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Статті в журналах з теми "Dynamic Constrained Problems"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Wang, Qiuzhen, Zhibing Liang, Juan Zou, Xiangdong Yin, Yuan Liu, Yaru Hu, and Yizhang Xia. "Dynamic Constrained Boundary Method for Constrained Multi-Objective Optimization." Mathematics 10, no. 23 (November 26, 2022): 4459. http://dx.doi.org/10.3390/math10234459.

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When solving complex constrained problems, how to efficiently utilize promising infeasible solutions is an essential issue because these promising infeasible solutions can significantly improve the diversity of algorithms. However, most existing constrained multi-objective evolutionary algorithms (CMOEAs) do not fully exploit these promising infeasible solutions. In order to solve this problem, a constrained multi-objective optimization evolutionary algorithm based on the dynamic constraint boundary method is proposed (CDCBM). The proposed algorithm continuously searches for promising infeasible solutions between UPF (the unconstrained Pareto front) and CPF (the constrained Pareto front) during the evolution process by the dynamically changing auxiliary population of the constraint boundary, which continuously provides supplementary evolutionary directions to the main population and improves the convergence and diversity of the main population. Extensive experiments on three well-known test suites and three real-world constrained multi-objective optimization problems demonstrate that CDCBM is more competitive than seven state-of-the-art CMOEAs.

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2

Raha, Soumyendu, and Linda R. Petzold. "Constraint partitioning for structure in path-constrained dynamic optimization problems." Applied Numerical Mathematics 39, no. 1 (October 2001): 105–26. http://dx.doi.org/10.1016/s0168-9274(01)00055-1.

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3

Raha, Soumyendu, and Linda R. Petzold. "Constraint Partitioning for Stability in Path-Constrained Dynamic Optimization Problems." SIAM Journal on Scientific Computing 22, no. 6 (January 2001): 2051–74. http://dx.doi.org/10.1137/s1064827500372390.

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4

Frank, Jeremy. "Revisiting dynamic constraint satisfaction for model-based planning." Knowledge Engineering Review 31, no. 5 (November 2016): 429–39. http://dx.doi.org/10.1017/s0269888916000242.

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AbstractAs planning problems become more complex, it is increasingly useful to integrate complex constraints on time and resources into planning models, and use constraint reasoning approaches to help solve the resulting problems. Dynamic constraint satisfaction is a key enabler of automated planning in the presence of such constraints. In this paper, we identify some limitations with the previously developed theories of dynamic constraint satisfaction. We identify a minimum set of elementary transformations from which all other transformations can be constructed. We propose a new classification of dynamic constraint satisfaction transformations based on a formal criteria, namely the change in the fraction of solutions. This criteria can be used to evaluate elementary transformations of a constraint satisfaction problem as well as sequences of transformations. We extend the notion of transformations to include constrained optimization problems. We discuss how this new framework can inform the evolution of planning models, automated planning algorithms, and mixed-initiative planning.

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5

Wang, J. T. "Inverse Dynamics of Constrained Multibody Systems." Journal of Applied Mechanics 57, no. 3 (September 1, 1990): 750–57. http://dx.doi.org/10.1115/1.2897087.

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A method for analyzing constrained multibody systems is presented. The method is applicable to a class of problems in which the multibody system is subjected to both force and kinematic constraints. This class of problems cannot be solved by using the classical methods. The method is based upon the concept of partial velocity and generalized forces of Kane’s method to permit the choice of constraint forces for fulfilling both kinematic and force constraints. Thus, the constraint forces or moments at convenient points or bodies may be specified in any desired form. For many applications, the method also allows analysts to choose a constant coefficient matrix for the undetermined force term to greatly reduce the burden of repeatedly computing its orthogonal complement matrix in solving the differential algebraic dynamic equations. Two examples illustrating the concepts are presented.

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6

Rustichini, Aldo. "Dynamic Programming Solution of Incentive Constrained Problems." Journal of Economic Theory 78, no. 2 (February 1998): 329–54. http://dx.doi.org/10.1006/jeth.1997.2371.

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7

Li, Xi, Sanyou Zeng, Changhe Li, and Jiantao Ma. "Many-objective optimization with dynamic constraint handling for constrained optimization problems." Soft Computing 21, no. 24 (July 27, 2016): 7435–45. http://dx.doi.org/10.1007/s00500-016-2286-8.

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8

Fu, Jingli, Lijun Zhang, Shan Cao, Chun Xiang, and Weijia Zao. "A Symplectic Algorithm for Constrained Hamiltonian Systems." Axioms 11, no. 5 (May 7, 2022): 217. http://dx.doi.org/10.3390/axioms11050217.

