On benchmarking functions for genetic algorithms

Digalakis, Jason G.; Margaritis, Konstantinos G.

doi:10.1080/00207160108805080

Cited by 374 publications

(156 citation statements)

References 6 publications

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“…At a saddle, the Hessian has both positive and negative character. The existence of landscape saddles has practical significance for OCT optimizations, since their presence may influence searches with a gradient algorithm [110,115] or even hinder the convergence efficiency of global stochastic algorithms [116]. The topic assessed in this paper is the role of saddles in seeking optimal controls, as reflected in the performance of a gradient-based algorithm which was chosen due to its sensitivity to landscape saddle features.…”

Section: A Backgroundmentioning

confidence: 99%

Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape

Riviello

Sun

et al. 2017

Phys. Rev. A

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The broad success of theoretical and experimental quantum optimal control is intimately connected to the topology of the underlying control landscape. For several common quantum control goals, including the maximization of an observable expectation value, the landscape has been shown to lack local optima if three assumptions are satisfied: (i) the quantum system is controllable, (ii) the Jacobian of the map from the control field to the evolution operator is full-rank, and (iii) the control field is not constrained. In the case of the observable objective, this favorable analysis shows that the associated landscape also contains saddles, i.e., critical points that are not local suboptimal extrema. In this paper, we investigate whether the presence of these saddles affects the trajectories of gradient-based searches for an optimal control. We show through simulations that both the detailed topology of the control landscape and the parameters of the system Hamiltonian influence whether the searches are attracted to a saddle. For some circumstances with a special initial state and target observable, optimizations may approach a saddle very closely, reducing the efficiency of the gradient algorithm. Encounters with such attractive saddles are found to be quite rare. Neither the presence of a large number of saddles on the control landscape nor a large number of system states increase the likelihood that a search will closely approach a saddle. Even for applications that encounter a saddle, well-designed gradient searches with carefully chosen algorithmic parameters will readily locate optimal controls.

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Section: A Backgroundmentioning

confidence: 99%

Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape

Riviello

Sun

et al. 2017

Phys. Rev. A

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“…The landscape topology has practical significance for quantum control optimizations, since local optima may trap gradient searches and can even affect the efficiency of genetic algorithms [150]. When the landscape lacks local traps, on the other hand, several OCT studies consisting of thousands of numerical simulations have shown that gradient searches can quickly locate globally optimal controls [130,[151][152][153].…”

Section: Introductionmentioning

confidence: 99%

Searching for quantum optimal controls under severe constraints

Riviello¹,

Tibbetts²,

Brif³

et al. 2015

Phys. Rev. A

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The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still introduce artificial traps. Proper management of these constraints is an issue of great practical importance for numerical simulations as well as optimization in the laboratory. Using optimal control simulations, we show that constraints on quantities such as the number of control variables, the control duration, and the field strength are potentially severe enough to prevent successful optimization of the objective. For each such constraint, we show that exceeding quantifiable limits can prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.

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“…Some of the essential characteristics of these functions are that the functions should be multimodal or unimodal in nature, the function should be nonseparable, and moreover, the functions should lag in the global structure. By keeping these virtues in consideration, benchmarking of the variants is done on five unimodal and five multimodal shifted and biased benchmark functions [31][32][33]. In the standard benchmark functions, the minima lies at zero; however, in multimodal functions, multioptima (local) can exist.…”

Section: Simulation and Resultsmentioning

confidence: 99%

Application and Development of Enhanced Chaotic Grasshopper Optimization Algorithms

Saxena

Shekhawat

Kumar

2018

Modelling and Simulation in Engineering

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In recent years, metaheuristic algorithms have revolutionized the world with their better problem solving capacity. Any metaheuristic algorithm has two phases: exploration and exploitation. e ability of the algorithm to solve a difficult optimization problem depends upon the efficacy of these two phases. ese two phases are tied with a bridging mechanism, which plays an important role. is paper presents an application of chaotic maps to improve the bridging mechanism of Grasshopper Optimisation Algorithm (GOA) by embedding 10 different maps. is experiment evolves 10 different chaotic variants of GOA, and they are named as Enhanced Chaotic Grasshopper Optimization Algorithms (ECGOAs). e performance of these variants is tested over ten shifted and biased unimodal and multimodal benchmark functions. Further, the applications of these variants have been evaluated on three-bar truss design problem and frequency-modulated sound synthesis parameter estimation problem. Results reveal that the chaotic mechanism enhances the performance of GOA. Further, the results of the Wilcoxon rank sum test also establish the efficacy of the proposed variants.

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On benchmarking functions for genetic algorithms

Cited by 374 publications

References 6 publications

Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape

Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape

Searching for quantum optimal controls under severe constraints

Application and Development of Enhanced Chaotic Grasshopper Optimization Algorithms

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