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Multiobjective evolutionary algorithm for dynamic nonlinear constrained optimization problems

Journal of Systems Engineering and Electronics 2009年第1期20卷 204-210页

作者： Liu Chun'an Wang Yuping Dept. of Mathematics Baoji Univ. of Arts and Science Baoji 721013 P. R. China School of Computer Engineering and Technology Xidian Univ. Xi'an 710071 P. R. China

A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.

关键词： dynamic optimization nonlinear constrained optimization evolutionary algorithm optimal solutions

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Improving the performance of weighted Lagrange-multiplier methods for nonlinear constrained optimization

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INFORMATION SCIENCES 2000年第1-4期124卷 241-272页

作者： Wah, BW Wang, T Shang, Y Wu, Z Univ Missouri Dept Comp Sci & Comp Engn Columbia MO 65211 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

nonlinear constrained optimization problems in discrete and continuous spaces are an important class of problems studied extensively in artificial intelligence and operations research. These problems can be solved by a Lagrange-multiplier method in continuous space and by an extended discrete Lagrange-multiplier method indiscrete space. When constraints are satisfied, these methods rely on gradient descents in the objective space to find high-quality solutions. On the other hand, when constraints are violated, these methods rely on gradient ascents in the Lagrange-multiplier space in order to increase the penalties on unsatisfied constraints and to force the constraints into satisfaction. The balance between gradient descents and gradient ascents depends on the relative weights between the objective function and the constraints, which indirectly control the convergence speed and solution quality of the Lagrangian method. To improve convergence speed without degrading solution quality, we propose an algorithm to dynamically control the relative weights between the objective and the constraints. Starting from an initial weight, the algorithm automatically adjusts the weights based on the behavior of the search progress. With this strategy, we are able to eliminate divergence, reduce oscillation, and speed up convergence. We show improved convergence behavior of our proposed algorithm on both nonlinear continuous and discrete problems. (C) 2000 Elsevier Science Inc. All rights reserved.

关键词： adaptive weights Lagrange-multiplier method multiplierless filter-bank design nonlinear constrained optimization nonlinear integer programming nonlinear programming QMF filter-bank design

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Simulated annealing with asymptotic convergence for nonlinear constrained optimization

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JOURNAL OF GLOBAL optimization 2007年第1期39卷 1-37页

作者： Wah, Benjamin W. Chen, Yixin Wang, Tao Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA Washington Univ Dept Comp Sci St Louis MO 63130 USA Synopsys Inc Mountain View CA 94043 USA

In this paper, we present constrained simulated annealing (CSA), an algorithm that extends conventional simulated annealing to look for constrained local minima of nonlinear constrained optimization problems. The algorithm is based on the theory of extended saddle points (ESPs) that shows the one-to-one correspondence between a constrained local minimum and an ESP of the corresponding penalty function. CSA finds ESPs by systematically controlling probabilistic descents in the problem-variable subspace of the penalty function and probabilistic ascents in the penalty subspace. Based on the decomposition of the necessary and sufficient ESP condition into multiple necessary conditions, we present constraint-partitioned simulated annealing (CPSA) that exploits the locality of constraints in nonlinear optimization problems. CPSA leads to much lower complexity as compared to that of CSA by partitioning the constraints of a problem into significantly simpler subproblems, solving each independently, and resolving those violated global constraints across the subproblems. We prove that both CSA and CPSA asymptotically converge to a constrained global minimum with probability one in discrete optimization problems. The result extends conventional simulated annealing (SA), which guarantees asymptotic convergence in discrete unconstrained optimization, to that in discrete constrained optimization. Moreover, it establishes the condition under which optimal solutions can be found in constraint-partitioned nonlinear optimization problems. Finally, we evaluate CSA and CPSA by applying them to solve some continuous constrained optimization benchmarks and compare their performance to that of other penalty methods.