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In this paper, a symplectic algorithm is utilized to investigate constrained Hamiltonian systems. However, the symplectic method cannot be applied directly to the constrained Hamiltonian equations due to the non-canonicity. We firstly discuss the canonicalization method of the constrained Hamiltonian systems. The symplectic method is used to constrain Hamiltonian systems on the basis of the canonicalization, and then the numerical simulation of the system is carried out. An example is presented to illustrate the application of the results. By using the symplectic method of constrained Hamiltonian systems, one can solve the singular dynamic problems of nonconservative constrained mechanical systems, nonholonomic constrained mechanical systems as well as physical problems in quantum dynamics, and also available in many electromechanical coupled systems.

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9

Cheng, Dong Mei, Jian Huang, Hong Jiang Li, and Jing Sun. "Dynamic Sub-Population Genetic Algorithm Combined with Dynamic Penalty Function to Solve Constrained Optimization Problems." Key Engineering Materials 450 (November 2010): 560–63. http://dx.doi.org/10.4028/www.scientific.net/kem.450.560.

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This paper presents a new method of dynamic sub-population genetic algorithm combined with modified dynamic penalty function to solve constrained optimization problems. The new method ensures the final optimal solution yields all constraints through re-organizing all individuals of each generation into two sub-populations according to the feasibility of individuals. And the modified dynamic penalty function gradually increases the punishment to bad individuals with the development of the evolution. With the help of the penalty function and other improvements, the new algorithm prevents local convergence and iteration wandering fluctuations. Typical instances are used to evaluate the optimizing performance of this new method; and the result shows that it can deal with constrained optimization problems well.

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10

Dadebo, S. A., and K. B. Mcauley. "Dynamic optimization of constrained chemical engineering problems using dynamic programming." Computers & Chemical Engineering 19, no. 5 (May 1995): 513–25. http://dx.doi.org/10.1016/0098-1354(94)00086-4.

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11

Djukic, Djordje. "Generalized Lagrange-D’Alembert principle." Publications de l'Institut Math?matique (Belgrade) 91, no. 105 (2012): 49–58. http://dx.doi.org/10.2298/pim1205049d.

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The major issues in the analysis of the motion of a constrained dynamic system are to determine this motion and calculate constraint forces. In the analytical mechanics, only the first of the two problems is analyzed. Here, the problem is solved simultaneously using: 1) Principle of liberation of constraints; 2) Principle of generalized virtual displacement; 3) Idea of ideal constraints; 4) Concept of generalized and ?supplementary" generalized coordinates. The Lagrange-D?Alembert principle of virtual work is generalized introducing virtual displacement as vectorial sum of the classical virtual displacement and virtual displacement in the ?supplementary" directions. From such principle of virtual work we derived Lagrange equations of the second kind and equations of dynamical equilibrium in the ?supplementary" directions. Constrained forces are calculated from the equations of dynamic equilibrium. At the same time, this principle can be used for consideration of equilibrium of system of material particles. This principle simultaneously gives the connection between applied forces at equilibrium state and the constrained forces. Finally, the principle is applied to a few particular problems.

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12

de Armas, Jesica, and Belén Melián-Batista. "Constrained dynamic vehicle routing problems with time windows." Soft Computing 19, no. 9 (January 6, 2015): 2481–98. http://dx.doi.org/10.1007/s00500-014-1574-4.

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13

Chentsov, A. G. "Dynamic programming method in extremal constrained routing problems." Journal of Computer and Systems Sciences International 49, no. 3 (June 2010): 392–405. http://dx.doi.org/10.1134/s1064230710030081.

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14

Nair, Manjusha, Jinesh Manchan Kannimoola, Bharat Jayaraman, Bipin Nair, and Shyam Diwakar. "Temporal constrained objects for modelling neuronal dynamics." PeerJ Computer Science 4 (July 23, 2018): e159. http://dx.doi.org/10.7717/peerj-cs.159.

