In many cases fitness landscapes are obtained as particular instances of random fields by randomly assigning a large number of parameters. Models of this type are often characterized reasonably well by their covarianc...
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In many cases fitness landscapes are obtained as particular instances of random fields by randomly assigning a large number of parameters. Models of this type are often characterized reasonably well by their covariance matrices. We characterize isotropic random fields on finite graphs in terms of their Fourier series expansions and investigate the relation between the covariance matrix of the random field model and the correlation structure of the individual landscapes constructed from this random field. Correlation measures are a good characteristic of "rugged landscapes" models as they are closely related to quantities like the number of local optima or the length of adaptive walks. Our formalism suggests to approximate landscape with known autocorrelation function by a random field model that has the same correlation structure.
Recent developments have aroused the interest of researchers in the application of chaotic neural networks to combinatorial optimization problems. In this paper, we introduce a new approach, which is termed as Sequent...
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ISBN:
(纸本)0769500137
Recent developments have aroused the interest of researchers in the application of chaotic neural networks to combinatorial optimization problems. In this paper, we introduce a new approach, which is termed as Sequential Chaotic Annealing. The approach combines chaotic neural networks and ideas from the theory of nonlinear optimization. The proposed neural networks are adaptive in the sense that the network "learns" the right cost or energy function to optimize. Sequential Chaotic Annealing is applied to multilayer channel routing using the reserved wiring model and restricted doglegging. We show that the proposed approach improves convergence to valid solutions and reduces the sensitivity to the initial states of the neurons.
In solving combinatorial optimization problems by Hopfield neural networks, mappings of the problems to the networks are not made so carefully. Although many mappings of, for example, the traveling salesman problems (...
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In solving combinatorial optimization problems by Hopfield neural networks, mappings of the problems to the networks are not made so carefully. Although many mappings of, for example, the traveling salesman problems (TSP) have been proposed, their theoretical comparisons are not yet made. In this paper, taking two typical mappings of TSP as examples, their theoretical comparisons are made to prove the superiority of one over the other by the asymptotical stability and unstability theory of the solutions shown by Matsuda [8, 9]. This theoretical comparison method could be applicable to mappings of many other combinatorial optimization problems.
In this paper, we investigate the possibility of integrating Artificial Intelligence (AI) and Operations Research (OR) techniques for solving the Crew Rostering Problem (CRP). CRP calls for the optimal sequencing of a...
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In this paper, we investigate the possibility of integrating Artificial Intelligence (AI) and Operations Research (OR) techniques for solving the Crew Rostering Problem (CRP). CRP calls for the optimal sequencing of a...
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In this paper, we investigate the possibility of integrating Artificial Intelligence (AI) and Operations Research (OR) techniques for solving the Crew Rostering Problem (CRP). CRP calls for the optimal sequencing of a given set of duties into rosters satisfying a set of constraints. The optimality criterion requires the minimization of the number of crews needed to cover the duties. This kind of problem has been traditionally solved by OR techniques. In recent years, a new programming paradigm based on Logic Programming, named Constraint Logic Programming (CLP), has been successfully used for solving hard combinatorial optimization problems. CLP maintains all the advantages of logic programming such as declarativeness, non-determinism and an incremental style of programming, while overcoming its limitations, mainly due to the inefficiency in exploring the search space, CLP achieves good results on hard combinatorial optimization problems which, however, are not comparable with those achieved by OR approaches, Therefore, we integrate both techniques in order to design an effective heuristic algorithm for CRP which fully exploits the advantages of the two methodologies: on the one hand, we maintain the declarativeness of CLP, its ease of representing knowledge and its rapid prototyping;on the other hand, we inherit from OR some efficient procedures based on a mathematical approach to the problem, Finally, we compare the results we achieved by means of the integration with those obtained by a pure OR approach, showing that AP and OR techniques for hard combinatorial optimization problems can be effectively integrated, (C) 1998 by John Wiley & Sons, Ltd.
Genetic algorithm (GA) is a general purpose optimization technique bused on mechanisms inspired from the natural genetics and natural selection. It is very suitable for solving nonlinear, multi-constraints, combinator...
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ISBN:
(纸本)0780342534
Genetic algorithm (GA) is a general purpose optimization technique bused on mechanisms inspired from the natural genetics and natural selection. It is very suitable for solving nonlinear, multi-constraints, combinatorial optimization problemsproblems are tough for conventional methods. However, the simple genetic algorithm(SGA) may have a slow convergence or even cannot reach the global optimum. Therefore, an enhanced GA is proposed ill this paper to solve the unit commitment problem in power systems. The new features of the enhanced GA include chromosome mapping, problem specific operators and a local search technique. As expected, it has a significantly improved performance of finding the optimal solution to the unit commitment problem.
We propose a novel segmentation algorithm which combines an image segmentation method into small regions with chaotic neurodynamics that has already been clarified to be effective for solving some combinatorial optimi...
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We propose a novel segmentation algorithm which combines an image segmentation method into small regions with chaotic neurodynamics that has already been clarified to be effective for solving some combinatorial optimization problems. The basic algorithm of an image segmentation is the variable-shape-block-segmentation (VB) which searches an optimal state of the segmentation by moving the vertices of quadrangular regions. However, since the algorithm for moving vertices is based upon steepest descent dynamics, this segmentation method has a local minimum problem that the algorithm gets stuck at undesirable local minima. In order to treat such a problem of the VB and improve its performance, we introduce chaotic neurodynamics for optimization. The results of our novel method are compared with those of conventional stochastic dynamics for escaping from undesirable local minima. As a result, the better results are obtained with the chaotic neurodynamical image segmentation.
We consider the construction of minimal multilayered perceptrons for solving combinatorial optimization problems. Though general in nature, the proposed construction method is presented as a case study for the sorting...
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We consider the construction of minimal multilayered perceptrons for solving combinatorial optimization problems. Though general in nature, the proposed construction method is presented as a case study for the sorting problem. The presentation starts with an O((n!)2) three-layered perceptron based on complete enumeration, that solves the sorting problem of n numbers. This network is then gradually reduced to an O(n2)three-layered perceptron, which can be viewed as a neural implementation of Preparata's parallel enumerative sorting algorithm.
This article analyzes the property of the fully interconnected neural networks as a method of solving combinatorial optimization problems in general. In particular, in order to escape local minimums in this model, we ...
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This article analyzes the property of the fully interconnected neural networks as a method of solving combinatorial optimization problems in general. In particular, in order to escape local minimums in this model, we analyze theoretically the relation between the diagonal elements of the connection matrix and the stability of the networks. It is shown that the position of the global minimum point of the energy function on the hyper sphere in n dimensional space is given by the eigen vector corresponding the maximum eigen value of the connection matrix. Then it is shown that the diagonal elements of the connection matrix can be improved without loss of generality. The equilibrium points of the improved networks are classified according to their properties, and their stability is investigated. In order to show that the change of the diagonal elements improves the potential for the global minimum search, computer simulations are carried out by using the theoretical values. In according to the simulation result on 10 neurons, the success rate to get the optimum solution is 97.5%. The result shows that the improvement of the diagonal elements has potential for minimum search.
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