Constrained Optimization Research Articles

A model estimating the level of floral transition in olive trees exposed to warm periods during winter.

Rising winter temperatures jeopardize the fruit yield of trees that require a prolonged and sufficiently cold winter to flower. Predicting the exact risk to different crop varieties is the first step in mitigating the harmful effects of climate change. This work focused on olive (Olea europaea) - a traditional crop in the Mediterranean basin whose flowering depends on the sufficiency of cold periods and the lack of warm ones during the preceding winter. Yet, a satisfactory quantitative model forecasting its expected flowering under natural temperature conditions is still lacking. The effect of different temperature regimes on olive flowering level and flowering-gene expression was empirically tested. A modified 'dynamic model' describing the response of a putative flowering factor to the temperature signal was constructed. The crucial component of the model was an unstable intermediate, produced and degraded at temperature-dependent rates. The model accounts for both the number of cold and warm hours but also for their sequence. Empirical flowering and temperature data were applied to fit the model parameters, applying numerical constrained optimization techniques; the model outcomes were successfully validated. The model accurately predicted low-to-moderate flowering under winters with warm periods and properly accounted for the effects of warm periods during winter.

Adaptive MSSRCPF filtering based on constrained optimization and fading memory for SINS/GNSS integrated navigation

To address particle degeneracy and the challenge of selecting importance density functions in traditional particle filters for complex nonlinear systems, we propose an adaptive mixed-order spherical simplex-radial cubature particle filter algorithm based on constrained optimization and fading memory. This algorithm integrates constrained optimization, an adaptive fading memory strategy, adaptive adjustment of particle numbers and weights, and the advantages of mixed-order spherical simplex-radial cubature Kalman filtering. By designing the importance density function using a mixed-order integration method, the algorithm significantly improves filtering accuracy over traditional cubature Kalman filters while maintaining lower computational complexity than high-order cubature Kalman filter methods. The adaptive fading memory strategy dynamically adjusts the covariance matrix, enhancing sensitivity to current measurement information and reducing the influence of historical data. By dynamically adjusting the noise covariance matrix and constraining the ratio between the error covariance and measurement noise covariance, the algorithm improves the convergence speed and accuracy of state estimation. An adaptive particle number and weight adjustment strategy based on effective sample size and entropy regularization dynamically adjusts the number of particles to reduce computational complexity while ensuring filtering accuracy, and employs entropy regularization to suppress weight over-concentration, thereby reducing the impact of outliers on the filtering results. Simulation results demonstrate that in complex SINS/GNSS integrated navigation systems, especially under high-noise and nonlinear conditions, the proposed algorithm significantly improves positioning accuracy compared to the CPF method, with the maximum latitude error reduced by approximately 54.8%, the maximum longitude error reduced by approximately 40.5%, and the maximum altitude error reduced by approximately 68.3%. Compared to the FMCPF method, the proposed algorithm also shows clear advantages in positioning accuracy, convergence speed, and computational efficiency, validating its effectiveness and practicality in complex environments.

An improved multi-objective artificial physics optimization algorithm based on R2 indicator and its application

Artificial Physics Optimization (APO) algorithms in solving constrained multi-objective problems often encounter challenges such as uneven population distribution and imbalances between global and local search capabilities. To address these issues, we propose the Constrained Rank Multi-Objective Artificial Physical Optimization based on the R2 indicator (R2-ICRMOAPO) algorithm. This algorithm integrates non-dominated sorting with the R2 indicator and updates the external storage set using the contribution value derived from the R2 indicator formula, ensuring both set distribution and convergence. It also dynamically adjusts inertia weights and gravitational factors to enhance its global and local search capabilities. To evaluate the performance of the R2-ICRMOAPO algorithm, we compared it with four other multi-objective optimization algorithms using standard test functions. The results indicate that it demonstrates superior distribution and optimization performance. Furthermore, we applied it to optimize the parameters of a hydro-pneumatic suspension system. The experimental results show that it can reduce the root mean square value of car body vertical acceleration by approximately 21.4% and the root mean square value of dynamic tire load by about 19.6%. This reduction effectively enhances vehicle smoothness within a reasonable range. Consequently, these results confirm the feasibility of the R2-ICRMOAPO algorithm to solve practical problems.

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.

