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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]

This paper focuses on the applicability of Zermelo's equation within the context of 3D commercial aircraft trajectory optimization problems. The associated optimal control problem includes two singular controls, specifically aerodynamic path angle and throttle setting, and one regular control, specifically heading angle. Using Pontryagin's maximum principle and the direct adjoining method, we show that the optimal heading angle is defined by Zermelo's equation. The significance of the presented analysis is that Zermelo's equation holds for 3D commercial aircraft flights, even in the presence of standard state-inequality constraints and a more general objective function. With the help of Zermelo's equation, the control problem is initially analyzed for a 3D time-optimal climb-phase scenario, which is solved by an indirect approach. Through the analysis of the switching function, we demonstrate the dependency of the optimal aerodynamic path angle on the optimal heading angle. Next, by tackling a 3D time-fuel-optimal free-routing flight, solved by a direct approach, we show that Zermelo's equation can help reduce the overall dimension of the associated nonlinear programming. To successfully handle the initial guess in both indirect and direct problems, it is proposed a diminutive nonlinear programming technique as a fast and robust initializer. This simple-yet-effective initializer provides sufficient information about the optimal controls and state dynamics required for initializing a direct optimization, as well as the optimal switching times and co-states required for initializing an indirect optimization. • Demonstrating the applicability of Zermelo's equation to constrained optimization of 3D aircraft flights. • Solving 3D time-optimal problem in climb phase with Zermelo's identity using an Indirect method. • Solving 3D time-fuel-optimal free-routing problem with Zermelo's identity using a new Direct transcription method. • Brief discussion on aNLP for initialization of both Indirect and Direct methods. [ABSTRACT FROM AUTHOR]

• A novel human-based algorithm: the flavoring search algorithm. • Flavoring search algorithm corresponds to the real-world flavoring process. • Flavoring search algorithm proposes a unique flavor factor. • A Markov model of the flavoring search algorithm is developed. • Flavoring search algorithm is applied to engineering problems and robot path planning. In this paper, a human-based meta-heuristic algorithm, the Flavoring Search Algorithm, is proposed and mathematically modeled with the aim of providing an alternative optimization method for solving practical engineering problems. Flavoring Search Algorithm is inspired by the human behavior of flavoring in everyday life, including basic flavoring, formal flavoring, and auxiliary flavoring. By introducing a unique taste factor, it not only succeeded in making the Flavoring Search Algorithm corresponds to the real flavoring process but also balanced the exploration and exploitation of the algorithm. With the help of the taste factors, Flavoring Search Algorithm performs basic flavoring (initial flavoring and random flavoring) in the exploration phase and formal flavoring and auxiliary flavoring in the exploitation phase. In addition, theoretical analysis and experiments have led to the conclusion that the taste factor can be used as an effective and practical new threshold conversion mechanism for meta-heuristic algorithms. This study also establishes a Markov model to rigorously analyze the Flavoring Search Algorithm as a globally convergent algorithm from a mathematical point of view. Through experimental and analytical comparisons with other excellent optimizers on 30 test functions, as well as on 3 real-world engineering design problems and 1 path planning problem. The results show that the Flavoring Search Algorithm generally outperforms the tested competitors in solving benchmark functions and engineering problems, validating the utility of the proposed optimizer in solving challenging real-world problems. [ABSTRACT FROM AUTHOR]

One of the most challenging robotic manipulator designs is finding an appropriate balance between the shaking force and shaking moment because this reduces vibrations. Several approaches have been introduced in the last decades; nevertheless, some assumptions must be established to make such a balance. In this paper, a dynamic balancing approach is proposed. The main novelty is the no dependence on specific trajectories to be executed by the manipulator, which allows finding a design with a similar tradeoff in the balancing under robot configuration changes. Also, the proposal incorporates mass distribution and link shape in a single design procedure. The proposal is stated as a constrained nonlinear optimization problem and applied to a hybrid serial-parallel robotic manipulator. The use of different bio-inspired algorithms and one gradient one in the solution of the balancing problem reveals that differential evolution finds the most suitable design. Besides, comparative simulation results of the obtained design with other design approaches show that the obtained design presents the most suitable tradeoff between the shaking force and the shaking moment when the manipulator executes tasks with different operating velocities. [ABSTRACT FROM AUTHOR]