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Background Several new programming languages and technologies have emerged in the past few decades in order to ease the task of modelling complex systems. Modelling the dynamics of complex systems requires various levels of abstractions and reductive measures in representing the underlying behaviour. This also often requires making a trade-off between how realistic a model should be in order to address the scientific questions of interest and the computational tractability of the model. Methods In this paper, we propose a novel programming paradigm, called temporal constrained objects, which facilitates a principled approach to modelling complex dynamical systems. Temporal constrained objects are an extension of constrained objects with a focus on the analysis and prediction of the dynamic behaviour of a system. The structural aspects of a neuronal system are represented using objects, as in object-oriented languages, while the dynamic behaviour of neurons and synapses are modelled using declarative temporal constraints. Computation in this paradigm is a process of constraint satisfaction within a time-based simulation. Results We identified the feasibility and practicality in automatically mapping different kinds of neuron and synapse models to the constraints of temporal constrained objects. Simple neuronal networks were modelled by composing circuit components, implicitly satisfying the internal constraints of each component and interface constraints of the composition. Simulations show that temporal constrained objects provide significant conciseness in the formulation of these models. The underlying computational engine employed here automatically finds the solutions to the problems stated, reducing the code for modelling and simulation control. All examples reported in this paper have been programmed and successfully tested using the prototype language called TCOB. The code along with the programming environment are available at http://github.com/compneuro/TCOB_Neuron. Discussion Temporal constrained objects provide powerful capabilities for modelling the structural and dynamic aspects of neural systems. Capabilities of the constraint programming paradigm, such as declarative specification, the ability to express partial information and non-directionality, and capabilities of the object-oriented paradigm especially aggregation and inheritance, make this paradigm the right candidate for complex systems and computational modelling studies. With the advent of multi-core parallel computer architectures and techniques or parallel constraint-solving, the paradigm of temporal constrained objects lends itself to highly efficient execution which is necessary for modelling and simulation of large brain circuits.

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15

Błaszczyk, Jacek, Andrzej Karbowski, and Krzysztof Malinowski. "Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point Methods." International Journal of Applied Mathematics and Computer Science 17, no. 4 (December 1, 2007): 515–37. http://dx.doi.org/10.2478/v10006-007-0043-y.

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Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point MethodsThe main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we briefly formulate and characterize the class of problems solved by our optimization classes. The solution of dynamic optimization problems with general constraints is performed by transformation into structured large-scale nonlinear programming problems and applying methods for nonlinear optimization. Two main algorithms of solvers for constrained dynamic optimization are presented in detail: the sequential quadratic programming (SQP) exploring the multistage structure of the dynamic optimization problem during the solution of a sequence of quadratic subproblems, and the nonlinear interior-point method implemented in a general-purpose large-scale optimizer IPOPT. At the end, we include a typical numerical example of the application of the constrained solvers to a large-scale discrete-time optimal control problem and we use the performance profiles methodology to compare the efficiency and robustness of different solvers or different options of the same solver. In conclusions, we summarize our experience gathered during the library development.

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16

Cinar, Ahmet, and Mustafa Kiran. "The Performance of Penalty Methods on Tree-Seed Algorithm for Numerical Constrained Optimization Problems." International Arab Journal of Information Technology 17, no. 5 (September 1, 2020): 799–807. http://dx.doi.org/10.34028/iajit/17/5/13.

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The constraints are the most important part of many optimization problems. The metaheuristic algorithms are designed for solving continuous unconstrained optimization problems initially. The constraint handling methods are integrated into these algorithms for solving constrained optimization problems. Penalty approaches are not only the simplest way but also as effective as other constraint handling techniques. In literature, there are many penalty approaches and these are grouped as static, dynamic and adaptive. In this study, we collect them and discuss the key benefits and drawbacks of these techniques. Tree-Seed Algorithm (TSA) is a recently developed metaheuristic algorithm, and in this study, nine different penalty approaches are integrated with the TSA. The performance of these approaches is analyzed on well-known thirteen constrained benchmark functions. The obtained results are compared with state-of-art algorithms like Differential Evolution (DE), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Genetic Algorithm (GA). The experimental results and comparisons show that TSA outperformed all of them on these benchmark functions

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17

Peng, Chaoda, Hai-Lin Liu, and Fangqing Gu. "A novel constraint-handling technique based on dynamic weights for constrained optimization problems." Soft Computing 22, no. 12 (April 18, 2017): 3919–35. http://dx.doi.org/10.1007/s00500-017-2603-x.

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18

Guo, Furi, JinRong Wang, and Jiangfeng Han. "Dynamic viscoelastic unilateral constrained contact problems with thermal effects." Applied Mathematics and Computation 424 (July 2022): 127034. http://dx.doi.org/10.1016/j.amc.2022.127034.

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19

Zhang, Qing, Sanyou Zeng, and Changhe Li. "Dynamic and random differential evolution solving constrained optimisation problems." International Journal of Computing Science and Mathematics 5, no. 2 (2014): 137. http://dx.doi.org/10.1504/ijcsm.2014.064055.