Deep reinforcement learning-guided coevolutionary algorithm for constrained multiobjective optimization

Deep reinforcement learning-guided coevolutionary algorithm for constrained multiobjective optimization

A Study on Normalization in Constraint Handling Techniques Based on Decomposition for Constrained Optimization

A Study on Normalization in Constraint Handling Techniques Based on Decomposition for Constrained Optimization

An inexact restoration direct multisearch filter approach to multiobjective constrained derivative-free optimization

Direct Multisearch (DMS) is a well-established class of methods for multiobjective derivative-free optimization, where constraints are addressed by an extreme barrier approach, only evaluating feasible points. In this work, we propose the replacement of this extreme barrier approach by a filter strategy, combined with an inexact feasibility restoration step, to address constraints in the DMS framework. The filter approach treats feasibility as an additional component of the objective function that needs to be minimized. The inexact restoration step attempts to generate new feasible points, contributing to prioritize this feasibility, a requirement for the good performance of any filter approach. Theoretical results are provided, analysing the different types of sequences of points generated by the new algorithm, and numerical experiments on a set of nonlinearly constrained biobjective problems are reported, stating the good algorithmic performance of the proposed approach.

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.

An adaptive helper and equivalent objective evolution strategy for constrained optimization

The matrix adaptation evolution strategy is a simplified covariance matrix adaptation evolution strategy with reduced computational cost. Using it as a search engine, several algorithms have been recently proposed for constrained optimization and have shown excellent performance. However, these algorithms require the simultaneous application of multiple techniques to handle constraints, and also require gradient information. This makes them inappropriate for handling non-differentiable functions. This paper proposes a new matrix adaption evolutionary strategy for constrained optimization using helper and equivalent objectives. The method optimizes two objectives but with no need for special handling of infeasible solutions and without gradient information. A new mechanism is designed to adaptively adjust the weights of the two objectives according to the convergence rate. The efficacy of the proposed algorithm is evaluated using computational experiments on the IEEE CEC 2017 Constrained Optimization Competition benchmarks. Experimental results demonstrate that it outperforms current state-of-the-art evolutionary algorithms. Furthermore, this paper provides sufficient conditions for the convergence of helper and equivalent objective evolutionary algorithms and proves that using helper objectives can reduce the likelihood of premature convergence.

Algorithm XXX: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear Optimization

Algorithm XXX: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear Optimization

Multi‐criteria hydraulic turbine optimization using a genetic algorithm and trust‐region postprocessing

AbstractA two‐stage, multi‐objective optimization approach is proposed to improve the overall efficiency of the time‐consuming and computationally expensive optimization process for hydraulic turbines. The purpose is to optimize the shape of the turbine blades, designed using 30 parameters, in order to maximize its efficiency and minimize both the cavitation volume and the deviation between the desired and the calculated design head. In the first step of the routine, the genetic algorithm “Non‐Dominated Sorting Genetic Algorithm II (NSGA‐II)” is used to generate an initial approximation of the Pareto front that covers a wide variety of possible solutions, that is, optimal trade‐offs between the conflicting objectives. Subsequently, to ensure convergence, the trust region optimizer “Constrained Multiobjective Problem Optimizer with Model Information to Save Evaluations (CoMPrOMISE)” is used, which is initialized with individuals selected from the Pareto set generated by the genetic algorithm.

Optimization of a roller coaster bogie considering fatigue life

This study explores the effectiveness of fatigue-life constrained topology optimization in roller coaster engineering, a previously unexplored field. Emphasizing the importance of fatigue life considerations, the research focuses on key components of roller coasters: the wheel assemblies. By integrating stress–life fatigue constraints, such an approach can lead to longer lasting and more efficiently designed roller coaster components. Multiaxial fatigue topology optimization using the method of moving asymptotes gradient-based optimization is examined to address the complex loading experienced by these bogies given a substantial load-time history in the high-cycle fatigue region. Using a validated optimization methodology, this study aims to reduce the bogie volume in selected domains while ensuring structural integrity and potentially extending service life. The optimization process successfully reduces the number of designable elements, resulting in decreased global volume and mass, and the results quantifiably demonstrate the impact of applying high-cycle fatigue constraints on the bogie’s performance.

