Constrained Optimization Problem Research Articles

Buffer Occupancy-Based Congestion Control Protocol for Wireless Multimedia Sensor Networks

Wireless multimedia sensor networks (WMSNs) have stringent constraints and need to deliver data packets to the sink node within a predefined limited time. However, due to congestion, buffer overflow occurs and leads to the degradation of the quality-of-service (QoS) parameters of event information. Congestion in WMSNs results in exhausted node energy, degraded network performance, increased transmission delays, and high packet loss. Congestion occurs when the volume of data trying to pass through a network exceeds its capacity. First, the BOCC protocol uses two congestion indicators to detect congestion. One is the buffer occupancy and other is the buffer occupancy change rate. Second, a rate controller is proposed to protect high-priority I-frame packets during congestion. BOCC sends a congestion notification to the source node to reduce congestion in the network. The source node adjusts its data transmission rate after receiving the congestion notification message. In the proposed algorithm, the rate adjustment is made by discarding low-priority P-frame packets from the source nodes. Third, to further improve the performance of the BOCC protocol, the problem is formulated as a constrained optimization problem and solved using convex optimization and sequential quadratic programming (SQP) methods. Experimental results based on Raspberry Pi sensor nodes show that the BOCC protocol achieves up to 16% reduction in packet loss and up to 23% reduction in average end-to-end delay compared to state-of-the-art congestion control algorithms.

Mechanical and Civil Engineering Optimization with a Very Simple Hybrid Grey Wolf—JAYA Metaheuristic Optimizer

Metaheuristic algorithms (MAs) now are the standard in engineering optimization. Progress in computing power has favored the development of new MAs and improved versions of existing methods and hybrid MAs. However, most MAs (especially hybrid algorithms) have very complicated formulations. The present study demonstrated that it is possible to build a very simple hybrid metaheuristic algorithm combining basic versions of classical MAs, and including very simple modifications in the optimization formulation to maximize computational efficiency. The very simple hybrid metaheuristic algorithm (SHGWJA) developed here combines two classical optimization methods, namely the grey wolf optimizer (GWO) and JAYA, that are widely used in engineering problems and continue to attract the attention of the scientific community. SHGWJA overcame the limitations of GWO and JAYA in the exploitation phase using simple elitist strategies. The proposed SHGWJA was tested very successfully in seven “real-world” engineering optimization problems taken from various fields, such as civil engineering, aeronautical engineering, mechanical engineering (included in the CEC 2020 test suite on real-world constrained optimization problems) and robotics; these problems include up to 14 optimization variables and 721 nonlinear constraints. Two representative mathematical optimization problems (i.e., Rosenbrock and Rastrigin functions) including up to 1000 variables were also solved. Remarkably, SHGWJA always outperformed or was very competitive with other state-of-the-art MAs, including CEC competition winners and high-performance methods in all test cases. In fact, SHGWJA always found the global optimum or a best cost at most 0.0121% larger than the target optimum. Furthermore, SHGWJA was very robust: (i) in most cases, SHGWJA obtained a 0 or near-0 standard deviation and all optimization runs practically converged to the target optimum solution; (ii) standard deviation on optimized cost was at most 0.0876% of the best design; (iii) the standard deviation on function evaluations was at most 35% of the average computational cost. Last, SHGWJA always ranked 1st or 2nd for average computational speed and its fastest optimization runs outperformed or were highly competitive with their counterpart recorded for the best MAs.

Extracting fiber paths from the optimized lamination parameters of variable-stiffness laminated shells based on physic-informed neural network

This paper presents a novel approach for extracting fiber paths from the optimized lamination parameters (LPs) of variable stiffness laminated shells, utilizing the framework of physics-informed neural network (PINN). In this methodology, each fiber layer is associated with a specific stream function, which is approximated by an independent neural network. The stream function is governed by a partial differential equation (PDE) derived from the fiber orientation field in the parameter space. Moreover, the isocontours of the stream function are transformed into the actual fiber paths in the physical space. To account for manufacturing constraints, Riemannian geometry serves as a computational tool to determine the intrinsic distance between adjacent fiber paths and the geodesic curvature of the isocontours. By incorporating regularization terms into the loss function based on the physical relationships, the constrained optimization problem is converted into an unconstrained one, making it more suitable for neural network training. Meanwhile, a fiber path extraction (FPE) algorithm is used to minimize the loss function at randomly sampled points through gradient descent. The numerical results suggest that the extraction of fiber paths using PINN can achieve satisfactory levels of accuracy while effectively satisfying the imposed constraints.