• Propose a topology optimization method for large deformation-induced frictionless contact structures. • Develop a novel nodal density interpolation for the node-to-segment contact model. • Develop the P-norm aggregated strain energy constraint for strength design. • Potentially applicable to the design of functionally demanding wearable devices and soft robots. This paper developed a strength constrained topology optimization method for hyperelastic structures with large deformation-induced frictionless contact. The Neo-Hookean hyperelastic constitutive equation is adopted as the material model that incorporates both material and geometric nonlinearity. The large deforming contact is described by the node-to-segment algorithm. The topology optimization model is developed under the SIMP framework. Given the SIMP-related fictitious domain, we develop a nodal variable-based interpolation scheme to build smooth correlation between the contact force and nodal density variables, thus enabling the smooth transition and variation of contact conditions. Moreover, to guarantee the structure strength, local strain energy constraints are formulated and aggregated by the P-norm function. The details of sensitivity analysis are explicitly explained. At last, several benchmark examples are conducted that validate the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a delayed distributed proportional control is developed for a class of multiple-input-multiple-output systems in order to reduce the effects of external disturbances and uncertain dynamics. The system under consideration is a three degrees-of-freedom planar robot, consisting of an active joint driving the first link and passive flexible joints for the second and third links. The control challenge for this system is to drive the flexible arm around the desired setpoint or trajectory by controlling the first link. Actually, by using a specific Lyapunov-Krasovskii storage functional associated with a constrained optimization problem, the robustness of the proposed proportional retarded control action is achieved. This analysis, together with the attractive ellipsoid concept allows to conclude with Ultimately-Uniformly-Bounded stability. The closed-loop control algorithm is tested in numerical simulation and a comparative study with some existing recent control schemes based on the performance error is presented. • The proposed control scheme belongs to a class of multivariable proportional time delay distributed controller. • After finite time the trajectories of a flexible manipulator stay within reduced size attractive ellipsoid. • Ultimate Uniformly Bounded Stability of the controlled system is demonstrated by using a Lyapunov-Krasovskii functional. • The proposed algorithm can also be adapted for a class of nonlinear uncertain/disturbed multivariable output systems. • A sufficient condition to guarantee the feasibility of specific Bilinear Matrix Inequality is presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved enhancement space-variant anisotropic PDE-constrained for image denoising, based on a learning optimization procedure. Since the tensor structure of the Weickert-type operators encodes three critical parameters: λ 1 , λ 2 and θ , which define the local direction geometry in the image and also controls smoothing intensity along image features. We have then adopted an automatic estimation of these parameters based on a PDE-constrained optimization with a learning step of the additional information about the clean image. For the numerical solution of the computed free-noise image, we introduce a non-smooth Alternating Direction Method of Multipliers (ADMM) algorithm. The numerous tests in the experiments part incense, visually and quantitatively, the incomes of this new spatial tensor for PDE smoothing over the other denoising approaches. • An improved enhancement space-variant anisotropic PDE-constrained for image denoising is introduced. • An automatic estimation of the diffusion-tensor parameters based on a bilevel optimization with a learning step is involved. • A non-smooth ADMM algorithm is also performed to compute the solution of the optimization-constrained problem. • The comparative results demonstrate the performance of the proposed algorithm against complex noise structures. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient bi-level energy management strategy (EMS) to optimize the operation cost of a grid-connected microgrid, considering the system operational constraints and uncertainties for renewable energy sources and load demand. The first level is optimal day-ahead scheduling based on two stages: the first stage is finding the optimal operating points of sources during the next day while the second one is controllable loads management. The second level of the proposed EMS is rescheduling and updating the set-points of sources in real-time according to the actual solar irradiance, wind speed, load, and grid tariff. In this paper, a novel real-time strategy is proposed to keep the economic operation during real-time under uncertainties. Also, a recent meta-heuristic algorithm called Honey Badger Algorithm (HBA) is used to solve the problem of day-ahead scheduling of batteries, which is a complex constrained non-linear optimization problem. Results obtained demonstrate that the HBA based bi-level EMS provides the real-time optimal economic operation of a grid tied microgrid under uncertainties in weather, utility tariff and load forecasts. • Bi-level energy management strategy for optimal operation of grid tied microgrids. • Load shifting approach that reshapes the load according to the target load profile. • A novel real-time scheduling strategy of grid tied microgrids under uncertainties. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is combining the augmented Lagrangian framework with adaptive sampling, resulting in an efficient optimization methodology validated with practical examples. To achieve the presented efficiency, we consider inexact solutions for the augmented Lagrangian subproblems, and through an adaptive sampling mechanism, we control the variance in the gradient estimates. Furthermore, we analyze the theoretical performance of the proposed scheme by showing equivalence to a gradient descent algorithm on a Moreau envelope function, and we prove sublinear convergence for convex objectives and linear convergence for strongly convex objectives with affine equality constraints. The worst-case sample complexity of the resulting algorithm, for an arbitrary choice of penalty parameter in the augmented Lagrangian function, is O (ϵ − 3 − δ) , where ϵ > 0 is the expected error of the solution and δ > 0 is a user-defined parameter. If the penalty parameter is chosen to be O (ϵ − 1) , we demonstrate that the result can be improved to O (ϵ − 2) , which is competitive with the other methods employed in the literature. Moreover, if the objective function is strongly convex with affine equality constraints, we obtain O (ϵ − 1 log ⁡ (1 / ϵ)) complexity. Finally, we empirically verify the performance of our adaptive sampling augmented Lagrangian framework in machine learning optimization and engineering design problems, including topology optimization of a heat sink with environmental uncertainty. [ABSTRACT FROM AUTHOR]