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20

Lu, Haiyan, and Weiqi Chen. "Dynamic-objective particle swarm optimization for constrained optimization problems." Journal of Combinatorial Optimization 12, no. 4 (September 20, 2006): 409–19. http://dx.doi.org/10.1007/s10878-006-9004-x.

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21

Zheng, Hongqing, and Yongquan Zhou. "A Cooperative Coevolutionary Cuckoo Search Algorithm for Optimization Problem." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/912056.

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Taking inspiration from an organizational evolutionary algorithm for numerical optimization, this paper designs a kind of dynamic population and combining evolutionary operators to form a novel algorithm, a cooperative coevolutionary cuckoo search algorithm (CCCS), for solving both unconstrained, constrained optimization and engineering problems. A population of this algorithm consists of organizations, and an organization consists of dynamic individuals. In experiments, fifteen unconstrained functions, eleven constrained functions, and two engineering design problems are used to validate the performance of CCCS, and thorough comparisons are made between the CCCS and the existing approaches. The results show that the CCCS obtains good performance in the solution quality. Moreover, for the constrained problems, the good performance is obtained by only incorporating a simple constraint handling technique into the CCCS. The results show that the CCCS is quite robust and easy to use.

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22

Xiong, Weili, Mingchen Xue, and Baoguo Xu. "Constrained Dynamic Systems Estimation Based on Adaptive Particle Filter." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/589347.

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For the state estimation problem, Bayesian approach provides the most general formulation. However, most existing Bayesian estimators for dynamic systems do not take constraints into account, or rely on specific approximations. Such approximations and ignorance of constraints may reduce the accuracy of estimation. In this paper, a new methodology for the states estimation of constrained systems with nonlinear model and non-Gaussian uncertainty which are commonly encountered in practice is proposed in the framework of particles filter. The main feature of this method is that constrained problems are handled well by a sample size test and two particles handling strategies. Simulation results show that the proposed method can outperform particles filter and other two existing algorithms in terms of accuracy and computational time.

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23

Chen, Junjie, Shurong Tong, Hongmei Xie, Yafei Nie, and Jingwen Zhang. "Model and Algorithm for Human Resource-Constrained R&D Program Scheduling Optimization." Discrete Dynamics in Nature and Society 2019 (April 3, 2019): 1–13. http://dx.doi.org/10.1155/2019/2320632.

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In resource-constrained project scheduling problems, renewable resources can be expanded into human resources with competency differences. A flexible resource-constrained project scheduling problem with competency differences is proposed, which is a practical extension close to Research and Development (R&D) program management, from the traditional multimode resource-constrained project scheduling problem. A parameter and estimation formula to measure staff competency is presented, and a mixed-integer programming model is established for the problem. The single-objective optimization problems of optimal duration and optimal cost are solved sequentially according to the biobjective importance. To solve the model, according to the assumptions and constraints of the model, the initial network diagram of multiple projects is determined, the enumeration algorithm satisfying constraint conditions provides the feasible solution sets, and the algorithm based on dynamic programming is designed for phased optimization. Experimental results show that the proposed optimization model considering competence differences can solve the problem effectively.

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24

Rosen, A., and E. Edelstein. "Investigation of a New Formulation of the Lagrange Method for Constrained Dynamic Systems." Journal of Applied Mechanics 64, no. 1 (March 1, 1997): 116–22. http://dx.doi.org/10.1115/1.2787261.

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Lagrange multipliers are often used in order to model constrained dynamic systems. This method results in problems of constraints violations and therefore various methods of constraints stabilization have been presented in the past. The purpose of the present paper is to present a new formulation of the method that stabilizes the constraints, but unlike other stabilization methods it is also consistent within the framework of variational methods. The new formulation can be applied to holonomic or nonholonomic constraints. After the presentation of the new formulation, its application to constrained rigid rod systems is presented. The results of the new method are compared with other stabilization techniques.

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25

Wong, R., and D. B. Cherchas. "Hybrid Constraint Space Dynamics and Control for Robot Manipulators." Journal of Vibration and Control 10, no. 11 (November 2004): 1563–84. http://dx.doi.org/10.1177/1077546304042025.