关键词： asymptotic convergence constrained local minimum constraint partitioning simulated annealing dynamic penalty methods extended saddle points nonlinear constrained optimization

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A line search exact penalty method with bi-object strategy for nonlinear constrained optimization

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2016年 300卷 245-258页

作者： Chen, Zhongwen Dai, Yu-Hong Soochow Univ Sch Math Sci Suzhou 215006 Peoples R China Chinese Acad Sci Acad Math & Syst Sci ICMSEC LSEC Beijing 100190 Peoples R China

The exact penalty methods are very popular because of their ability to handle degenerate problems and inconsistent constraint linearizations. This paper presents a line search exact penalty method with bi-object strategy (LSBO) for nonlinear constrained optimization. In the algorithm LSBO, the penalty parameter is selected at every iteration such that the sufficient progress toward feasibility and optimality is guaranteed along the search direction. In contrast with classical exact penalization approaches, LSBO method has two goals to determine whether the current iteration is successful or not. One is improving the feasibility and the other is reducing the value of the objective function. Moreover, the penalty parameter is only related to the information at the current iterate point. The sequence of the penalty parameter is non-monotone, which does not affect the global convergence in theory and is seen to be advantageous in practice. It is shown that the algorithm enjoys favorable global convergence properties under the weaker assumptions. Numerical experiments illustrate the behavior of the algorithm on various difficult situations. (C) 2016 Elsevier B.V. All rights reserved.

关键词： nonlinear constrained optimization Exact penalty methods Bi-object strategy Global convergence

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A penalty derivative-free algorithm for nonlinear constrained optimization

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optimization LETTERS 2015年第6期9卷 1213-1229页

作者： Lv, Wei Sun, Qiang Lin, He Sui, Ruirui Shanghai Univ Dept Math Shanghai 200444 Peoples R China Chinese Acad Sci Dept Mat & Energy Res Shanghai Inst Appl Phys Shanghai 201204 Peoples R China

In this paper, we modify a derivative-free line search algorithm (DFL) proposed in the Ref. (Liuzzi et al. SIAM J Optimiz 20(5):2614-2635, 2010) to minimize a continuously differentiable function of box constrained variables or unconstrained variables with nonlinear constraints. The first-order derivatives of the objective function and of the constraints are assumed to be neither calculated nor explicitly approximated. Different line-searches are used for box-constrained variables and unconstrained variables. Accordingly the convergence to stationary points is proved. The computational behavior of the method has been evaluated on a set of test problems. The performance and data profiles are used to compare with DFL.

关键词： Derivative-free algorithm nonlinear constrained optimization Box constrained variables Unconstrained variables

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Double-track particle swarm optimizer for nonlinear constrained optimization problems

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INFORMATION SCIENCES 2023年 622卷 587-628页

作者： Lu, Hao-Chun Tseng, Hsuan-Yu Lin, Shih-Wei Natl Yang Ming Chiao Tung Univ Dept Management Sci Hsinchu 300 Taiwan Fu Jen Catholic Univ Grad Inst Business Adm New Taipei 242 Taiwan Chang Gung Univ Dept Informat Management Taoyuan 333 Taiwan Ming Chi Univ Technol Dept Ind Engn & Management New Taipei 243 Taiwan Keelung Chang Gung Mem Hosp Dept Emergency Med Keelung 204 Taiwan

Particle swarm optimization (PSO) is a popular stochastic algorithm for solving nonlinear optimization problems. It has been used in various industrial applications because of its few parameters and ease of implementation. Various optimal problems must be frequently formed as nonlinear constrained optimization (NCO) problems because of global resource limitations. These problem-specific nonlinear constraints can result in many infeasible regions in the search space. Current PSO-based approaches are inherently designed for unconstrained optimization problems and cannot directly handle the constraint issue;therefore, they add the constraint handling technique (CHT) to account for NCO problems. This study proposes a double-track schema inside PSO called double-track PSO (DTPSO) to address the NCO problem. When an infeasible region blocks a particle, the DTPSO creates a copy of the particle. The original and copied particles utilize different search strategies to move to feasible and infeasible regions. The results indicate that the proposed DTPSO out-performs the seven referenced PSO-based methods in all 33 NCO problems and five recent strong methods in 19 mechanical design problems belonging to the IEEE CEC 2020 compe-tition on real-world single-objective constrained optimization problems. Furthermore, the experiment results demonstrate the quality of the solution and the effective computation of the proposed DTPSO.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Particle swarm optimization nonlinear constrained optimization Double -track Constraint handling technique Exploration Exploitation

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Remarks on a benchmark nonlinear constrained optimization problem

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Journal of Systems Engineering and Electronics 2006年第3期17卷 551-553页

作者： Luo Yazhong Lei Yongjun Tang Guojin Coll. of Aerospace and Material Engineering National Univ. of Defense Technology Changsha 410073 P. R. China

Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn Tucker conditions.

