A combined genetic algorithms-shooting method approach to solving optimal control problems

Sim, Y. C.; Leng, Supeng; Subramaniam, Velusamy

doi:10.1080/002077200291488

Cited by 26 publications

(16 citation statements)

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“…On the other aspect, GA can be distinguished from calculus-based and enumerative methods for optimization by the following characteristics [22,23,24,25,26,27,28]:…”

Section: Steps Of Cga Techniquementioning

confidence: 99%

Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems

Arqub¹,

Abo-Hammour²,

Momani³

2014

Appl. Math. Inf. Sci.

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Abstract:In this paper, a numerical algorithm, based on the use of genetic algorithm technique, is presented for solving a class of nonlinear systems of second-order boundary value problems. In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraints boundary condtions, and is then solved using continuous genetic algorithm. In general, the proposed technique uses smooth operators and avoids sharp jumps in the parameter values. The applicability, efficiency, and accuracy of the proposed algorithm for the solution of different problems is investigated. Meanwhile, the convergence analysis based on the resulting statistical data is also discussed.

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“…On the other aspect, GA can be distinguished from calculus-based and enumerative methods for optimization by the following characteristics [22,23,24,25,26,27,28]:…”

Section: Steps Of Cga Techniquementioning

confidence: 99%

Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems

Arqub¹,

Abo-Hammour²,

Momani³

2014

Appl. Math. Inf. Sci.

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“…They don't really need good initial guesses and deterministic rules. Some of these methods are; Genetic algorithm (GA), see [1,23,24], Genetic programming (GP), see [18], Particle swarm optimization (PSO), see [3,4,21], Ant colony optimization (ACO), see [27] and Differential evolution (DE), see [8,19,28]. Many authors proposed many types of metaheuristics for solving NOCPs.…”

Section: Introductionmentioning

confidence: 99%

“…Lee et al [19] used a modified DE algorithm for dynamic optimization of a continuous polymer reactor. Sim et al [24] combined a GA and the shooting method for solving NOCP. Cruz et al [8] used efficient DE algorithms for solving multi-modal NOCPs.…”

Section: Introductionmentioning

confidence: 99%

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

Ghanbari

Nezhadhosein

Heidari

2014

IJAMR

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Here, a two-phase algorithm based on integrating particle swarm optimization (PSO) with modified hybrid genetic algorithm (MHGA) is proposed for solving the associated nonlinear programming problem of a nonlinear optimal control problem. In the first phase, PSO starts with a completely random initial swarm of particles, where each of them contains two random matrices in time nodes. After phase 1, to achieve more accurate solutions, the number of time nodes is increased. The values of the associated new control inputs are estimated by linear or spline interpolations using the curves computed in the phase 1. In addition, to maintain the diversity in the population, some additional individuals are added randomly. Next, in the second phase, MHGA, starts by the new population constructed by the above procedure and tries to improve the obtained solutions at the end of phase 1. MHGA combines a GA with a successive quadratic programming, SQP, as a local search. Finally, we implement the proposed algorithm on some well-known nonlinear optimal control problems. The numerical results show that the proposed algorithm can find almost better solution than other proposed algorithms.

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“…On the other hand, dynamic optimization [6][7][8] computes the controls, the state, and possibly the final time that minimize a cost function, subject to state equations and to various other constraints, as required by the problem at hand. There are basically two alternative strategies for the numerical solution of a dynamic optimization problem.…”

Section: Introductionmentioning

confidence: 99%

“…Then the problem is reduced to a TPBVP (twopoint boundary value problem) in the infinite dimension and a suitable MSM (multiple-shooting method) can be used to resolve it in the finite dimension. [8][9][10] The second is the direct method, 6,7) which uses the discretized or parameterized equation for state equations, constraint equations and a cost function in the finite dimension. The result becomes a nonlinear programming problem which can be solved by one of the efficient NLP (non-linear programming) methods.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Optimal Control Analysis of Helicopter Maneuver Problems Using the Indirect Method

Kim

Lee

Byun

et al. 2008

Trans. Japan Soc. Aero. S Sci.

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This paper deals with a nonlinear optimal control approach to helicopter inverse simulation. The reference trajectory is prescribed in prior, and the integral deviation from this trajectory is treated as an additional penalty cost to convert the system optimality to an unconstrained optimal control problem. The resultant two-point boundary value problem has been solved by a multiple-shooting algorithm. The nonlinear helicopter model in this study includes main rotor flap dynamics and a dynamic inflow model. The applications cover the inverse simulation for bob up, turn, and slalom maneuvers. This paper focuses on resolving the convergence issue using the indirect method, the main root causes of which are related to the inherent system instability of the helicopter and with poor initial guesses on state and costate variables. For this reason we will investigate the effect of the shooting node number on convergence and use a hybrid-model approach, where the optimal state and costate variables, calculated using the linear model, are used as initial guesses for those using the nonlinear model. The analyses show good convergence history and capability of tracking the prescribed trajectory. So the results in this paper can provide a valuable motivation for applying indirect methods to nonlinear helicopter flight mechanic analysis.

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A combined genetic algorithms-shooting method approach to solving optimal control problems

Cited by 26 publications

References 0 publications

Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems

Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

Nonlinear Optimal Control Analysis of Helicopter Maneuver Problems Using the Indirect Method

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