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In this paper we present the development of a hybrid constraint space dynamics modeling technique and position/force controller for robotic manipulator control in constrained environments. The method utilizes a constraint space dynamic model in which the model coordinates are displacement along the constraint trajectory and the normal force between the manipulator end-effector and the environment. The dynamic model is constructed by transforming the conventional joint space manipulator dynamics equations into their constraint space equivalents through the application of mapping functions, which relate differential displacements and velocities in the constraint space coordinate system to the joint space coordinate system. Control algorithms may then be applied to the simplified dynamic structure of the constraint space equations of motion in order to produce a vector of manipulator joint torques which will satisfy both position and force requirements along the environmental constraint. Actuator constraints and momentum compensating techniques are also used to ensure that the position and force control problems are completely decoupled from one another. A computer torque control algorithm is then applied to a two-degrees-of-freedom prismatic robot and simulations are carried out with two different constraint surfaces, i.e. a planar, and a concave circular environment. The results of these simulations show that the controller, implemented in hybrid constraint space provides good position and force control.

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26

Khan, Izaz Ullah, and Muhammad Aftab. "Dynamic programming approach for fuzzy linear programming problems FLPs and its application to optimal resource allocation problems in education system." Journal of Intelligent & Fuzzy Systems 42, no. 4 (March 4, 2022): 3517–35. http://dx.doi.org/10.3233/jifs-211577.

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This research is about the development of a dynamic programming model for solving fuzzy linear programming problems. Initially, fuzzy dynamic linear programming model FDLP is developed. This research revises the established dynamic programming model for solving linear programming problems in a crisp environment. The mentioned approach is upgraded to address the problem in an uncertain environment. Dynamic programming model can either be passing forward or backward. In the proposed approach backward dynamic programming approach is adopted to address the problem. It is then followed by implementing the proposed method on the education system of Pakistan. The education system of Pakistan comprises of the Primary, Middle, Secondary, and Tertiary education stages. The problem is to maximize the efficiency of the education system while achieving the targets with minimum usage of the constrained resources. Likewise the model tries to maximize the enrollment in the Primary, Middle, Secondary and Tertiary educational categories, subject to the total available resources in a fuzzy uncertain environment. The solution proposes that the enrollment can be increased by an amount 9997130, by increasing the enrollment in the Middle and Tertiary educational categories. Thus the proposed method contributes to increase the objective function value by 30%. Moreover, the proposed solutions violate none of the constraints. In other words, the problem of resources allocation in education system is efficiently managed to increase efficiency while remaining in the available constrained resources. The motivation behind using the dynamic programming methodology is that it always possesses a numerical solution, unlike the other approaches having no solution at certain times. The proposed fuzzy model takes into account uncertainty in the linear programming modeling process and is more robust, flexible and practicable.

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27

Trevizan, Felipe, Sylvie Thiébaux, Pedro Santana, and Brian Williams. "Heuristic Search in Dual Space for Constrained Stochastic Shortest Path Problems." Proceedings of the International Conference on Automated Planning and Scheduling 26 (March 30, 2016): 326–34. http://dx.doi.org/10.1609/icaps.v26i1.13768.

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We consider the problem of generating optimal stochastic policies for Constrained Stochastic Shortest Path problems, which are a natural model for planning under uncertainty for resource-bounded agents with multiple competing objectives. While unconstrained SSPs enjoy a multitude of efficient heuristic search solution methods with the ability to focus on promising areas reachable from the initial state, the state of the art for constrained SSPs revolves around linear and dynamic programming algorithms which explore the entire state space. In this paper, we present i-dual, which, to the best of our knowledge, is the first heuristic search algorithm for constrained SSPs. To concisely represent constraints and efficiently decide their violation, i-dual operates in the space of dual variables describing the policy occupation measures. It does so while retaining the ability to use standard value function heuristics computed by well-known methods. Our experiments on a suite of PPDDL problems augmented with constraints show that these features enable i-dual to achieve up to two orders of magnitude improvement in run-time and memory over linear programming algorithms.

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28

Chen, Qingda, Jinliang Ding, Shengxiang Yang, and Tianyou Chai. "A Novel Evolutionary Algorithm for Dynamic Constrained Multiobjective Optimization Problems." IEEE Transactions on Evolutionary Computation 24, no. 4 (August 2020): 792–806. http://dx.doi.org/10.1109/tevc.2019.2958075.

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29

Mare, José B., and José A. De Doná. "DYNAMIC PROGRAMMING SOLUTION OF STATE ESTIMATION PROBLEMS WITH CONSTRAINED DISTURBANCES." IFAC Proceedings Volumes 38, no. 1 (2005): 1299–304. http://dx.doi.org/10.3182/20050703-6-cz-1902.00217.

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30

Jae Huh, Gyoung, and Byung Man Kwak. "Constrained variational approach for dynamic analysis of elastic contact problems." Finite Elements in Analysis and Design 10, no. 2 (November 1991): 125–36. http://dx.doi.org/10.1016/0168-874x(91)90037-y.