Multi-objective immune algorithm (MOIA) is a heuristic algorithm based on artificial immune system model. Due to its characteristics of antibody clonal selection, automatic antigen recognition and immune memory in the immune system, artificial immune algorithm has become a research hotspot in the field of multi-objective optimization after the evolutionary algorithms. In this paper, most MOIAs can be classified into three main categories according to the type of problem solving, i.e., they are mostly designed to solve multi-objective optimization problems (MOPs), dynamic MOPs, and constrained MOPs. In this paper, a comprehensive survey is presented to summarize most existing MOIAs, in which their corresponding characteristics, principles and theoretical analyses are discussed in details. Moreover, the performance of MOIAs on solving various kinds of MOPs and many-objective optimization problems is also studied in our experimental comparisons. Finally, a brief conclusion is given to summarize the current drawbacks, challenges, and some future directions for MOIAs. [ABSTRACT FROM AUTHOR]

Dynamic Constrained Multiobjective Optimization Problems (DCMOPs) are very difficult to solve because both of the objectives and constraints may change over time. The existing approaches for solving DCMOPs mainly develop dynamic response techniques and constraint handling techniques. But they do not focus on the search capability of the static optimizer in each environment, which ignores the intrinsic requirement of quickly locating Pareto-optimal Front (PF) in each environment when solving DCMOPs. To this end, this paper proposes a dual-population evolutionary algorithm for solving DCMOPs, called as DpEA, which maintains a population without considering constraints (called UP) for exploration and a population with considering constraints (called CP) for exploitation in each environment. In each iteration of a new environment, UP firstly adopts a stratified mutation strategy (SMS) and a dominated solution repairment strategy (DSR) to enhance the exploration ability of finding promising regions where the PF may reside. SMS uses solutions from different nondominated fronts to generate offspring, while DSR repairs the single-optimal variables of the dominated solutions by sampling from the distribution of those variables of nondominated solutions. Secondly, this paper uses an adaptive offspring ratio adjustment strategy to control the offspring number generated by UP and CP according to the normalized Hausdorff distance between nondominated solution sets from the two latest generations of UP. This strategy is helpful to balance the intensity between exploration and exploitation and thereby ensures efficient search. Experimental results on CEC 2023 DCF test suite show that DpEA has a superior performance over six state-of-the-art algorithms. • First EA that focuses on the search capability of static optimizer in solving DCMOPs. • Two offspring generation strategies to enhance the exploration ability. • An adaptive strategy to balance the intensity between exploration and exploitation. [ABSTRACT FROM AUTHOR]

Nature- and society-inspired metaheuristic algorithms have recently become the most promising technological model. To solve more complex optimization problems and complicated engineering applications, this paper proposes a new people duality psychological tendency and feedback mechanism-based Inherited Optimization Algorithm(IOA), which is inspired by people showing positive-negative duality cognitive tendency and adaptive feedback behavior when selecting information resources with different identity attributes. The IOA algorithm contains the symmetric two exploration phases. The exploitation phase adaptively regulates the dualistic psychological balance of people in inheriting the information resources with better existence value through a feedback regulation mechanism controlled by the profitability awareness to increase population diversity. This paper qualitatively and quantitatively evaluates the optimization performance of IOA on 84 benchmarks, including swarm convergence behavior, effectiveness, convergence, robustness, and significance. The scalability of the IOA is investigated using the CEC2017 suites. The algorithm performance in solving constrained optimization is verified on 8 engineering problems. All statistical results of the IOA are compared with the most promising 12 metaheuristics, which shows that the absolute computational efficiency of IOA on four types of functions is 95%, 96.67%, 80.95%, and 76.92%, respectively, the average rank (rank sum ratio) of IOA is 1.08 (1.19%) among the 13 algorithms, ranking first. The Wilcoxon signed rank test results on the CEC2017 suites show that IOA contains 1437 significance indicators out of 1440 comparisons, with the proportion of significant differences 99.79%, which suggests the proposed IOA maintains efficient search efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a formal verification guided approach for a principled design and implementation of robust and resilient learning-enabled systems. We focus on learning-enabled state estimation systems (LE-SESs), which have been widely used in robotics applications to determine the current state (e.g., location, speed, direction, etc.) of a complex system. The LE-SESs are networked systems, composed of a set of connected components including: Bayes filters for state estimation, and neural networks for processing sensory input. We study LE-SESs from the perspective of formal verification, which determines the satisfiabilty of a system model against the specified properties. Over LE-SESs, we investigate two key properties – robustness and resilience – and provide their formal definitions. To enable formal verification, we reduce the LE-SESs to a novel class of labelled transition systems, named {PO}2-LTS in the paper, and formally express the properties as constrained optimisation objectives. We prove that the verification problems are NP-complete. Based on {PO}2-LTS and the optimisation objectives, practical verification algorithms are developed to check the satisfiability of the properties on the LE-SESs. As a major case study, we interrogate a real-world dynamic tracking system which uses a single Kalman Filter (KF) – a special case of Bayes filter – to localise and track a ground vehicle. Its perception system, based on convolutional neural networks, processes a high-resolution Wide Area Motion Imagery (WAMI) data stream. Experimental results show that our algorithms can not only verify the properties of the WAMI tracking system but also provide representative examples, the latter of which inspired us to take an enhanced LE-SESs design where runtime monitors or joint-KFs are required. Experimental results confirm the improvement in the robustness of the enhanced design. [ABSTRACT FROM AUTHOR]