Generalized [formula omitted] observer for road profile estimation in the automotive suspension system

This study develops a generalized H2 observer to estimate the road profile in the semi-active automotive suspension system. The dynamics of the quarter-car model are represented in the descriptor nonlinear parameter-varying system framework, with the road profile as a system's state that is of arbitrary dynamics. Then, a road profile estimation method is designed by using a generalized H2 observer, which utilizes the onboard accelerometers as the observer's input. The adverse impact of measurement noises on the accuracy of estimation results is alleviated via the generalized H2 framework. The proposed observer is designed by solving an LMI-based constrained optimization problem. Frequency domain analysis and time domain simulations illustrate the efficiency of the proposed strategy

Adaptive control scheme for cooperative transport systems navigation under uncertainty

An adaptive robust control scheme for a cooperative transport system is proposed to tackle the challenges arising from parameter uncertainty, external interference, measurement errors, and other factors. The cooperative transport system consists of a leader automated ground vehicle, a baggage carrier, and a follower automated ground vehicle. Firstly, a mechanics-based independent dynamic model without constraints is established for each component within the system, and the coupling relationship between components is analyzed to design the constraint function. Secondly, to address inaccuracies in initial conditions, the trajectory errors in both their zero- and first-order forms are introduced. A closed-form dynamic model that is subject to constraints is then developed for the entire cooperative system, incorporating both structural and performance constraints. Thirdly, an innovative adaptive robust control scheme is introduced for mechanical systems facing uncertainty. An adaptive law is devised to estimate the bounds of uncertainty. The control is deterministic and can be mathematically expressed in a closed-form. Fourthly, a constrained optimization problem is formulated using the fuzzy information of uncertainty to choose an appropriate optimal gain kopt of the adaptive law. This is achieved by minimizing the combination of average fuzzy system performance and control effort. Finally, numerical simulations are conducted to verify the effectiveness and adaptability of the proposed control method. The performance of controlled cooperative transport system is both deterministically guaranteed and fuzzily optimized.

Evasion Maneuver and Timing Strategy for UAVs Under Direct Force Control

Given the capabilities of modern high-performance missiles, efficient evasion maneuver strategies are crucial for enhancing UAV survivability. This paper addresses the integration of evasion strategies and maneuver timing for targeted UAVs. First, a three-dimensional engagement scenario is modeled using the relative motion mechanism. Subsequently, a fundamental evasion strategy focusing on large roll maneuvers and two-phase acceleration is developed. With the initiation timing of direct force control designated as the control variable, the formulation of a constrained optimization problem to maximize miss distance is fully articulated. While preserving the high fidelity of the established switching model, the feasible timing intervals and the optimal timing are determined through numerical optimization. Finally, simulation experiments are conducted focusing on omnidirectional attacks from the upper hemisphere. The results demonstrate that by implementing specific evasion maneuvers at optimal timing, the target successfully escapes the effective range of the proximity fuse, thus confirming the feasibility of the proposed evasion maneuver and timing strategy.

Robust Optimality and Duality for Nonsmooth Multiobjective Programming Problems with Vanishing Constraints Under Data Uncertainty

This article investigates robust optimality conditions and duality results for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (UNMPVC). Mathematical programming problems with vanishing constraints constitute a distinctive class of constrained optimization problems because of the presence of complementarity constraints. Moreover, uncertainties are inherent in various real-life problems. The aim of this article is to identify an optimal solution to an uncertain optimization problem with vanishing constraints that remains feasible in every possible future scenario. Stationary conditions are necessary conditions for optimality in mathematical programming problems with vanishing constraints. These conditions can be derived under various constraint qualifications. Employing the properties of convexificators, we introduce generalized standard Abadie constraint qualification (GS-ACQ) for the considered problem, UNMPVC. We introduce a generalized robust version of nonsmooth stationary conditions, namely a weakly stationary point, a Mordukhovich stationary point, and a strong stationary point (RS-stationary) for UNMPVC. By employing GS-ACQ, we establish the necessary conditions for a local weak Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we derive sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type and Mond–Weir-type robust dual models corresponding to the primal problem, UNMPVC.