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31

Faísca, Nuno P., Konstantinos I. Kouramas, Pedro M. Saraiva, Berç Rustem, and Efstratios N. Pistikopoulos. "A multi-parametric programming approach for constrained dynamic programming problems." Optimization Letters 2, no. 2 (June 27, 2007): 267–80. http://dx.doi.org/10.1007/s11590-007-0056-3.

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32

Zhu, Hao, Yumei Hu, and Weidong Zhu. "A dynamic adaptive particle swarm optimization and genetic algorithm for different constrained engineering design optimization problems." Advances in Mechanical Engineering 11, no. 3 (March 2019): 168781401882493. http://dx.doi.org/10.1177/1687814018824930.

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Анотація:

A dynamic adaptive particle swarm optimization and genetic algorithm is presented to solve constrained engineering optimization problems. A dynamic adaptive inertia factor is introduced in the basic particle swarm optimization algorithm to balance the convergence rate and global optima search ability by adaptively adjusting searching velocity during search process. Genetic algorithm–related operators including a selection operator with time-varying selection probability, crossover operator, and n-point random mutation operator are incorporated in the particle swarm optimization algorithm to further exploit optimal solutions generated by the particle swarm optimization algorithm. These operators are used to diversify the swarm and prevent premature convergence. Tests on nine constrained mechanical engineering design optimization problems with different kinds of objective functions, constraints, and design variables in nature demonstrate the superiority of the dynamic adaptive particle swarm optimization and genetic algorithm against several other meta-heuristic algorithms in terms of solution quality, robustness, and convergence rate in most cases.

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33

Sharan, A. M., J. Jain, and P. Kalra. "Efficient Methods for Solving Dynamic Problems of Flexible Manipulators." Journal of Dynamic Systems, Measurement, and Control 114, no. 1 (March 1, 1992): 78–88. http://dx.doi.org/10.1115/1.2896510.

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In this work, efficient methods for solving dynamic problems in the robotics area are discussed. The nonlinear dynamic equations are derived and their linearization is verified. The unconstrained dynamic problems for a flexible arm robot are solved by four efficient numerical techniques. The constrained problems are solved by Revised Simplex Method and the Karmarkar’s Algorithm.

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34

Hernández-Ocaña, Betania, José Hernández-Torruco, Oscar Chávez-Bosquez, Juana Canul-Reich, and Luis Gerardo Montané-Jiménez. "Bacterial foraging optimization algorithm with mutation to solve constrained problems." Acta Universitaria 29 (October 23, 2019): 1–16. http://dx.doi.org/10.15174/au.2019.2335.

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A simple version of a Swarm Intelligence algorithm called bacterial foraging optimization algorithm with mutation and dynamic stepsize (BFOAM-DS) is proposed. The bacterial foraging algorithm has the ability to explore and exploit the search space through its chemotactic operator. However, premature convergence is a disadvantage. This proposal uses a mutation operator in a swim, similar to evolutionary algorithms, combined with a dynamic stepsize operator to improve its performance and allows a better balance between the exploration and exploitation of the search space. BFOAM-DS was tested in three well-known engineering design optimization problems. Results were analyzed with basic statistics and common measures for nature-inspired constrained optimization problems to evaluate the behavior of the swim with a mutation operator and the dynamic stepsize operator. Results were compared against a previous version of the proposed algorithm to conclude that BFOAM-DS is competitive and better than a previous version of the algorithm.

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35

Sennott, Linn I. "COMPUTING AVERAGE OPTIMAL CONSTRAINED POLICIES IN STOCHASTIC DYNAMIC PROGRAMMING." Probability in the Engineering and Informational Sciences 15, no. 1 (January 2001): 103–33. http://dx.doi.org/10.1017/s0269964801151089.

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A stochastic dynamic program incurs two types of cost: a service cost and a quality of service (delay) cost. The objective is to minimize the expected average service cost, subject to a constraint on the average quality of service cost. When the state space S is finite, we show how to compute an optimal policy for the general constrained problem under weak conditions. The development uses a Lagrange multiplier approach and value iteration. When S is denumerably infinite, we give a method for computation of an optimal policy, using a sequence of approximating finite state problems. The method is illustrated with two computational examples.

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36

Sahu, PK, and S. Saha Ray. "Comparison on wavelets techniques for solving fractional optimal control problems." Journal of Vibration and Control 24, no. 6 (July 25, 2016): 1185–201. http://dx.doi.org/10.1177/1077546316659611.

