasible points, which could be used for adaptive machining of curved thin-walled part. The results of a case study validated the feasibility of the proposed process shape construction approach. • The framework for a novel process shape construction approach was presented for adaptive machining. • A non-linear constrained optimization model was established to search for the feasible points in the tolerance ranges. • The profile occupancy, thickness occupancy and non-uniformity of machining allowances were carefully considered. [ABSTRACT FROM AUTHOR]

Well-conditioned matrices are often required in science and engineering, such as signal processing and finance. Problem to find the nearest positive definite matrix by explicitly imposing a constraint on the condition number are considered in this paper. A new algorithm based on geometric perspective is proposed for getting the required well-conditioned matrix. Based on these, a condition number-constrained matrix minimization problem is further considered, where the constraints are imposed for avoiding degenerate solutions in which parameter matrices become rank deficient. An inexact version of alternating direction method with truly implementable inexactness criteria is proposed for solving this problem. Numerical experiments, including comparison with some existing methods, are performed to illustrate the efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a deterministic optimization strategy to solve the economic-environmental power dispatch (EEPD) problem of an electrical power system, using a Broyden Fletcher Goldfarb Shanno based on the augmented Lagrangian (BFGS-AL) algorithm. This problem is a nonlinear constrained multi-objective optimization. The objectives of this optimization are minimized the total fuel cost and emission amount for thermal generators while satisfying electric power systems equality and inequality constraints. The proposed approach is applied on the standard IEEE 30 bus test system, where the power transmission losses are taken into account. Simulation results proved that the proposed approach gives better-quality solution in terms of accuracy and convergence to the best compromise solution compared to other deterministic and meta-heuristic optimization techniques. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm based on collective neurodynamic system is investigated for distributed constrained convex optimization, whose objective function is a sum of smooth convex functions and non-smooth L 1 -norm functions. Inspired by recent advances in distributed convex optimization, the continuous-time and discrete-time distributed optimization algorithms described by collective neurodynamic systems are proposed. In the systems, each of the smooth objective functions is allocated to each node as well as each of the L 1 -norm functions. However, the L 1 -norm functions are realized by projection operators. Meanwhile, each node satisfies the local linear and bound constraints. Then a connected network is constituted from all the nodes with consensus to find the optimal solutions. [ABSTRACT FROM AUTHOR]