Constrained Optimization Problem Research Articles

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.

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.

Learning an Autonomous Dynamic System to Encode Periodic Human Motion Skills.

Learning an autonomous dynamic system (ADS) encoding human motion rules has been shown as an effective way for human motion skills transfer. However, most existing approaches focus on goal-directed motion skills transfer, and the study on periodic motion skills transfer is rare. One popular approach for periodic motion skills transfer is learning periodic dynamic movement primitive (DMP); however, periodic DMP is sensitive to spatial disturbances due to the introduction of the phase parameters. To solve this issue, this brief presents a novel approach to learn an ADS with a stable limit cycle without introducing phase parameters. First, a data-driven Lyapunov function (energy function) is learned, such that one of its level surfaces is consistent with periodic human demonstration trajectories. Then, an ADS is learned by sequentially solving energy function-related constrained optimization problems. With a proper design of constraint functions, we can ensure that the trajectory generated by the ADS will converge to an energy function-level surface, of which the shape is similar to periodic human demonstration trajectories. Experiments are conducted to show the effectiveness of the proposed approach (PA).

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

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

Slime Mould Algorithm Based on a Gaussian Mutation for Solving Constrained Optimization Problems

The slime mould algorithm may not be enough and tends to trap into local optima, low population diversity, and suffers insufficient exploitation when real-world optimization problems become more complex. To overcome the limitations of SMA, the Gaussian mutation (GM) with a novel strategy is proposed to enhance SMA and it is named as SMA-GM. The GM is used to increase population diversity, which helps SMA come out of local optima and retain a robust local search capability. Additionally, the oscillatory parameter is updated and incorporated with GM to set the balance between exploration and exploitation. By using a greedy selection technique, this study retains an optimal slime mould position while ensuring the algorithm’s rapid convergence. The SMA-GM performance was evaluated by using unconstrained, constrained, and CEC2022 benchmark functions. The results show that the proposed SMA-GM has a more robust capacity for global search, improved stability, a faster rate of convergence, and the ability to solve constrained optimization problems. Additionally, the Wilcoxon rank sum test illustrates that there is a significant difference between the optimization outcomes of SMA-GM and each compared algorithm. Furthermore, the engineering problem such as industrial refrigeration system (IRS), optimal operation of the alkylation unit problem, welded beam and tension/compression spring design problem are solved, and results prove that the proposed algorithm has a better optimization efficiency to reach the optimum value.

Three-dimensional spring-loaded inverted pendulum walking model considering human moving 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 moving speed and frequency. To address this knowledge gap, this paper develops a new SLIP model which includes roller foot, massless spring and concentrated mass. The governing equations-of-motion for SLIP model during its double support phase are derived. It is noted that in the current formulation, the motion of roller foot is prescribed so only the equations for the concentrated mass needs to be solved. In order to yield model parameters leading to a periodic walking gait, a constrained optimization problem is formulated and solved using 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, the predicted human walking data is also compared with published experimental data, finding reasonable accuracy.

Dual-stage and dual-population cooperative evolutionary algorithm for solving constrained multiobjective problems

During the search process, the characteristics of the feasible regions encountered by the population continually change in Constrained Multiobjective Optimization Problems (CMOPs). This variability poses a challenge for traditional evolutionary algorithms, which often struggle to adapt to the diverse problem characteristics of the encountered feasible regions. To overcome this limitation, we propose a Dual-Stage and Dual-Population Cooperative Evolutionary Algorithm (DDCEA) to address CMOPs characterized by diverse feasible regions. DDCEA employs a dual-stage mechanism to adapt the offspring generation strategy and establishes two distinct populations to evaluate offspring using constraint-sensitive and constraint-free strategies. Comparative analyses reveal that DDCEA surpasses chosen state-of-the-art CMOEAs in adapting to the changing feasible regions and then approximating the constrained Pareto fronts.