Avoiding singularities is a crucial task in robotics and path planning. This paper proposes a novel algorithm for detecting the closest singularity to a given pose for nine interpretations of the 3-RPR manipulator. The algorithm utilizes intrinsic metrics based on the framework's total elastic strain energy density, employing the physical concept of Green-Lagrange strain. The constrained optimization problem for detecting the closest singular configuration with respect to these metrics is solved globally using tools from numerical algebraic geometry implemented in the software package Bertini. The effectiveness of the proposed algorithm is demonstrated on a 3-RPR manipulator executing a one-parametric motion. Additionally, the obtained intrinsic singularity distances are compared with extrinsic metrics. Finally, the paper illustrates the advantage of employing a well-defined metric for identifying the closest singularities in comparison with the existing methods in the literature, highlighting its application in design optimization. [ABSTRACT FROM AUTHOR]

Constrained multitasking optimization (CMTO) obtains increasing attention recently. The goal of CMTO is to handle multiple constrained tasks simultaneously. There are two limitations of existing studies on CMTO: (i) existing knowledge transfer techniques for CMTO may not work due to non-intersecting feasible domains and the unconsidered relationship between constraints and objectives; and (ii) knowledge diversity is lacking in existing CMTO algorithms because the representation of knowledge is biased to feasible solutions. To address these limitations, this paper proposes a co-evolution and domain adaptation (CEDA) method for CMTO. First, a new constraint relaxation-based domain adaptation technique for knowledge transfer is devised. Domain adaptation can effectively address the limitations imposed by non-intersecting feasible domains. In addition, as the population evolves, the knowledge representation is biased to different kinds of solutions. Second, a co-evolutionary strategy is proposed to improve the knowledge diversity. The two proposed techniques are with generality and can be readily integrated into different multitasking frameworks. In this paper, the CEDA method is combined with two popular multitasking (i.e., multifactorial-based and multi-population-based) frameworks. The constructed CEDA-based algorithms are compared with fifteen state-of-the-art algorithms on a CMTO benchmark suite and a real-world application. Experimental results demonstrate the superiority of the proposed CEDA method. [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]

• A Kriging-assisted global reliability-based design optimization (KG-RBDO) algorithm is proposed. • KG-RBDO consists of a global optimization module and a local optimization module. • A new infill criterion considering both the optimality and the reliability requirement of the solutions is proposed. • KG-RBDO is more approximate to the global reliability-based design optimization problems. Surrogate models have been extensively used in reliability-based design optimization (RBDO); however, few studies have focused on the global optimality of RBDO. This paper proposes a global RBDO framework that employs Kriging surrogate models to approximate both the objective function and performance functions. The proposed algorithm comprises two major modules: the global optimization module and the local optimization module. The former module aims to identify the interested region containing potential optima, while the latter module refines the local optima. To address the time-consuming acquisition of samples, two different infill strategies are implemented in these two modules. Furthermore, in addition to evaluating the optimal solution in the local optimization module for infill, a reliability-constrained expected improvement infill criterion is developed for the global optimization module. This criterion inherits the property of the expected improvement from the Kriging model, which balances the exploration and the exploitation of the objective space, while taking reliability into account by introducing the shifting vector into the calculation of the probability of feasibility. Numerical experiments indicate that the performance of the proposed infill criterion is significantly superior to others in searching for optima. Several examples verify the global optimization capability of the proposed algorithm and illustrate that it is more suitable for RBDO problems with multiple local optima. [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]

In this paper, we present two-timescale neurodynamic optimization approaches to distributed minimax optimization. We propose four multilayer recurrent neural networks for solving four different types of generally nonlinear convex–concave minimax problems subject to linear equality and nonlinear inequality constraints. We derive sufficient conditions to guarantee the stability and optimality of the neural networks. We demonstrate the viability and efficiency of the proposed neural networks in two specific paradigms for Nash-equilibrium seeking in a zero-sum game and distributed constrained nonlinear optimization. [ABSTRACT FROM AUTHOR]

