Showing papers on "Extremal optimization published in 2003"

Particle swarm optimization for traveling salesman problem

Abstract: This paper proposes a new application of particle swarm optimization for traveling salesman problem. We have developed some special methods for solving TSP using PSO. We have also proposed the concept of swap operator and swap sequence, and redefined some operators on the basis of them, in this way the paper has designed a special PSO. The experiments show that it can achieve good results.

Extremal Optimization: An Evolutionary Local-Search Algorithm

Abstract: A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms ofself-organized criticality, a concept introduced to describe emergent complexity in physical systems. This method, calledextremal optimization, successively replaces the value of extremely undesirable variables in a sub-optimal solution with new, random ones. Large, avalanche-like fluctuations in the cost function self-organize from this dynamics, effectively scaling barriers to explore local optima in distant neighborhoods of the configuration space while eliminating the need to tune parameters. Drawing upon models used to simulate the dynamics of granular media, evolution, or geology, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such assimulated annealing. It may be but one example of applying new insights intonon-equilibrium phenomenasystematically to hard optimization problems. This method is widely applicable and so far has proved competitive with — and even superior to — more elaborate general-purpose heuristics on testbeds of constrained optimization problems with up to 105variables, such as bipartitioning, coloring, and satisfiability. Analysis of a suitable model predicts the only free parameter of the method in accordance with all experimental results.

New Stochastic Algorithm for Design Optimization

Abstract: A new stochastic algorithm for design optimization is introduced. Called generalized extremal optimization (GEO), it is intended to be used in complex optimization problems where traditional gradient-based methods may become inefficient, such as when applied to a nonconvex or disjoint design space, or when there are different kinds of design variables in it. The algorithm is easy to implement, does not make use of derivatives, and can be applied to unconstrained or constrained problems, and nonconvex or disjoint design spaces, in the presence of any combination of continuous, discrete, or integer variables. It is a global search metaheuristic, as are genetic algorithms (GAs) and simulated annealing (SA), but with the a priori advantage of having only one free parameter to adjust. The algorithm is presented in two implementations and its performance is assessed on a set of test functions. A simple application to the design of a glider airfoil is also presented. It is shown that the GEO algorithm is competitive in performance with the GA and SA and is an attractive tool to be used on applications in the aerospace field.

Solving multi objective optimization problems using particle swarm optimization

Abstract: An algorithm for solving multiobjective optimization problems is presented based on PSO through the improvement of the selection manner for global and individual extremum. The search for the Pareto optimal set of multiobjective optimization problems is performed. Numerical simulations show the effectiveness of the proposed algorithm.

Model Specification Searches Using Ant Colony Optimization Algorithms.

Abstract: Ant colony optimization is a recently proposed heuristic procedure inspired by the behavior of real ants. This article applies the procedure to model specification searches in structural equation modeling and reports the results. The results demonstrate the capabilities of ant colony optimization algorithms for conducting automated searches.

A genetic algorithm-based solution methodology for modular design

Abstract: Combinatorial optimization problems usually have a finite number of feasible solutions. However, the process of solving these types of problems can be a very long and tedious task. Moreover, the cost and time for getting accurate and acceptable results is usually quite large. As the complexity and size of these problems grow, the current methods for solving problems such as the scheduling problem or the classification problem have become obsolete, and the need for an efficient method that will ensure good solutions for these complicated problems has increased. This paper presents a genetic algorithm (GA)-based method used in the solution of a set of combinatorial optimization problems. A definition of a combinatorial optimization problem is first given. The definition is followed by an introduction to genetic algorithms and an explanation of their role in solving combinatorial optimization problems such as the traveling salesman problem. A heuristic GA is then developed and used as a tool for solving various combinatorial optimization problems such as the modular design problem. A modularity case study is used to test and measure the performance of the developed algorithm.

An ant colony optimization heuristic for solving maximum independent set problems

Abstract: In this paper, ant colony optimization heuristic is extended for solving maximum independent set (MIS) problems. MIS problems are quite different from the travelling salesman problems (TSP) etc., in which no concept of "path or order" exists in its solutions. Based on such characteristics, the ant colony optimization heuristic is modified in this paper in the following ways: (i) a new computation method for heuristic information is adapted; (ii) the pheromone update rule is augmented; (iii) a complement solution construction process is designed. The simulation shows that the proposed ant colony optimization heuristic is effective and efficient for MIS problems.

Inverse Design of Airfoils Based on a Novel Formulation of the Ant Colony Optimization Method

Abstract: In the past, Ant Colony Optimization (ACO) methods were used to solve combinatorial optimization problems such as the well-known Traveling Salesman Problem. The present article introduces an extension of the ACO method that is capable of solving optimization problems involving free variables with continuous search spaces. To this purpose, various notions, which are implicit in the ACO techniques, have been modified in order to account for design parameters that may vary continuously between lower and upper user-defined bounds. The intention was to create a tool for a particular class of engineering problems, namely the inverse design of isolated or turbomachinery blade airfoils and to demonstrate its effectiveness. Computational Fluid Dynamics codes are used for the evaluation of candidate solutions.

An adaptive ant colony system algorithm for continuous-space optimization problems.

Abstract: Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates. Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.