A novel metaheuristic based on object-oriented programming concepts for engineering optimization

This paper presents a novel, robust, efficient, and simple optimization algorithm called the Object-Oriented Programming Optimization Algorithm (OOPOA) for tackling constrained and unconstrained optimization problems. The algorithm is inspired by the inheritance concept of Object-Oriented programming languages, where the features of a class are classified into three types according to inheritance probability: public, private, and protected. The object-oriented programming inheritance concept is implemented in the algorithm to update the population for the next generations. The proposed algorithm ensures exploitation by selecting the solution with the highest fitness to be inherited in each iteration. It ensures exploration by applying a mutation process that helps explore wide regions in the search space. The performance of this technique is demonstrated by solving 34 different optimization tasks, including 20 standard benchmark problems, ten IEEE Congress of Evolutionary Computation benchmark test functions, and four constrained real-world engineering design problems.

Constrained Bayesian Optimization with Lower Confidence Bound

In this article, we present a hybrid Bayesian optimization (BO) framework to solve constrained optimization problems by adopting a state-of-the-art acquisition function from the unconstrained BO literature, the well-known lower confidence bound acquisition function and propose a novel variant that analyzes the feasible and infeasible regions which ensure the theoretical convergence guarantee. The proposed variant is compared with the existing state-of-the-art approaches in the constrained BO literature via implementing these approaches on six different problems, including black-box, classical engineering, and hyperparameter tuning problems. Further, we demonstrate the effectiveness of our approach through graphical and statistical testing.

Optimal surface clothing with elastic nets

The clothing problem aims at identifying the shape of a planar fabric for covering a target surface in the three-dimensional space. It poses significant challenges in various applications, ranging from fashion industry to digital manufacturing. Here, we propose a novel inverse design approach to the elastic clothing problem that is formulated as a constrained optimization problem. We assume that the textile behaves as an orthotropic, nonlinear elastic surface with fibers distributed along its warp and weft threads, and we enforce mechanical equilibrium as a variational problem. The target surface is frictionless, except at its boundary where the textile is pinned, imposing a unilateral obstacle condition for the reactive forces at the target surface. The constrained optimization problem also accounts for an elongation condition of the warp and weft fibers, possibly with bounded shearing angle. We numerically solve the resulting constrained optimization problem by means of a gradient descent algorithm. The numerical results are first validated against known clothing solutions for Chebyshev nets, taking the limit of inextensible fibers. We later unravel the interplay between thread and shear stiffness for driving the optimal cloth shape covering the hemisphere and the hemicatenoid. We show how the metric of these target surfaces strongly affects the resulting distribution of the reaction forces. When considering the limit of covering the full sphere, we show how clothing with elastic nets allows to avoid the onset of singularities in the corresponding Chebyshev net, by developing corners at the cloth boundary.

Edge Caching Data Distribution Strategy with Minimum Energy Consumption.

In the context of the rapid development of the Internet of Vehicles, virtual reality, automatic driving and the industrial Internet, the terminal devices in the network show explosive growth. As a result, more and more information is generated from the edge of the network, which makes the data throughput increase dramatically in the mobile communication network. As the key technology of the fifth-generation mobile communication network, mobile edge caching technology which caches popular data to the edge server deployed at the edge of the network avoids the data transmission delay of the backhaul link and the occurrence of network congestion. With the growing scale of the network, distributing hot data from cloud servers to edge servers will generate huge energy consumption. To realize the green and sustainable development of the communication industry and reduce the energy consumption of distribution of data that needs to be cached in edge servers, we make the first attempt to propose and solve the problem of edge caching data distribution with minimum energy consumption (ECDDMEC) in this paper. First, we model and formulate the problem as a constrained optimization problem and then prove its NP-hardness. Subsequently, we design a greedy algorithm with computational complexity of O(n2) to solve the problem approximately. Experimental results show that compared with the distribution strategy of each edge server directly requesting data from the cloud server, the strategy obtained by the algorithm can significantly reduce the energy consumption of data distribution.

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.

