Constrained Optimization Problem Research Articles

Accelerated Driving-Training-Based Optimization for Solving Constrained Bi-Objective Stochastic Optimization Problems

The constrained bi-objective stochastic optimization problem (CBSOP) considers the optimization problem with stochastic bi-objective functions subject to deterministic constraints. The CBSOP is part of a set of hard combinatorial optimization problems regarding time complexity. Ordinal optimization (OO) theory provides a commonly recognized structure to handle hard combinatorial optimization problems. Although OO theory may solve hard combinatorial optimization problems quickly, the deterministic constraints will critically influence computing performance. This work presents a metaheuristic approach that combines driving-training-based optimization (DTBO) with ordinal optimization (OO), abbreviated as DTOO, to solve the CBSOP with a large design space. The DTOO approach comprises three major components: the surrogate model, diversification, and intensification. In the surrogate model, the regularized minimal-energy tensor product with cubic Hermite splines is utilized as a fitness estimation of design. In diversification, an accelerated driving-training-based optimization is presented to determine N remarkable designs from the design space. In intensification, a reinforced optimal computing budget allocation is used to find an extraordinary design from the N remarkable designs. The DTOO approach is applied to a medical resource allocation problem in the emergency department. Simulation results obtained by the DTOO approach are compared with three heuristic approaches to examine the performance of the DTOO approach. Test results show that the DTOO approach obtains an extraordinary design with higher solution quality and computational efficiency than the three heuristic approaches.

Neural network approach to portfolio optimization with leverage constraints: a case study on high inflation investment

Motivated by the current global high inflation scenario, we aim to discover a dynamic multi-period allocation strategy to optimally outperform a passive benchmark while adhering to a bounded leverage limit. We formulate an optimal control problem to outperform a benchmark portfolio throughout the investment horizon. To obtain strategies under the bounded leverage constraint among other realistic constraints, we propose a novel leverage-feasible neural network (LFNN) to represent the control, which converts the original constrained optimization problem into an unconstrained optimization problem that is computationally feasible with gradient descent, without dynamic programming. We establish mathematically that the LFNN approximation can yield a solution that is arbitrarily close to the solution of the original optimal control problem with bounded leverage. We further validate the performance of the LFNN empirically by deriving a closed-form solution under jump-diffusion asset price models and show that a shallow LFNN model achieves comparable results on synthetic data. In the case study, we apply the LFNN approach to a four-asset investment scenario with bootstrap-resampled asset returns from the filtered high inflation regimes. The LFNN strategy is shown to consistently outperform the passive benchmark strategy by about 200 bps (median annualized return), with a greater than 90% probability of outperforming the benchmark at the end of the investment horizon.

Delay effects on distributed constrained optimization over double‐integrator multi‐agent systems

AbstractCommunication plays a pivotal role in distributed optimization problems, where unavoidable communication delays are presented. This research studies the distributed constrained optimization problem concerning second‐order multi‐agent systems with double‐integrator under time‐varying communication delays. An adaptive distributed optimization algorithm using multi‐agent system consensus technique and Karush–Kuhn–Tucker conditions is developed to deal with this problem. The local constraint term is solved adaptively through local dual Lagrange multipliers. When the cost function is strongly convex, and the communication topology is undirected and connected, we employ the Lasalle invariance principle to analyze the delay effects on convergence analysis. Moreover, we give an upper bound on communication delay. Finally, the provided numerical simulation examples demonstrate that the developed method is robust for the limited communication delay and the derived results are conservative.

Congruential Summation-Triggered Identification of FIR Systems under Binary Observations and Uncertain Communications

With the advancement of network technology, there has been an increase in the volume of data being transmitted across networks. Due to the bandwidth limitation of communication channels, data often need to be quantized or event-triggered mechanisms are introduced to conserve communication resources. On the other hand, network uncertainty can lead to data loss and destroy data integrity. This paper investigates the identification of finite impulse response (FIR) systems under the framework of stochastic noise and the combined effects of the event-triggered mechanism and uncertain communications. The study provides a reference for the application of remote system identification under transmission-constrained and packet loss scenarios. First, a congruential summation-triggered communication scheme (CSTCS) is introduced to lower the communication rate. Then, parameter estimation algorithms are designed for scenarios with known and unknown packet loss probabilities, respectively, and their strong convergence is proved. Furthermore, an approximate expression for the convergence rate is obtained by data fitting under the condition of uncertain packet loss probability, treating the trade-off between convergence performance and communication resource usage as a constrained optimization problem. Finally, the rationality and correctness of the algorithm are verified by numerical simulations.