A rapid-convergent particle swarm optimization approach for multiscale design of high-permeance seawater reverse osmosis systems

Directly solving sophisticated partial differential equation constrained optimization problems is not only extremely time-consuming, but also very hard to find unique optimal solutions. Here, we propose stable and efficient surrogate models for seawater reverse osmosis desalination processes that enable thorough quantitative description of hydrodynamics and local transport characteristics in narrow flow channels. Without iteratively solving complex multi-physics simulation problem taking several hours, the proposed multi-scale design optimization framework significantly reduces the problem complexity by computing the surrogate models in seconds. Moreover, a fast-converging active subspace particle swarm optimization framework is proposed to address the optimal design problem. Compared to the standard particle swarm optimization algorithm, the proposed method enhances the average optimum by 14% and the standard deviation of optimum results for multiple runs is reduced by no less than ten times. The optimized desalination system achieves 9% reduction on energy consumption and 30% improvement on water production efficiency.

A simple method for automatic recreation of railway horizontal alignments

AbstractThis paper deals with the problem of recreating horizontal alignments of existing railway lines. The main objective is to propose a simple method for automatically obtaining optimized recreated alignments located as close as possible to an existing one. Based on a previously defined geometric model, two different constrained optimization problems are formulated. The first problem uses only the information provided by a set of points representing the track centerline while the second one also considers additional data about the existing alignment. The proposed methodology consists of a two-stage process in which both problems are solved consecutively using numerical techniques. The main results obtained applying this methodology are presented to show its performance and to prove its practical usefulness: an academic example used to compare with other methods, and a case study of a railway section located in Parga (Spain) in which the geometry of its horizontal alignment is successfully recovered.

Joint passive beamforming and deployment design for active intelligent reflecting surface-assisted energy harvesting-cognitive radio sensor networks.

To prolong the network lifetime of energy harvesting-cognitive radio sensor networks (EH-CRSNs), this paper integrates active intelligent reflecting surface (IRS) to support both downlink EH and uplink data transmissions and formulates a constrained non-convex optimization problem that maximizes the net energy gain. To solve this problem, a joint passive beamforming and IRS deployment mechanism is proposed to determine the optimal deployment location of the active IRS and optimally configure the IRS reflection coefficient matrices. Specifically, the net energy gain maximization problem at a specified location is divided into two sub-problems according to its characteristics: maximizing the cumulative energy harvested by all CRSNs nodes in the downlink and minimizing the energy consumption of cluster heads in uplink data transmissions, with each sub-problem being solved independently. Furthermore, this paper explores how factors such as the number of active reflecting elements and the amplification power budget influence the optimal deployment location of the active IRS. The findings from this investigation can guide the design of active IRS-assisted EH-CRSNs under specified parameters. Simulation results confirm the aforementioned conclusions and highlight the benefits of the proposed joint mechanism in enhancing net energy gain over various benchmark mechanisms.

Comparison of Aiming Point Strategy Algorithms and Their Assessment for Volumetric Solar Receivers

The present work summarizes the work done within the scope of CATION, CHLOE, and HECTOR projects related to the aiming point strategies optimization algorithms applied to volumetric solar receivers. Several optimization methods have been applied in the literature for optimizing the aiming strategy of solar power tower plants. However, the use of these algorithms for the requirements of volumetric solar receivers and solar fuel applications has not been accomplished. Herein, the problem is formulated as a constrained optimization problem whose objective function is a combination of the total power on the receiver surface and the flux homogeneity. A comparison of the results is presented in this work. It will be seen that TABU search and SA algorithms are the most efficient in terms of computation time and, in addition, the first one shows very good results in power and spillage. The rest of the mentioned algorithms are much slower and, in general, the results are slightly worse.

The Synthesis of Spherical Four-bars for Biomimetic Motion through Complete Solutions for Approximate Rigid Body Guidance

Abstract In this paper, we form a constrained optimization problem for spherical four-bar motion generation. Instead of using local optimization methods, all critical points are found using homotopy continuation solvers. The complete solution set provides a full view of the optimization landscape and gives the designer more freedom in selecting a mechanism. The motion generation problem admits 61 critical points, of which two must be selected for each four-bar mechanism. We sort solutions by objective value and perform a second order analysis to determine if the solution is a minimum, maximum, or saddle point. We apply our approximate synthesis technique to two applications: a hummingbird wing mechanism and a sea turtle flipper gait. Suitable mechanisms were selected from the respective solution sets and used to build physical prototypes.