This paper uses the mirror descent algorithm with periodic dynamic quantization to solve constrained distributed optimization problems with limited communication channels. Due to the imperfect network environment, obtaining accurate information is impractical, and thus a communication scheme under quantization needs to be considered. A periodic dynamic quantizer with finite quantization levels is proposed in this paper to achieve exact optimization. Moreover, a time-varying control parameter in the mirror descent algorithm is designed to control the quantization error. After a comprehensive analysis, the proposed algorithm can obtain an optimal value, and the optimal convergence rate is O (1 / T 0. 25). [ABSTRACT FROM AUTHOR]

The railway world is undergoing major changes. The advent of new technologies allows us to rethink the train system and face new challenges, but one must not forget all the ecological constraints that are now accentuated by the increase in energy costs. This paper focuses on the optimization of the driver commands to limit the energy consumption of the trains under punctuality and security constraints. This problem falls within the framework of control optimization problems for nonlinear dynamic mechanical systems in the presence of constraints and uncertainties. A four-step approach is then proposed in this paper to solve this problem: (1) the introduction of simplified and fast-to-evaluate models to model the nonlinear dynamic behavior of the train and its energy consumption; (2) the identification in a Bayesian formalism of the parameters on which these models depend from on-track measurements on commercial trains; (3) the reformulation of the optimization problem so that it integrates the uncertainties related to an imperfect knowledge of these estimated parameters; (4) the resolution of the optimization problem using evolutionary algorithms. The main specificity of this work lies in the fact that not only the objective function to be minimized, here the energy consumed by the train, is impacted by the uncertainties, but also the admissibility constraints of the solution, here punctuality and operating safety. The integration of the uncertainties in the search for the control function is thus not trivial and requires several original adaptations in order to make the final optimization problem well posed. • The paper considers a particular constrained control optimization problem. • Uncertainties on the cost function and constraints make the problem difficult. • The control problem is first reformulated to make the constraints deterministic. • Evolutionary algorithms are then used to identify optimized control functions. • An application to the minimization of the train electrical consumption is presented. [ABSTRACT FROM AUTHOR]

Particle Swarm Optimization (PSO) is a robust stochastic optimization algorithm for solving complex and constrained optimization problems. This paper aims to systematically investigate the influence of diverse random number distributions on the learning parameters of PSO and evaluate the algorithm's sensitivity based on these parameters. To this end, several exhaustive numerical experiments were conducted on several test functions, including asymmetric Sphere, Easom, and Csendes. Initially, appropriate random distributions were identified for the learning parameters and proceeded to compare these distributions using all potential combinations. The sensitivity of PSO to these parameters was evaluated using the mean best score, the relative proximity of the best particle to the theoretical optimum, and the average objective function evaluations. The most significant contribution of this research lies in the insights derived from the experimental data. The discovery was that highly skewed and long-tailed distributions such as Chi, Chi-square, Lomax, and Exponential often underperform. On the other hand, distributions that are bounded proportionally to the problem domain consistently surpass the performance of the standard uniform distribution. These findings significantly enhance the understanding of PSO algorithms and provide valuable guidelines for their practical deployment. [ABSTRACT FROM AUTHOR]

Regarding a general class of integrating processes subject to uncertain delays, this paper investigates a two-degree-of-freedom (2-Dof) control scheme with a proportional–derivative (PD) controller and disturbance observer (DOB). Relative delay margin is introduced as a paramount metric to evaluate the delay robustness, with which a set of novel and explicit tuning formulae for PD controller is analytically derived under the single external loop. In this individual frame, the stability boundaries associated with the governing parameters are first studied, indicating the nominal stability conditions for the 2-Dof control system. Then the optimal tracking problem is formulated and addressed with such delay robustness constraints. For the design of the internal loop, the performance of DOB will be quantified by the trade-off between the external relative delay margin and the disturbance rejection, thus retaining the original PD controller design. Besides, the stability in the nominal delay range is primarily concerned when demarcating the low-pass filter in DOB, based on which a critical time constant is obtained through exhaustive testing. Following the route of combining analytical design with quantitative adjustment, the synthetic tuning rules can provide prescribed robustness against delay uncertainty for integrating processes. Through conducting illustrative simulations and a water tank experiment, the efficiency and merit of the proposed scheme are demonstrated. • A set of novel tuning formulae for PD controller is derived for integrating process. • Delay robustness constrained optimal tracking is formulated and resolved. • Filter design is quantified by a trade-off between delay robustness and performance. • The continuous stability within the nominal delay range would be ensured. [ABSTRACT FROM AUTHOR]