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

Inaccurate search based sequential approximate constrained optimization method for Solid Rocket Motor design

Surrogate based constrained optimization methods are widely utilized in practical solid rocket motor (SRM) design problems. To improve the design performance, this paper proposes an inaccurate search based sequential approximate constrained optimization (ISSACO) method consisting of an efficient recursive evolution Latin hypercube design (RELHD) method and a three-stage constrained sampling method. The RELHD method divides large-sample experiment design problem into several small-sample design problems to ensure the computational efficiency and the design uniformity at the same time. The three-stage constrained sampling method employs the elite archives mechanism to balance the feasibility and the optimality in optimization. Results of the numerical cases indicate that the proposed ISSACO algorithm is competitive with other state-of-art constrained optimization method in efficiency and effectiveness. The finocyl grain design and the impulse mass ratio optimization are also conducted to make further verifications, and the ISSACO method can efficiently obtain feasible optimum and proves to be a potential method for computationally intensive solid rocket motor design problems.

A comparative study of evolutionary algorithms and particle swarm optimization approaches for constrained multi-objective optimization problems

Many real-world optimization problems contain multiple conflicting objectives as well as additional problem constraints. These problems are referred to as constrained multi-objective optimization problems (CMOPs). Many meta-heuristics for solving CMOPs, called constrained multi-objective meta-heuristics (CMOMHs) have been introduced in the literature, including those using particle swarm optimization (PSO)(Kennedy and Eberhart, 1995), genetic algorithms (GAs)(Man et al., 1996), and differential evolution (DE)(Storn and Price, 1997). CMOMHs can be grouped into four different classes: classic CMOMHs, co-evolutionary approaches, multi-stage approaches, and multi-tasking approaches. An extensive comparative study of twenty different CMOMHs on a wide variety of test problems, including real-world CMOPs in the fields of science and engineering, is conducted. A multi-swarm PSO approach called constrained multi-guide particle swarm optimization (ConMGPSO) is introduced and compared to the best-performing previous approaches according to the comparative study. The performance of each algorithm was found to be problem dependent, however the best overall approaches were ConMGPSO, paired-offspring constrained evolutionary algorithm (POCEA)(He et al., 2021), adaptive non-dominated sorting genetic algorithm III (A-NSGA-III)(Jain and Deb, 2014), and constrained multi-objective framework using Q-learning and evolutionary multi-tasking (CMOQLMT)(Ming and Gong, 2023). ConMGPSO and POCEA had the best performance on the CF benchmark set, which contains examples of bi-objective and tri-objective CMOPs with disconnected CPOFs. The CMOQLMT approach had the best performance on the DAS-CMOP benchmark set, which contain additional difficulty in terms of feasibility-, convergence-, and diversity-hardness. For the selected real-world CMOPs, A-NSGA-III had the best performance overall. ConMGPSO was shown to have the best performance on the process, design, and synthesis problems, and had competitive performance for the power system optimization problems.

Classification of high-resolution remote sensing images based on interval type-2 fuzzy logic system

Abstract Aiming at the complexity and uncertainty of remote sensing image classification, this paper proposes a high-resolution remote sensing image classification method based on Interval type-2 Fuzzy Logic Systems for Remote Sensing (IT2FLS-RS), which focuses on dealing with multiple uncertainties and aims to improve the accuracy and reliability of remote sensing image classification. The method establishes a more complex interval two-type fuzzy system covering two types of fuzzifiers, a rule base and an inference machine, and finally uses an integrated algorithm as a defuzzifier to achieve accurate pixel-level classification. In addition, the model uses Constrained Optimization BY Linear Approximations (COBYLA) to optimise the key parameters. In the DLRSD dataset, the accuracy of this model is improved by about 20%, 14%, 24% and 10% compared to the state-of-the-art interval two-type fuzzy neural network algorithm and the benchmark model XGBoost, respectively. On the WHDLD dataset, the accuracy of the proposed method is improved by about 12% and 10% compared to the state-of-the-art interval type-2 fuzzy neural network algorithm and the benchmark model XGBoost, respectively. The experimental results confirm the robustness of the proposed method in processing high-resolution remote sensing image classification, especially the excellent adaptability and scalability in complex feature scenes.

Balancing Objective Optimization and Constraint Satisfaction in Expensive Constrained Evolutionary Multiobjective Optimization

Balancing Objective Optimization and Constraint Satisfaction in Expensive Constrained Evolutionary Multiobjective Optimization