关键词： nonlinear constrained optimization parallel simulated annealing Kuhn-Tucker theorem.

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A filter sequential adaptive cubic regularization algorithm for nonlinear constrained optimization

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NUMERICAL ALGORITHMS 2023年第4期93卷 1481-1507页

作者： Pei, Yonggang Song, Shaofang Zhu, Detong Henan Normal Univ Coll Math & Informat Sci Engn Lab Big Data Stat Anal & Optimal Control Construct Rd Xinxiang 453007 Henan Peoples R China Shanghai Normal Univ Math & Sci Coll Guilin Rd Shanghai 200234 Peoples R China

In this paper, we propose a filter sequential adaptive regularization algorithm using cubics (ARC) for solving nonlinear equality constrained optimization. Similar to sequential quadratic programming methods, an ARC subproblem with linearized constraints is considered to obtain a trial step in each iteration. Composite step methods and reduced Hessian methods are employed to tackle the linearized constraints. As a result, a trial step is decomposed into the sum of a normal step and a tangential step which is computed by a standard ARC subproblem. Then, the new iteration is determined by filter methods and ARC framework. The global convergence of the algorithm is proved under some reasonable assumptions. Preliminary numerical experiments and comparison results are reported.

关键词： nonlinear constrained optimization Cubic regularization Filter methods Sequential quadratic programming Global convergence

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Modeling Beach Rotation Using a Novel Legendre Polynomial Feedforward Neural Network Trained by nonlinear constrained optimization 12th

Modeling Beach Rotation Using a Novel Legendre Polynomial Fe...

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12th IFIP WG 12.5 International Conference on Artificial Intelligence Applications and Innovations (AIAI)

作者： Rigos, Anastasios Tsekouras, George E. Chatzipavlis, Antonios Velegrakis, Adonis F. Univ Aegean Dept Cultural Technol & Commun Mitilini Greece Univ Aegean Dept Marine Sci Mitilini Greece

ISBN: (纸本)9783319449449;9783319449432

A Legendre polynomial feedforward neural network is proposed to model/predict beach rotation. The study area is the reef-fronted Ammoudara beach, located at the northern coastline of Crete Island (Greece). Specialized experimental devices were deployed to generate a set of input-output data concerning the inshore bathymetry, the wave conditions and the shoreline position. The presence of the fronting beachrock reef (parallel to the shoreline) increases complexity and imposes high non-linear effects. The use of Legendre polynomials enables the network to capture data non-linearities. However, in order to maintain specific functional requirements, the connection weights must be confined within a pre-determined domain of values;it turns out that the network's training process constitutes a constrained nonlinear programming problem, solved by the barrier method. The performance of the network is compared to other two neural-based approaches. Simulations show that the proposed network achieves a superior performance, which could be improved if an additional wave parameter (wave direction) was to be included in the input variables.

关键词： Beach rotation Feedforward neural network Legendre polynomials Perched beach nonlinear constrained optimization

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New multi-objective genetic algorithm for nonlinear constrained optimization problems

New multi-objective genetic algorithm for nonlinear constrai...

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IEEE International Conference on Automation and Logistics

作者： Liu, Chun-an Baoji Univ Arts & Sci Dept Math Baoji 721013 Shaanxi Peoples R China

ISBN: (纸本)9781424415304

A new approach is presented to solve the nonlinear constrained optimization problem. It neither uses any penalty function nor distinguishes the feasible solutions and the infeasible solutions. Firstly, the constrained optimization problem is transformed into a bi-objective optimization problem. One objective is the objective function of the original nonlinear constrained optimization problem, and the other is the scalar constraints violation. Based on the dominating relation of the Pareto, a new choosing strategy is first designed, and then by combining the choosing strategy with the reasonable design of the genetic operation and different parameters, a new genetic algorithm is finally proposed. The numerical experiment shows that the algorithm is effective in dealing with the nonlinear constraint optimization problem.

关键词： nonlinear constrained optimization multiobjective optimization genetic algorithm

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