This paper presents a number of power grid network design and optimization techniques that consider the electromigration (EM) effects for multi-segment interconnect wires. First, we consider a new EM immortality constraint due to EM void saturation volume for multi-segment interconnects. It helps reduce conservativeness in the EM-aware on-chip power grid design. Along with the EM nucleation phase immortality constraint, we show that both EM immortality constraints can be naturally integrated into the existing programming based power grid optimization framework. Second, to mitigate the overly conservativeness of the immortality constrained optimization methods, we further explore three strategies: we first size up failed wires to meet one of the immortality conditions subject to the design rules; second, we consider the EM-induced aging effects on power supply networks for a target lifetime, which allows some short-lived wires to fail and optimizes the remaining wires; third, we propose a large change sensitivity-based optimization scheme to perform localized fixing based on recently proposed coupled EM-IR drop analysis method. Numerical results on a number of IBM-format power grid networks demonstrate that the new method can reduce more power grid area compared to the existing EM immortality constrained optimizations. Moreover, the new method is able to optimize power grids with nucleated wires, which would not be possible with the existing methods. Results also show the sensitivity-based localized power girds fixing can fix EM-induced IR drop violations in a few minutes for synthesized power grid networks from ARM core designs. • This paper introduces new power grid design and optimization techniques considering EM aging effects for a target lifetime. • A new EM immortality constraint due to EM void saturation volume is integrated into the framework • Three strategies are explored to further mitigate the conservativeness of the immortality constrained optimization method. • Experimental results validated the soundness of the proposed methods. [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]

Interpretability and explainability of machine learning systems have received ever-increasing attention, especially for deep neural networks. In the case of convolutional neural networks (CNNs), their properties are usually explained by generating local explanation maps (e.g., visualizing the contribution of individual pixels to a given prediction). In this paper, we propose a new framework that analyzes the inner workings of CNNs in terms of neural activations. To be precise, we consider a forward-pass as sequential activations of neurons and develop its inverse process, so that the inverse preserves the physical meaning of neuron activations. Our inverse process is formulated as a constrained optimization problem, and we solve the problem with the gradient projection algorithm. The proposed approach can provide equivalent visualization results to several conventional methods, and thus can be a reference tool for CNN visualization. Also, the attributions generated by our inverse method yield the state-of-the-art deletion scores and visualize the contribution of colors as well as shape features. [ABSTRACT FROM AUTHOR]

Reliable and real-time active diagnosis of system faults with uncertainties is strongly dependent on the input design. This paper establishes a data-driven framework for integrated design of active fault diagnosis and control while ensuring the tracking performance. To be specific, the input design is formulated as a constrained optimization problem that can be solved with the aid of constrained reinforcement learning algorithms. Moreover, based on the maximum mean discrepancy metric, a novel active fault isolation scheme is proposed to implement model discrimination using system outputs. At the end, the effectiveness of the proposed approach is evaluated in two case studies in the presence of probabilistic disturbances and uncertainties. • A data-driven framework for active fault diagnosis with tracking performance guarantees. • Constrained reinforcement learning is applied in the integrated design of active inputs. • A fault isolation strategy to implement model discrimination based on system outputs. [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]

• A new advanced whale optimization algorithm for global optimization is proposed. • Armed force program and strategic adjustment are integrated with the original method. • CEC 2014 functions are tested to verify the effectiveness of the proposed optimizer. • The proposed optimizer is compared with others in solving engineering problems. In this paper, we propose a new whale army optimization algorithm with a view to solving multifarious optimization problems. The key novelty of our approach is to modify the original whale optimization algorithm to make it effective to solve the complicated, large-scale and constrained optimization problems. Our modifications mainly embody two aspects: the beneficial strategic adjustment to set key parameters and to help establish base principles in the original optimizer and the introduction of armed force program which classifies the search whales into different categories to achieve efficient cooperation. We evaluate the performance of the proposed algorithm, using three simple benchmark test functions over thirty CEC-2014 real-parameter numerical optimization problems and three constraint engineering design problems. The test results indicate that this algorithm can provide a faster local convergence rate, a higher convergence accuracy, and a lower computational complexity in comparison to traditional whale optimization algorithms and other sophisticated state of the art whale optimizers. Performance wise, it also surpasses many advanced methods for large-scaled complex functions. Furthermore, in this paper we propose a variant of whale army optimization algorithm to specifically address and solve optimizing constrained problems with a high degree of precision. [ABSTRACT FROM AUTHOR]

In this paper, a novel synchronous off-policy method is given to solve multi-player zero-sum (ZS) game under the condition that the knowledge of system data are completely unknown, the actuators of controls are constrained and the disturbances are bounded simultaneously. The cost functions are built by nonquadratic functions to reflect the constrained properties of inputs. The integral reinforcement learning (IRL) technology is employed to solve Hamilton–Jacobi–Bellman equation, so that the system dynamics are not necessary anymore. The obtained value function is proved to converge to the optimal game values. And the equivalent of traditional policy iteration (PI) algorithm and the proposed algorithm is given in solving the multi-player ZS game with constrained inputs. Three neural networks in this paper are utilized, the critic neural network (CNN) to approach the cost function, the action neural network (ANN) to approach the control policies and the disturbance neural networks (DNN) to approach the disturbances are utilized. Finally, a simulation example is given to demonstrate the convergence and performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A nonsmooth distributed optimization problem subject to affine equality and convex inequality is considered in this paper. All the local objective functions in the distributed optimization problem possess a common decision variable. And taking privacy into consideration, each agent doesn't share its local information with other agents, including the information about the local objective function and constraint set. To cope with this distributed optimization, a neurodynamic approach based on the penalty-like methods is proposed. It is proved that the presented neurodynamic approach is convergent to an optimal solution to the considered distributed optimization problem. The proposed neurodynamic approach in this paper has lower model complexity and computational load via reducing auxiliary variables. In the end, two illustrative examples are given to show the effectiveness and practical application of the proposed neural network. [ABSTRACT FROM AUTHOR]