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

Beamforming optimization of meta-learning algorithm based on gradient descent in RIS-assisted ISAC system

In this paper, we study an integrated sensing and communication (ISAC) system assisted by reconfigurable intelligent surface (RIS). Our goal is to minimize the transmit power of the BS by jointly optimizing the active beamforming and the passive beamforming under the constraints of the signal-to-interference-plus-noise ratio (SINR) of users, the Cramer–Rao bound (CRB) of sensing and the unit-modulus of RIS reflection elements. The optimization problem is difficult to solve because the objective function is non-convex and the variables are coupled. In addition, a large number of base station (BS) antennas lead to high-dimensional transmit beamforming vectors. We first prove that the optimization variables in the optimization problem are low-dimensional coefficient matrices and passive beamforming, rather than active and passive beamforming, which reduces the complexity compared with the original problem. In addition, when the sensing channel space belongs to the communication channel space, the dedicated sensing signal is not needed. Inspired by the meta-learning technology that can solve non-convex problems, we propose a meta-learning algorithm based on gradient descent (MLAGD) to design beamforming, which tends to learn dynamic optimization strategies and iteratively update optimization variables. Specifically, we first introduce Lagrangian multipliers to transform the constrained optimization problem into the Lagrangian dual domain, and the manifold-based optimization is employed to handle the unit-modulus constraint. The meta-learning neural networks are constructed to update optimization variables through local loss function, and then network parameters are updated through global loss function. The numerical results show the effectiveness of the algorithm.

A new optimal strategy for energy minimization in wireless sensor networks

In recent years, evolutionary and metaheuristic algorithms have emerged as crucial tools for optimization in the field of artificial intelligence. These algorithms have the potential to revolutionize various aspects of our lives by leveraging the multidisciplinary nature of wireless sensor networks (WSNs). This study aims to introduce genetic and simulated annealing algorithms as effective solutions for enhancing WSN performance. Our contribution entails two main phases. Firstly, we establish mathematical models and formulate objectives as a nonlinear constrained optimization problem. Secondly, we develop two algorithmic solutions to address the formulated optimization problem. The obtained results from multiple simulations demonstrate the positive impact of the proposed strategies on improving network performance in terms of energy consumption.

A three-dimensional spring-loaded inverted pendulum walking model considering human movement speed and frequency

The spring-loaded inverted pendulum (SLIP) model is an effective model to capture the essential dynamics during human walking and/or running. However, most of the existing three-dimensional (3D) SLIP model does not explicitly account for human movement speed and frequency. To address this knowledge gap, this paper develops a new SLIP model, which includes a roller foot, massless spring, and concentrated mass. The governing equations-of-motion for the SLIP model during its double support phase are derived. It is noted that in the current formulation, the motion of the roller foot is prescribed; therefore, only the equations for the concentrated mass need to be solved. To yield model parameters leading to a periodic walking gait, a constrained optimization problem is formulated and solved using a gradient-based approach with a global search strategy. The optimization results show that when the attack angle ranges from 68° to 74°, the 3D SLIP model can yield a periodic walking gait with walking speeds varying from 0.5 to 2.0 m s−1. The predicted human walking data are also compared with published experimental data, showing reasonable accuracy.

Stability of Minima in Constrained Optimization Problems and Implicit Function Theorem

Stability of Minima in Constrained Optimization Problems and Implicit Function Theorem

A surrogate-assisted a priori multiobjective evolutionary algorithm for constrained multiobjective optimization problems

AbstractWe consider multiobjective optimization problems with at least one computationally expensive constraint function and propose a novel surrogate-assisted evolutionary algorithm that can incorporate preference information given a priori. We employ Kriging models to approximate expensive objective and constraint functions, enabling us to introduce a new selection strategy that emphasizes the generation of feasible solutions throughout the optimization process. In our innovative model management, we perform expensive function evaluations to identify feasible solutions that best reflect the decision maker’s preferences provided before the process. To assess the performance of our proposed algorithm, we utilize two distinct parameterless performance indicators and compare them against existing algorithms from the literature using various real-world engineering and benchmark problems. Furthermore, we assemble new algorithms to analyze the effects of the selection strategy and the model management on the performance of the proposed algorithm. The results show that in most cases, our algorithm has a better performance than the assembled algorithms, especially when there is a restricted budget for expensive function evaluations.

Population state-driven surrogate-assisted differential evolution for expensive constrained optimization problems with mixed-integer variables

AbstractMany surrogate-assisted evolutionary algorithms (SAEAs) have been shown excellent search performance in solving expensive constrained optimization problems (ECOPs) with continuous variables, but few of them focus on ECOPs with mixed-integer variables (ECOPs-MI). Hence, a population state-driven surrogate-assisted differential evolution algorithm (PSSADE) is proposed for solving ECOPs-MI, in which the adaptive population update mechanism (APUM) and the collaborative framework of global and local surrogate-assisted search (CFGLS) are combined effectively. In CFGLS, a probability-driven mixed-integer mutation (PMIU) is incorporated into the classical global DE/rand/2 and local DE/best/2 for improving the diversity and potentials of candidate solutions, respectively, and the collaborative framework further integrates both the superiority of global and local mutation for the purpose of achieving a good balance between exploration and exploitation. Moreover, the current population is adaptively reselected based on the efficient non-dominated sorting technique in APUM when the population distribution is too dense. Empirical studies on 10 benchmark problems and 2 numerical engineering cases demonstrate that the PSSADE shows a more competitive performance than the existing state-of-the-art algorithms. More importantly, PSSADE provides excellent performance in the design of infrared stealth material film.

