Showing papers on "Extremal optimization published in 1996"

Ant system: optimization by a colony of cooperating agents

Abstract: An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call ant system (AS). We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation, and the use of a constructive greedy heuristic. Positive feedback accounts for rapid discovery of good solutions, distributed computation avoids premature convergence, and the greedy heuristic helps find acceptable solutions in the early stages of the search process. We apply the proposed methodology to the classical traveling salesman problem (TSP), and report simulation results. We also discuss parameter selection and the early setups of the model, and compare it with tabu search and simulated annealing using TSP. To demonstrate the robustness of the approach, we show how the ant system (AS) can be applied to other optimization problems like the asymmetric traveling salesman, the quadratic assignment and the job-shop scheduling. Finally we discuss the salient characteristics-global data structure revision, distributed communication and probabilistic transitions of the AS.

Solving optimization problems with variable-constraint by an extended Cohen-Grossberg model

Abstract: A variety of real-world problems can be formulated as continuous optimization problems with variable constraint. It is well-known, however, that it is difficult to develop a unified method for obtaining their feasible solutions. We have recognized that the recent work of solving the traveling salesman problem (TSP) by the Hopfield model explores an innovative approach to them as well as combinatorial optimization problems. The Hopfield model is generalized into the Cohen-Grossberg model (CGM) to which a specific Lyapunov function has been found. This paper thus extends the Hopfield method onto the CGM in order to develop a unified solving-method of continuous optimization problems with variable-constraint. Specifically, we consider a certain class of continuous optimization problems with a constraint equation including the Hopfield version of the TSP as a particular member. Then we theoretically develop a method that, from any given problem of that class, derives a network of an extended CGM to provide feasible solutions to it. The main idea for constructing that extended CGM lies in adding to it a synapse dynamical system concurrently operating with its current unit dynamical system so that the constraint equation can be enforced to satisfaction at final states. This construction is also motivated by previous neuron models in biophysics and learning algorithms in neural networks.

Network Optimization Using Evolutionary Strategies

Abstract: Network optimization which has to consider both the connection distance (detour) between different nodes and the total length (costs) of the network, belongs to the class of frustrated optimization problems. Here, evolutionary strategies which include both thermodynamic and biological elements, are used to find different optimized solutions (graphs of varying density) for the network in dependence on the degree of frustration. We show, that the optimization process occurs on two different time scales, and that in the asymptotic limit a a fixed relation between the mean connection distance (detour) and the total lenght (costs) of the network exist.

Parallel Search-Based Methods in Optimization

Abstract: Search-based methods like Branch and Bound and Branch and Cut are essential tools in solving difficult problems to optimality in the field of combinatorial optimization, and much experience has been gathered regarding the design and implementation of parallel methods in this field.

Ergodic theorems for some classical problems in combinatorial optimization

Abstract: We show that the stochastic versions of some classical problems in combinatorial optimization may be imbedded in multiparameter subadditive processes having an intrinsic ergodic structure. A multiparameter generalization of Kingman's subadditive ergodic theorem is used to capture strong laws for these optimization problems, including the traveling salesman and minimal spanning tree processes. In this way we make progress on some open problems and provide alternate proofs of some well known asymptotic results.

Democratic Optimization for Discrete and Continuous Systems

Abstract: A novel strategy for finding optimal solutions to complex problems with many competing requirements is proposed. It consists in a simultaneous optimization of the energy, cost or fitness function of the system itself, and of sub-systems of all sizes with an appropriate weight function. For various travelling salesman problems and spin glasses as well as for an example of a continuous-valued system (the optical multilayer problem) the corresponding Monte Carlo algorithm is shown to yield results superior to those obtained by previous optimization techniques.

Combinatorial optimization with coupled chemical reaction cells

Abstract: Many combinatorial optimization problems in industry can be reduced to a so-called assignment problem. This assignment problem can be handled by an adapted form of the nonlinear differential equations which are used to model the macroscopic behavior of complex physical systems. To get the necessary adaption specific coupling terms are used to result in a suitable selection and feasible solutions as stable points of the dynamical system. In comparison to many other methods this approach has the advantage that additional constraints of the optimization problem can easily be considered. Furthermore, parallel hardware realizations of this approach are possible because of the similarity to models of complex physical and chemical systems. A realization with coupled chemical reaction cells is suggested in this paper.