In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination of the total losses where the risk is measured by a distortion risk measure and the reinsurance premium is calculated according to a distortion premium principle. In the first place, we show how to formulate the unconstrained optimization problem and constrained optimization problem in a unified way. Then, we propose a geometric approach to solve optimal reinsurance problems directly. This paper considers a class of increasing convex ceded loss functions and derives the explicit solutions of the optimal reinsurance, which can be in forms of quota-share, stop-loss, change-loss, the combination of quota-share and change-loss or the combination of change-loss and change-loss with different retentions. Finally, we consider two specific cases of the distortion risk measures: Value at Risk (VaR) and Tail Value at Risk (TVaR). [ABSTRACT FROM AUTHOR]

In this paper, a generalized neural network with a novel auxiliary function is proposed to solve a distributed non-differentiable optimization over a multi-agent network. The constructed auxiliary function can ensure that the state solution of proposed neural network is bounded, and enters the inequality constraint set in finite time. Furthermore, the proposed neural network is demonstrated to reach consensus and ultimately converges to the optimal solution under several mild assumptions. Compared with the existing methods, the neural network proposed in this paper has a simple structure with a low amount of state variables, and does not depend on projection operator method for constrained distributed optimization. Finally, two numerical simulations and an application in power system are delineated to show the characteristics and practicability of the presented neural network. [ABSTRACT FROM AUTHOR]

This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at all-times. The proposed solutions can address various model nonlinearities, for example, due to quantization and/or saturation. Further, it allows to reach faster convergence or to robustify the solution against impulsive noise or uncertainties. We prove convergence over weakly connected networks using convex analysis and Lyapunov theory. Our findings show that convergence can be reached for general sign-preserving odd nonlinearity. We further propose delay-tolerant mechanisms to handle general bounded heterogeneous time-varying delays over the communication network of agents while preserving all-time feasibility. This work finds application in CPU scheduling and coverage control among others. This paper advances the state-of-the-art by addressing (i) possible nonlinearity on the agents/links, meanwhile handling (ii) resource-demand feasibility at all times, (iii) uniform-connectivity instead of all-time connectivity, and (iv) possible heterogeneous and time-varying delays. To our best knowledge, no existing work addresses contributions (i) - (iv) altogether. Simulations and comparative analysis are provided to corroborate our contributions. • Distributed all-time feasible strategies that solve resource allocation. • Algorithm with tolerating heterogeneous bounded delays over the communication network. • Convergence over uniformly-connected networks, even disconnected at some times. • Addressing possible nonlinearity on the nodes or links for different applications. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of dynamics control with a long control period for an Autonomous Underwater Vehicle (AUV) equipped with four independent stern control planes. The goal is to minimize frequent actuator operations. To tackle the difficulties posed by the extended control period, the paper proposes a hierarchy controller architecture comprising high-level dynamics control and low-level control allocation. The dynamics controller is developed using the Nonlinear Model Predictive Control (NMPC) technique. It aims to generate optimal virtual steering moments while considering the differences in the periods of model updating, state prediction, and control output. Additionally, a constrained optimization problem is formulated for control allocation, taking into account the characteristics of the control planes. To validate the proposed approach, a test AUV is designed for experimental validation. The hydrodynamic parameters required for state prediction are identified through Computational Fluid Dynamics (CFD) analysis and verified by comparing characteristic indexes from maneuvering trials. Comparison with the Linear Quadratic Regulator (LQR) in dynamics control highlights that the proposed control methods offer a stable and effective control framework, particularly when dealing with a long control period. [ABSTRACT FROM AUTHOR]