A stochastic moving ball approximation method for smooth convex constrained minimization

AbstractIn this paper, we consider constrained optimization problems with convex objective and smooth convex functional constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve this class of problems, where at each iteration we first take a (sub)gradient step for the objective function and then perform a projection step onto one ball approximation of a randomly chosen constraint. The computational simplicity of SMBA, which uses first-order information and considers only one constraint at a time, makes it suitable for large-scale problems with many functional constraints. We provide a convergence analysis for the SMBA algorithm using basic assumptions on the problem, that yields new convergence rates in both optimality and feasibility criteria evaluated at some average point. Our convergence proofs are novel since we need to deal properly with infeasible iterates and with quadratic upper approximations of constraints that may yield empty balls. We derive convergence rates of order $${\mathcal {O}} (k^{-1/2})$$ O ( k - 1 / 2 ) when the objective function is convex, and $${\mathcal {O}} (k^{-1})$$ O ( k - 1 ) when the objective function is strongly convex. Preliminary numerical experiments on quadratically constrained quadratic problems demonstrate the viability and performance of our method when compared to some existing state-of-the-art optimization methods and software.

A staged fuzzy evolutionary algorithm for constrained large-scale multiobjective optimization

Constrained multiobjective optimization problems (CMOPs) are prevalent in practical applications, where constraints play a significant role. Building on techniques from constrained single-objective optimization, classical methods such as the constrained dominance principle have been extended to CMOPs. However, these methods struggle with CMOPs characterized by complex infeasible regions. Furthermore, as the number of decision variables increases, the search efficiency of algorithms deteriorates dramatically. To solve those issues, we propose a staged fuzzy evolutionary algorithm (i.e., SFEA) for constrained large-scale problems. To balance exploration and exploitation, a fuzzy stage adjustment strategy based on the sigmoid function is proposed. Furthermore, this article develops an improved fuzzy operator to perform fuzzy operations on various vectors (e.g., solutions or constraint violations). Computational experiments were conducted on CMOP test suites with up to 500 decision variables and a series of real-world applications. The experimental results demonstrate that, compared to existing peer algorithms, our algorithm exhibits superior or competitive performance.

An adaptive co-evolutionary competitive particle swarm optimizer for constrained multi-objective optimization problems

In constrained multi-objective optimization problems, it is challenging to balance the convergence, diversity and feasibility of the population, especially encountering complex infeasible regions. In order to effectively balance the three indicators, from the aspects of the handling of infeasible solution and the quality of individuals, a multi-population co-evolutionary competitive particle swarm optimization algorithm hybridized with infeasible solution transfer and an adaptive technique (ACCPSO) is proposed. Firstly, the information of feasible and infeasible individuals is fully utilized and the individuals are classified by Hamming distance. Then, a novel constraint handling technique based on learning from the promising feasible direction is designed to make individuals cross large infeasible regions and explore more potential feasible regions. Moreover, aiming to provide robust search capability and consequently further generate high-quality solutions, the genetic operators and the particle swarm optimization operator with the competitive mechanism are introduced as operators with an adaptive mechanism. Finally, compared with the state-of-the-art methods, the performance of the proposed algorithm is verified on LIR-CMOP, MW and DTLZ, as well as two real-world problems. The results indicate that ACCPSO exhibits stronger competitiveness in terms of convergence, the solution quality, and distribution diversity on the feasible Pareto front.

Two-layer surrogate-assisted collaborative framework for expensive constrained optimization problems involving mixed integer variables

Many surrogate-assisted evolutionary algorithms (SAEAs) have been shown exceptional abilities in solving expensive constrained optimization problems (ECOPs). However, few of them are designed for ECOPs involving mixed integer variables (ECOPs-MI). Therefore, a two-layer surrogate-assisted collaborative framework called TLSACF is designed, in which the radial basis function (RBF) and Gaussian Process (GP)-based mixed-integer collaborative frameworks are combined effectively. In the RBF-based collaborative framework, the combination between RBF-assisted prescreening and RBF-based local search achieves effective population update by balancing the exploration and exploitation on high potential parental information. For the GP-based collaborative framework, a variable type-based cooperative mutation is utilized to obtain potential candidate individuals by assigning targeted mutation for different variables, and a hypervolume-based complete expected improvement matrix function is derived to prescreen these candidate solutions from the perspective of balancing the optimization on constraints and the objective for the effective search on disconnected sub-feasible regions caused by integer variables. Experimental results on ten classical problems show that TLSACF performs excellent in solving ECOPs-MI.