Hunger games search algorithm based on stochastic individual information for engineering design optimization problems

Abstract The hunger games search algorithm (HGS) is a newly proposed meta-heuristic algorithm that emulates hunger-driven foraging behaviors in a population. It combines fitness values to determine individual weights and updates them based on fitness value size, resulting in high adaptability and effective optimization. However, HGS faces issues like low convergence accuracy and susceptibility to local optima in complex optimization problems. To address these problems, an improved version called BDFXHGS is introduced. BDFXHGS incorporates a collaborative feeding strategy based on HGS's design advantages. Individuals approach others based on hunger degree, facilitating information exchange and resolving convergence and accuracy issues. BDFXHGS combines a disperse foraging strategy and a directional crossover strategy to enhance exploration and convergence speed. The paper conducts qualitative analysis and ablation experiments to examine the effectiveness of the strategies. Comparative experiments are performed using IEEE CEC 2017 benchmark functions to compare BDFXHGS with competitive algorithms, including previous champion algorithms in different dimensions. Additionally, BDFXHGS is evaluated on 25 constrained optimization problems from the IEEE CEC 2020 competition and 5 real engineering optimization problems. Experimental results show that BDFXHGS performs well on benchmarks and outperforms other algorithms in real-world applications.

Research on hybrid reservoir scheduling optimization based on improved walrus optimization algorithm with coupling adaptive ε constraint and multi-strategy optimization

Reservoir flood control scheduling is a challenging optimization task, particularly due to the complexity of various constraints. This paper proposes an innovative algorithm design approach to address this challenge. Combining the basic walrus optimization algorithm with the adaptive ε-constraint method and introducing the SPM chaotic mapping for population initialization, spiral search strategy, and local enhancement search strategy based on Cauchy mutation and reverse learning significantly enhances the algorithm's optimization performance. On this basis, innovate an adaptive approach ε A New Algorithm for Constraints and Multi Strategy Optimization Improvement (ε-IWOA). To validate the performance of the ε-IWOA algorithm, 24 constrained optimization test functions are used to test its optimization capabilities and effectiveness in solving constrained optimization problems. Experimental results demonstrate that the ε-IWOA algorithm exhibits excellent optimization ability and stable performance. Taking the Taolinkou Reservoir, Daheiting Reservoir, and Panjiakou Reservoir in the middle and lower reaches of the Luanhe River Basin as a case study, this paper applies the ε-IWOA algorithm to practical reservoir scheduling problems by constructing a three-reservoir flood control scheduling system with Luanxian as the control point. A comparative analysis is conducted with the ε-WOA, ε-DE and ε-PSO (particle swarm optimization) algorithms.The experimental results indicate that ε-IWOA algorithm performs the best in optimization, with the occupied flood control capacity of the three reservoirs reaching 89.32%, 90.02%, and 80.95%, respectively. The control points in Luan County can reduce the peak by 49%.This provides a practical and effective solution method for reservoir optimization scheduling models. This study offers new ideas and solutions for flood control optimization scheduling of reservoir groups, contributing to the optimization and development of reservoir scheduling work.

Complete Solutions for the Approximate Synthesis of Spherical Four-Bar Function Generators

Abstract Kinematic synthesis to meet an approximate motion specification naturally forms a constrained optimization problem. Instead of using local methods, we conduct global design searches by direct computation of all critical points. The idea is not new, but performed at scale is only possible through modern polynomial homotopy continuation solvers. Such a complete computation finds all minima, including the global, which allows for a full exploration of the design space, whereas local solvers can only find the minimum nearest to an initial guess. We form equality-constrained objective functions that pertain to the synthesis of spherical four-bar linkages for approximate function generation. We consider the general case where all mechanism dimensions may vary and a more specific case that enables the placement of ground pivots. The former optimization problem is shown to permit 268 sets of critical points, and the latter permits 61 sets. Critical points are classified as saddles or minima through a post-process eigenanalysis of the projected Hessian. The discretization points are contained within the coefficients of the stationarity polynomials, so the algebraic structure of the synthesis equations remains invariant to the number of points. The results of our computational work were used to design a mechanism that coordinates the folding wings. We also use this method to parameterize mechanism dimensions for a family of hyperbolic curves.