• Impact of demand response (DR) strategy on the optimal design of microgrid (MG). • Techno-economic feasibility assessment of a grid-tied MG considering DR strategy. • Proposing renewable Generation-based dynamic pricing to optimize MG configuration. • Employing the dandelion algorithm to solve the sizing problem of MG optimally. Integrating microgrids into the existing power system increases utility grid reliability and efficiency. Optimal sizing and configuration of Microgrid (MG) components are essential at the design stage for minimizing the overall cost and emissions of the MG. This paper presents a novel mathematical model for optimizing the configuration and operation of a grid-connected microgrid exploiting Demand-Side Management (DSM). This paper studies the impact of Demand Response (DR)-based DSM on optimal MG design from the customers' and utility's perspectives, considering both economic and technical performance metrics. A comparative performance study of six DR programs is investigated in order to verify the effectiveness of the proposed Renewable Generation-based Dynamic Pricing (RGDP)-based DR. In this paper, the sizing problem of MG is formulated as a bi-objective optimization in order to fulfil two objective functions: minimizing the total annual cost and minimizing life cycle emissions. An advanced evolutionary algorithm named the Dandelion Algorithm is utilized in order to solve the complex and constrained nonlinear optimization problem. The results demonstrate that considering RGDP-based DR in the MG sizing problem reduces the installation and operating costs of the MG without load shedding. The proposed DR strategy satisfies the customers' needs with high efficiency and low cost. [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]

This paper proposes a perception-aware online trajectory generation system that facilitates prescribed manoeuvres of an unmanned surface vehicle (USV) in a dynamic unstructured environment. The proposed system is developed based on the principles of the inverse dynamics in the virtual domain (IDVD) method and an event-triggered receding horizon control (ETRHC) mechanism. This approach transforms the underlying nonconvex constrained optimization problem into a virtual space with a differentially flat dynamics and uses relatively few decision variables to prototype feasible quasi-optimal trajectories. The closed-loop configuration is provided by a computationally efficient ETRHC mechanism that uses situational awareness of operating environment to trigger trajectory replanning if/when required. This addresses the challenge of continuously updating a closed-loop trajectory which imposes unnecessary computational burden on a system with the limited onboard resources. To investigate the performance of the proposed trajectory generating system, a dynamic unstructured environment including variable and uncertain no-fly zone areas as well as variable current vector fields are modeled. Further, different operating conditions incorporating the uncertainties of environment and sudden failure on the USV propulsion system are introduced to examine the effectiveness, agility, and robustness of the proposed trajectory generating system. A comparative study with benchmark solutions generated by the hp-adaptive Radau pseudo-spectral method is conducted to provide a detailed statistical analysis of the proposed approach robustness, computational complexity, and effectiveness. The simulation results confirm the effectiveness of the proposed trajectory generator and ability to produce a solution for online realization. • This paper proposes a perception-aware online trajectory generation system that facilitates prescribed manoeuvres of an USV. • The proposed system is developed based on the principals of the IDVD method and an ETRHC mechanism. • The closed-loop configuration is provided by the ETRHC mechanism to trigger trajectory replanning if/when required. • The robustness and effectiveness of the proposed systems is investigated and verified in a dynamic unstructured environment. [ABSTRACT FROM AUTHOR]

A periodic close encounter orbit is an orbit that periodically surveys a target spacecraft. The design of such orbits is important for both military and civil missions. As an example, it can be used for a preliminary mission design to better plan the repair of damaged, expensive, strategic, or extremely critical space assets. Indeed, this paper proposes an optimization approach and algorithm to reach periodic close encounter orbits through n -impulse maneuvers within the framework of Keplerian motion. The optimization is constrained to several bound requirements, such as a) distance bounds at encounter, b) total Δ v tot cost, c) single impulse cost Δ v k , d) encounter illumination angle, e) daily observation time, f) minimum perigee radius, g) maximum repetition time, h) maximum eccentricity, and i) maximum encounter time. The optimization, performed using Genetic Algorithm, has been validated by several numerical examples using the TLEs of existing satellites. The simulations showed good results and the reliability of the proposed approach via the Genetic Algorithm has been validated by a comparison with the Particle Swarm Optimization algorithm. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problem (CMOP) considers the convergence, diversity and feasibility of the population in the optimization process, so it is challenging to find desirable solutions of CMOP. Existing evolutionary multi-objective optimization algorithms have good performance on unconstrained multi-objective optimization problems, but have difficulties in solving CMOPs in discrete feasible regions. Aiming at this issue, this paper proposes a novel multi-level population hybrid search evolution algorithm (MLHSEA). First, a new multi-level hybrid search strategy (i.e. MHSS) is designed in the algorithm, which divides the population into three-level subpopulations based on Pareto ranks, constraint violation degree values, and feasible thresholds. Each subpopulation has its own unique evolution strategy to maximize the evolutionary potential of each subpopulation, which is beneficial to make some feasible solutions break through the discrete feasible region and reach the Pareto frontier. Then, a new population fusion degree strategy (i.e. PFDS) is proposed to timely perform population fusion and information exchange according to the population fusion degree (PFD) of each sub-population, thus improving the searchability of the target space. Finally, a novel detection reset strategy (i.e. DRS) is proposed for the lowest inferior subpopulation. This strategy can make inferior subpopulations avoid unnecessary evolutionary iterations and improve population diversity. Based on constrained test suites with four different characteristics, the experimental results show that the proposed MLHSEA outperforms other state-of-the-art constrained multi-objective optimization algorithms in performance. [ABSTRACT FROM AUTHOR]