Improving the Global Convergence of Inexact Restoration Methods for Constrained Optimization Problems

Improving the Global Convergence of Inexact Restoration Methods for Constrained Optimization Problems

Power distribution system restoration based on soft open points and islanding by distributed generations

Abstract A powerful and efficient program for restoring the electrical distribution system by effectively utilizing the maximum capabilities within the system, including soft open points, distributed generation resources, and network configuration changes, can significantly reduce both the quantity and duration of lost loads caused by permanent faults. In this research study, we address the issue of distribution network restoration with a focus on soft open points (SOPs) and intentional islanding using distributed generations. This problem is formulated as a constrained optimization problem in order to determine the optimal distribution network configuration, quality of intentional islanding through DGs, control function of SOPs, and amount of load shedding. The objective is to minimize lost load while minimizing switching operations and preferably minimal islanding. Given that this problem involves multiple complexities such as combinatorial nature, mixed-integer variables, non-linearity, non-convexity along with numerous variables and constraints; we employ an evolutionary method known as simulated annealing (SA) algorithm to solve it without any simplifications or assumptions about convexity. To enhance efficiency during implementation of SA algorithm, Kruskal’s algorithm is utilized for generating radial solutions which restricts search space to feasible solutions resulting in quicker attainment of high-quality optimal solutions. Finally, the outcomes of implementing the suggested approach on the 69-bus IEEE distribution system are presented and examined. It is demonstrated that by leveraging the potential of soft open points in load transfer control and network voltage regulation, along with utilizing intentional islanding capability provided by distributed generation resources, the restoration capability of the distribution system can be greatly enhanced.

Optimal Strictly Stealthy Attack Design on Cyber-Physical Systems: A Data-Driven Approach.

In this article, an issue of data-driven optimal strictly stealthy attack design for the stochastic linear invariant systems is investigated, with the aim of maximizing the system performance degradation under an energy bounded constraint and bypassing the parity-space-based attack detector. Importantly, the proposed attack policy refrains from the assumption that the system knowledge is known to attackers. A novel strictly stealthy attack sequence (SSAS), coordinating the sensor and actuator signals simultaneously, is proposed with a sufficient and necessary condition for the existence of such an attack presented. Specifically, the SSAS is parameterized as a vector in the null space of a specific matrix which is constructed by a parity matrix and the system Markov parameters. For the purpose of data-driven attack realization, modified subspace identification methods are utilized to achieve an unbiased estimation of the required parameters via the closed-loop data. On this basis, the attack design is formulated as a constrained optimization problem, an explicit solution to which is given to characterize the optimal strictly stealthy attack. Finally, the vulnerability of the cyber-physical systems is analysed from the perspective of the parameter selection for the parity space-based detector. A case study on a three-tank model verifies the efficiency of the proposed approach.

From human explanations to explainable AI: Insights from constrained optimization

Many complex decision-making scenarios encountered in the real-world, including energy systems and infrastructure planning, can be formulated as constrained optimization problems. Solutions for these problems are often obtained using white-box solvers based on linear program representations. Even though these algorithms are well understood and the optimality of the solution is guaranteed, explanations for the solutions are still necessary to build trust and ensure the implementation of policies. Solution algorithms represent the problem in a high-dimensional abstract space, which does not translate well to intuitive explanations for lay people. Here, we report three studies in which we pose constrained optimization problems in the form of a computer game to participants. In the game, called Furniture Factory, participants manage a company that produces furniture. In two qualitative studies, we first elicit representations and heuristics with concurrent explanations and validate their use in post-hoc explanations. We analyze the complexity of the explanations given by participants to gain a deeper understanding of how complex cognitively adequate explanations should be. Based on insights from the analysis of the two qualitative studies, we formalize strategies that in combination can act as descriptors for participants’ behavior and optimal solutions. We match the strategies to decisions in a large behavioral dataset (>150 participants) gathered in a third study, and compare the complexity of strategy combinations to the complexity featured in participants’ explanations. Based on the analyses from these three studies, we discuss how these insights can inform the automatic generation of cognitively adequate explanations in future AI systems.