Distributed gradient-free and projection-free algorithm for stochastic constrained optimization

Distributed stochastic zeroth-order optimization (DSZO), in which the objective function is allocated over multiple agents and the derivative of cost functions is unavailable, arises frequently in large-scale machine learning and reinforcement learning. This paper introduces a distributed stochastic algorithm for DSZO in a projection-free and gradient-free manner via the Frank-Wolfe framework and the stochastic zeroth-order oracle (SZO). Such a scheme is particularly useful in large-scale constrained optimization problems where calculating gradients or projection operators is impractical, costly, or when the objective function is not differentiable everywhere. Specifically, the proposed algorithm, enhanced by recursive momentum and gradient tracking techniques, guarantees convergence with just a single batch per iteration. This significant improvement over existing algorithms substantially lowers the computational complexity. Under mild conditions, we prove that the complexity bounds on SZO of the proposed algorithm are O(n/ϵ2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{O}(n/\\epsilon ^{2})$\\end{document} and O(n(21ϵ))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{O}(n(2^{\\frac{1}{\\epsilon}}))$\\end{document} for convex and nonconvex cases, respectively. The efficacy of the algorithm is verified on black-box binary classification problems against several competing alternatives.

A new adaptive Kriging-based optimization (AKBO) framework for constrained optimization problems: A case study on shared autonomous electric vehicle system design

Adaptive Kriging-based optimization (AKBO) efficiently performs optimization by employing adaptive sampling methods that sequentially update Kriging model. To solve constrained optimization problems, existing adaptive sampling methods add samples based on probability of feasibility (PoF) representing the probability that all constraints are satisfied. However, these methods have the limitation that samples are added inefficiently when the PoF is inaccurate. Therefore, this study proposes a new AKBO framework that is robust to instability of PoF in adaptive sampling. To this end, a near constraint boundary region that is expected to be close to the constraint boundary is defined based on a probability measure. Then, a near constraint boundary search (NCBS) algorithm, which explores the sample point that minimizes the objective function within the near constraint boundary region, is developed for global search, whereas a near optimum search (NOS) algorithm, which searches for better solutions that may exist near the current optimum candidate, is developed for local search. To alleviate the distortions of the Kriging model that may occur due to the highly nonlinear response, a truncated constraint function (TCF) method that limits the extremely violated constraint values used in the design of experiment (DoE) of the Kriging model is also proposed. This study verifies the performance of the proposed AKBO framework through the shared autonomous electric vehicle (SAEV) system design optimization problem. Comparison of optimum designs derived from various optimization methods shows that the proposed AKBO framework derives the feasible global optimum with high accuracy and efficiency.

Local perturbation-based black-box federated learning attack for time series classification

The widespread adoption of intelligent machines and sensors has generated vast amounts of time series data, leading to the increasing use of neural networks in time series classification. Federated learning has emerged as a promising machine learning paradigm that reduces the risk of user privacy leakage. However, federated learning is vulnerable to backdoor attacks, which pose significant security threats. Furthermore, existing unrealistic white-box methods for attacking time series result in insufficient adaptation and inferior stealthiness. To overcome these limitations, this paper proposes a gradient-free black-box method called local perturbation-based backdoor Federated Learning Attack for Time Series classification (FLATS). The attack is formulated as a constrained optimization problem and is solved using a differential evolution algorithm, without requiring any knowledge of the internal architecture of the target model. In addition, the proposed method considers the time series shapelet interval as a local perturbation range and adopts a soft target poisoning approach to minimize the difference between the attacker model and the benign model. Experimental results demonstrate that our proposed method can effectively attack federated learning time series classification models with potential security issues while generating imperceptible poisoned samples that can evade various defence methods.

A novel multi-population evolutionary algorithm based on hybrid collaboration for constrained multi-objective optimization

Multi-population-based methods are widely employed for solving constrained multiobjective optimization problems (CMOPs). The population collaboration strategy is a critical part of multi-population algorithms, and different collaboration strategies perform well on different complex CMOPs. However, these single-population collaboration strategies are still challenging to adapt to various CMOPs with different characteristics. To address this issue, we propose a novel tri-population hybrid collaboration evolutionary algorithm called TP-HCEA, which includes a constraint-relaxed population (denoted as mainpop), a constraint-ignored auxiliary population (denoted as auxpop1), and an auxiliary population (denoted as auxpop2) for the original CMOP, to search optimal solutions in the feasible region. Specifically, due to the different complementarities of the two auxiliary populations, mainpop collaborates with auxpop1 and auxpop2 in a dynamic choice between strong and weak cooperation. The effectiveness of TP-HCEA is validated through comparative analysis with seven state-of-the-art algorithms in four CMOP benchmark suites and nine real-world problems.