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This paper presents efficient numerical techniques for solving fractional optimal control problems (FOCP) based on orthonormal wavelets. These wavelets are like Legendre wavelets, Chebyshev wavelets, Laguerre wavelets and Cosine And Sine (CAS) wavelets. The formulation of FOCP and properties of these wavelets are presented. The fractional derivative considered in this problem is in the Caputo sense. The performance index of FOCP has been considered as function of both state and control variables and the dynamic constraints are expressed by fractional differential equation. These wavelet methods are applied to reduce the FOCP as system of algebraic equations by applying the method of constrained extremum which consists of adjoining the constraint equations to the performance index by a set of undetermined Lagrange multipliers. These algebraic systems are solved numerically by Newton's method. Illustrative examples are discussed to demonstrate the applicability and validity of the wavelet methods.

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37

Hu, Yudong, Changsheng Gao, and Wuxing Jing. "Joint State and Parameter Estimation for Hypersonic Glide Vehicles Based on Moving Horizon Estimation via Carleman Linearization." Aerospace 9, no. 4 (April 14, 2022): 217. http://dx.doi.org/10.3390/aerospace9040217.

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Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly.

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38

Sousa-Ferreira, Ivo, and Duarte Sousa. "A review of velocity-type PSO variants." Journal of Algorithms & Computational Technology 11, no. 1 (September 18, 2016): 23–30. http://dx.doi.org/10.1177/1748301816665021.

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This paper presents a review of the particular variants of particle swarm optimization, based on the velocity-type class. The original particle swarm optimization algorithm was developed as an unconstrained optimization technique, which lacks a model that is able to handle constrained optimization problems. The particle swarm optimization and its inapplicability in constrained optimization problems are solved using the dynamic-objective constraint-handling method. The dynamic-objective constraint-handling method is originally developed for two variants of the basic particle swarm optimization, namely restricted velocity particle swarm optimization and self-adaptive velocity particle swarm optimization. Also on the subject velocity-type class, a review of three other variants is given, specifically: (1) vertical particle swarm optimization; (2) velocity limited particle swarm optimization; and (3) particle swarm optimization with scape velocity. These velocity-type particle swarm optimization variants all have in common a velocity parameter which determines the direction/movements of the particles.

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39

Hartono, Hartono. "Resolution of Dynamic Optimization Problems Constrained by the Fraction Penalty Method." Indonesian Journal of Information Systems 2, no. 2 (February 28, 2020): 51. http://dx.doi.org/10.24002/ijis.v2i2.3223.

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This article discusses the application of fractional penalty method to solve dynamic optimization problem with state constraints. The main theories supporting the use of the method are described in some theorem and corollary. The theorems give sufficient conditons for the application of the method. Therefore, if all conditions mentioned in the theorems are met then the resulted solution will converge to the analytic solution. In addition, there are some examples to support the theory. The numerical simulation shows that the accuracy of the method is quite good. Hence, this method can play a role as an alternative method for solving dynamic optimization problem with state constrints.

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40

Matijascic, Marko, Maja Jurisic Bellotti, Mladen Vucic, and Goran Molnar. "Optimum Synthesis of Pencil Beams with Constrained Dynamic Range Ratio." International Journal of Antennas and Propagation 2022 (November 16, 2022): 1–14. http://dx.doi.org/10.1155/2022/3664607.

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In antenna array design, low dynamic range ratio (DRR) of excitation coefficients is important because it simplifies array’s feeding network and enables better control of mutual coupling. Optimization-based synthesis of pencil beams allows explicit control of DRR. However, incorporating DRR into an optimization problem leads to nonconvex constraints, making its solving challenging. In this paper, a framework for global optimization of linear pencil beams with constrained DRR is presented. By using this framework, the methods for synthesis of pencil beams with minimum sidelobe level and minimum sidelobe power are developed. Both methods utilize convex problems suitable for the synthesis of pencil beams whose coefficients’ signs are known in advance. By incorporating these problems into a branch and bound algorithm, the procedures for global optimizations are formed which systematically search the space of all coefficient signs. The method for minimization of sidelobe power is further analyzed in the context of beam efficiency. It is shown that this method can be utilized in an approximate and at the same time global design of pencil beam arrays with maximum beam efficiency and constrained DRR. Based on this approach, a method for the design of pencil beam arrays with minimum DRR and specified beam efficiency is proposed.