Singularity distance computations for 3-RPR manipulators using intrinsic metrics

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.

Constrained tensorial total variation problem based on an alternating conditional gradient algorithm

The present paper aims to regularize ill-posed high-dimensional problems using a constrained total variation minimization approach. The analysis of the continuous model via the dual formulation converts this minimization problem into a constrained minimax problem. Three main issues stand before the resolution of this problem: The minimization over a constraint, the high dimensional representation of the model, and the non-linearity and non-differentiability of the cost function. On the one hand, multidimensional data analysis will be performed using the tensor representation. On the other hand, a new alternating approach based on a proposed pseudo-Lagrangian operator will be developed to deal with the non-linearity and the non-differentiability of this constrained optimization problem. The proposed technique aims to decompose the main tensorial problem into feasible subproblems that can be solved using the conditional gradient method. The convergence of the proposed algorithm is proved and some numerical results are given to illustrate the effectiveness of the presented approach in different fields of image and video processing.

Joint reconstruction and prediction regions for unobserved exponential lifetimes under doubly Type II censoring

ABSTRACT The doubly Type II censoring scheme, in which some of the smallest and largest lifetimes are censored, is an important and widely used censoring scheme in life-testing experiments and reliability. In this paper, the problem of simultaneous reconstruction and prediction for unobserved lifetimes in a doubly Type II censored sample from the one-parameter exponential distribution is discussed. For this purpose, the joint reconstruction and prediction (JRP) regions are obtained based on two independent pivotal quantities. First, the balanced JRP regions for the unobserved lifetimes are derived, and then a constrained optimization problem is formulated and solved to find the JRP regions with the smallest area. For illustrative and comparative purposes, a simulation study and two illustrative examples are presented.

MaGENEgerZ: An Efficient Artificial Intelligence-Based Framework Can Extract More Expressed Genes and Biological Insights Underlying Breast Cancer Drug Response Mechanism

Understanding breast cancer drug response mechanisms can play a crucial role in improving treatment outcomes and survival rates. Existing bioinformatics-based approaches are far from perfect and do not adopt computational methods based on advanced artificial intelligence concepts. Therefore, we introduce a novel computational framework based on an efficient support vector machine (esvm) working as follows: First, we downloaded and processed three gene expression datasets related to breast cancer responding and non-responding to treatments from the gene expression omnibus (GEO) according to the following GEO accession numbers: GSE130787, GSE140494, and GSE196093. Our method esvm is formulated as a constrained optimization problem in its dual form as a function of λ. We recover the importance of each gene as a function of λ, y, and x. Then, we select p genes out of n, which are provided as input to enrichment analysis tools, Enrichr and Metascape. Compared to existing baseline methods, including deep learning, results demonstrate the superiority and efficiency of esvm, achieving high-performance results and having more expressed genes in well-established breast cancer cell lines, including MD-MB231, MCF7, and HS578T. Moreover, esvm is able to identify (1) various drugs, including clinically approved ones (e.g., tamoxifen and erlotinib); (2) seventy-four unique genes (including tumor suppression genes such as TP53 and BRCA1); and (3) thirty-six unique TFs (including SP1 and RELA). These results have been reported to be linked to breast cancer drug response mechanisms, progression, and metastasizing. Our method is available publicly on the maGENEgerZ web server.

Dissipative imitation learning for discrete dynamic output feedback control with sparse data sets

AbstractImitation learning enables synthesis of controllers for systems with complex objectives and uncertain plant models. However, ensuring an imitation learned controller is stable requires copious amounts of data and/or a known plant model. In this paper, we explore an input–output (IO) stability approach to imitation learning, which achieves stability with sparse data sets while only requiring coarse knowledge of the energy characteristics of the plant. A constrained optimization problem is developed, in which the controller learns to mimic expert data while maintaining stabilizing energy characteristics induced by the plant. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to learn the controller. In numerical examples, it is shown that with little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance.

Discrete-time Euler-smoothing methods for time-varying convex constrained optimization

In this paper, we propose two kinds of prediction–correction methods, discrete-time Euler-smoothing methods, for solving the general time-varying convex constrained optimization problem. By using the complementarity function and smoothing technique, the Karush–Kuhn–Tucker (KKT) trajectory of the problem can be reformulated as a system of smooth equations and considering the dynamics of the system of smooth equations in a discrete constant time-sampling periods scheme. The proposed methods mainly consist of the prediction step derived by Euler approximation and the correction step generated by one or multiple Newton iterations. Under some reasonable conditions, the approximate solution trajectories produced by the methods achieve the asymptotic error bound behaving as O(h4) with respect to optimal trajectory both in the primal and dual space as the smoothing parameter approaches to zero, where h is the sampling period. Finally, the experimental results show that our methods are efficient, and the steady-state tracking errors are much smaller than the other prediction–correction methods under the same conditions.