A pareto fronts relationship identification-based two-stage constrained evolutionary algorithm

Striking a balance between diverse constraints and conflicting objectives is one of the most crucial issues in solving constrained multi-objective optimization problems (CMOPs). However, it remains challenging to existing methods, due to the reduced search space caused by the constraints. For this issue, this paper proposes a Pareto fronts relationship identification-based two-stage constrained evolutionary algorithm called RITEA, which balances objective optimization and constraint satisfaction by identifying and utilizing the relationship between the unconstrained Pareto front (UPF) and the constrained Pareto front (CPF). Specifically, the evolutionary process is divided into two collaborative stages: training stage and reinforcement stage. In the training stage, a relationship identification method is developed to estimate the relationship between UPF and CPF, which guides the population search direction. In the reinforcement stage, the corresponding evolutionary strategies are designed based on the identified relationship to enhance the accurate search on the CPF. Furthermore, a dynamic preference fitness function (termed DPF) is designed to adaptively maintain the balance of search preference between convergence and diversity. Compared to seven state-of-the-art algorithms on 36 benchmark CMOPs in three popular test suites, RITEA obtains 77.8% of the best IGD values and 66.7% of the best HV values. The experimental results show that RITEA exhibits highly competitively when dealing with CMOPs.

An Improved Aquila Optimizer with Local Escaping Operator and Its Application in UAV Path Planning

Background: With the development of intelligent technology, Unmanned aerial vehicles (UAVs) are widely used in military and civilian fields. Path planning is the most important part of UAV navigation system. Its purpose is to find a smooth and feasible path from the start to the end. Objective: In order to obtain a better flight path, this paper presents an improved Aquila optimizer combing the opposition-based learning and the local escaping operator, named LEOAO, to deal with the UAV path planning problem in three-dimensional environments. Methods: UAV path planning is modelled as a constrained optimization problem in which the cost function consists of one objective: path length and four constraints: safe distance, flight height, turning angle and climbing/diving angle. In this paper, the LEOAO is introduced to find the optimal path by minimizing the cost function, and B-Spline is invited to represent a smooth path. The local escaping operator is used to enhance the search ability of the algorithm. Results: To test the performance of LEOAO, two scenarios are applied based on basic terrain function. Experiments show that the proposed LEOAO outperforms other algorithms such as the grey wolf optimizer, whale optimization algorithm, including the original Aquila optimizer. Conclusion: The proposed algorithm combines the opposition-based learning and local escaping operator. The opposition-based learning algorithm has the ability to accelerate convergence. And the introduction of LEO effectively balances the exploration and exploitation abilities of the algorithm and improves the quality of the population. Finally, the improved Aquila optimizer obtains a better path.

A novel variational approach for multiphoton microscopy image restoration: from PSF estimation to 3D deconvolution

In multi-photon microscopy (MPM), a recent in-vivo fluorescence microscopy system, the task of image restoration can be decomposed into two interlinked inverse problems: firstly, the characterization of the point spread function (PSF) and subsequently, the deconvolution (i.e. deblurring) to remove the PSF effect, and reduce noise. The acquired MPM image quality is critically affected by PSF blurring and intense noise. The PSF in MPM is highly spread in 3D and is not well characterized, presenting high variability with respect to the observed objects. This makes the restoration of MPM images challenging. Common PSF estimation methods in fluorescence microscopy, including MPM, involve capturing images of sub-resolution beads, followed by quantifying the resulting ellipsoidal 3D spot. In this work, we revisit this approach, coping with its inherent limitations in terms of accuracy and practicality. We estimate the PSF from the observation of relatively large beads (approximately 1 μm in diameter). This goes through the formulation and resolution of an original non-convex minimization problem, for which we propose a proximal alternating method along with convergence guarantees. Following the PSF estimation step, we then introduce an innovative strategy to deal with the high level multiplicative noise degrading the acquisitions. We rely on a heteroscedastic noise model for which we estimate the parameters. We then solve a constrained optimization problem to restore the image, accounting for the estimated PSF and noise, while allowing a minimal hyper-parameter tuning. Theoretical guarantees are given for the restoration algorithm. These algorithmic contributions lead to an end-to-end pipeline for 3D image restoration in MPM, that we share as a publicly available Python software. We demonstrate its effectiveness through several experiments on both simulated and real data.