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41

Yuan, Jiawei. "Dynamic grid-based uniform search for solving constrained multiobjective optimization problems." Memetic Computing 13, no. 4 (November 13, 2021): 497–508. http://dx.doi.org/10.1007/s12293-021-00349-2.

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42

Zhang, Zhuhong, Min Liao, and Lei Wang. "Immune Optimization Approach for Dynamic Constrained Multi-Objective Multimodal Optimization Problems." American Journal of Operations Research 02, no. 02 (2012): 193–202. http://dx.doi.org/10.4236/ajor.2012.22022.

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43

Liu, Chun-an. "An imperialist competitive algorithm for solving dynamic nonlinear constrained optimization problems." Journal of Intelligent & Fuzzy Systems 30, no. 2 (February 9, 2016): 759–72. http://dx.doi.org/10.3233/ifs-151797.

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44

Luus, Rein, and Oscar Rosen. "Application of dynamic programming to final state constrained optimal control problems." Industrial & Engineering Chemistry Research 30, no. 7 (July 1991): 1525–30. http://dx.doi.org/10.1021/ie00055a018.

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45

Norbis, Mario I., and J. MacGregor Smith. "A multiobjective, multi-level heuristic for dynamic resource constrained scheduling problems." European Journal of Operational Research 33, no. 1 (January 1988): 30–41. http://dx.doi.org/10.1016/0377-2217(88)90251-2.

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46

Xiao, Jianhua, Juan-juan He, Ping Chen, and Yun-yun Niu. "An improved dynamic membrane evolutionary algorithm for constrained engineering design problems." Natural Computing 15, no. 4 (July 8, 2016): 579–89. http://dx.doi.org/10.1007/s11047-016-9569-y.

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47

Qian, Shuqu, Yanmin Liu, Yongqiang Ye, and Guofeng Xu. "An enhanced genetic algorithm for constrained knapsack problems in dynamic environments." Natural Computing 18, no. 4 (January 16, 2019): 913–32. http://dx.doi.org/10.1007/s11047-018-09725-3.

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48

Yu, Peng, Cheng Fang, and Brian Williams. "Resolving Uncontrollable Conditional Temporal Problems Using Continuous Relaxations." Proceedings of the International Conference on Automated Planning and Scheduling 24 (May 11, 2014): 341–48. http://dx.doi.org/10.1609/icaps.v24i1.13623.

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Uncertainty is commonly encountered in temporal scheduling and planning problems, and can often lead to over-constrained situations. Previous relaxation algorithms for over-constrained temporal problems only work with requirement constraints, whose outcomes can be controlled by the agents. When applied to uncontrollable durations, these algorithms may only satisfy a subset of the random outcomes and hence their relaxations may fail during execution. In this paper, we present a new relaxation algorithm, Conflict-Directed Relaxation with Uncertainty (CDRU), which generates relaxations that restore the controllability of conditional temporal problems with uncontrollable durations. CDRU extends the Best-first Conflict-Directed Relaxation (BCDR) algorithm to uncontrollable temporal problems. It generalizes the conflict-learning process to extract conflicts from strong and dynamic controllability checking algorithms, and resolves the conflicts by both relaxing constraints and tightening uncontrollable durations. Empirical test results on a range of trip scheduling problems show that CDRU is efficient in resolving large scale uncontrollable problems: computing strongly controllable relaxations takes the same order of magnitude in time compared to consistent relaxations that do not account for uncontrollable durations. While computing dynamically controllable relaxations takes two orders of magnitude more time, it provides significant improvements in solution quality when compared to strongly controllable relaxations.

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49

Wiedemann, Johannes. "Higher-order exponential integrators for constrained semi-linear parabolic problems." GAMM Archive for Students 2, no. 1 (February 16, 2020): 14–20. http://dx.doi.org/10.14464/gammas.v2i1.421.

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This paper provides an introduction to exponential integrators for constrained parabolic systems. In addition, building on existing results, schemes with an expected order of convergence of three and four are established and numerically tested on parabolic problems with nonlinear dynamic boundary conditions. The simulations reinforce the subjected error behaviour.

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50

Luo, Xin-long, Jia-ru Lin, and Wei-ling Wu. "A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/845459.

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This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalent-constrained optimization problem. Second, according to the Karush-Kuhn-Tucker conditions of this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Third, based on the implicit Euler method and an analogous trust-region technique, a prediction-correction method is constructed to follow this system of differential-algebraic equations to compute its steady-state solution. Consequently, the smallest generalized eigenvalue of the original problem is obtained. The local superlinear convergence property for this new algorithm is also established. Finally, in comparison with other methods, some promising numerical experiments are presented.

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