Ant-Tree: an ant colony optimization approach to the generalized minimum spanning tree problem

Abstract: The ant colony optimization is a meta-heuristic inspired by knowledge sharing amongst ants using pheromone, which serves as a kind of collective memory. Since the past few years, there have been several successful applications of this new approach for finding approximate solutions for computationally difficult problems in reasonable times. In this paper, we study the generalized minimum spanning tree problem that involves the design of a minimum weight connected network spanning at least one node out of every disjoint subset of the nodes in a graph. This problem has a wealth of pertinence to a wide range of applications in different areas. As the problem is known as computationally challenging, we adopt the ant colony optimization strategy and present a new solution method, called Ant-Tree, to develop approximate solutions. As an initial attempt, our study aims to provide an investigation of the ant colony optimization approach for coping with tree optimization problems. Through computational experiments,...

Efficient initial solution to extremal optimization algorithm for weighted MAXSAT problem

Abstract: Stochastic local search algorithms are proved to be one of the most effective approach for computing approximate solutions of hard combinatorial problems. Most of them are based on a typical randomness related to uniform distributions for generating initial solutions. Particularly, Extremal Optimization is a recent metaheuristic proposed for finding high quality solutions to hard optimization problems. In this paper, we introduce an algorithm based on another distribution, known as the Bose-Einstein distribution in quantum physics, which provides a new stochastic initialization scheme to an Extremal Optimization procedure. The resulting algorithm is proposed for the approximated solution to an instance of the weighted maximum satisfiability problem (MAXSAT). We examine its effectiveness by computational experiments on a large set of test instances and compare it with other existing meta-heuristic methods. Our results are remarkable and show that this approach is appropriate for this class of problems.

Generalized extremal optimization for solving complex optimal design problems

Abstract: Recently, Boettcher and Percus [1] proposed a new optimization method, called Extremal Optimization (EO), inspired by a simplified model of natural selection developed to show the emergence of Self-Organized Criticality (SOC) in ecosystems [2]. Although having been successfully applied to hard problems in combinatorial optimization, a drawback of the EO is that for each new optimization problem assessed, a new way to define the fitness of the design variables has to be created [2]. Moreover, to our knowledge it has been applied so far to combinatorial problems with no implementation to continuous functions. In order to make the EO easily applicable to a broad class of design optimization problems, Sousa and Ramos [3,4] have proposed a generalization of the EO that was named the Generalized Extremal Optimization (GEO) method. It is of easy implementation, does not make use of derivatives and can be applied to unconstrained or constrained problems, non-convex or disjoint design spaces, with any combination of continuous, discrete or integer variables. It is a global search meta-heuristic, as the Genetic Algorithm (GA) and the Simulated Annealing (SA), but with the a priori advantage of having only one free parameter to adjust. Having been already tested on a set of test functions, commonly used to assess the performance of stochastic algorithms, the GEO proved to be competitive to the GA and the SA, or variations of these algorithms [3,4]. The GEO method was devised to be applied to complex optimization problems, such as the optimal design of a heat pipe (HP). This problem has difficulties such as an objective function that presents design variables with strong non-linear interactions, subject to multiple constraints, being considered unsuitable to be solved by traditional gradient based optimization methods [5]. To illustrate the efficacy of the GEO on dealing with such kind of problems, we used it to optimize a HP for a space application with the goal of minimizing the HP's total mass, given a desirable heat transfer rate and boundary conditions on the condenser. The HP uses a mesh type wick and is made of Stainless Steel. A total of 18 constraints were taken into account, which included operational, dimensional and structural ones. Temperature dependent fluid properties were considered and the calculations were done for steady state conditions, with three fluids being considered as working fluids: ethanol, methanol and ammonia. Several runs were performed under different values of heat transfer

Hysteretic optimization for the traveling salesman problem

Abstract: Hysteretic optimization is a recently proposed heuristic optimization method inspired by the demagnetization of magnetic materials by an alternating external field of decreasing amplitude. We demonstrate that its extension to general optimization problems works reasonably well for the traveling salesman problem. We propose an improvement for the general scheme.

A multilevel ant-colony optimization algorithm for mesh partitioning

Abstract: In this paper we present a multilevel ant-colony optimization algo- rithm, which is a relatively new metaheuristic technique for solving combinato- rial optimization problems. We apply this algorithm to the mesh partitioning problem, which is an important problem with extensive applications in vari- ous real world engineering problems. The algorithm outperforms the classical k-METIS and Chaco algorithms. In addition, it is comparable even to the combined evolutionary/multilevel scheme used in JOSTLE algorithm.

Solving three-objective optimization problems using evolutionary dynamic weighted aggregation: results and analysis

Abstract: The main purposes of this paper is twofold. First, the evolutionary dynamic weighted aggregation (EDWA) [1] approaches are extended to the optimization of three-objective problems. Fig. 1 shows two example patterns for weight change. Through two three-objective test problems [2], the methods have shown to be effective. Theoretical analyses reveal that the success of the weighted aggregation based methods can largely be attributed to the following facts:

Proximate optimality principle based Tabu Search

Abstract: This paper proposes an algorithm-Multi Criteria Tabu Search coordinating the intensification and the diversification based on Proximate Optimality Principle (POP)-which has several advantages for solving combinatorial optimization problems. The proposed algorithm is applied to some traveling salesman problems which are typical combinatorial optimization problems in order to verify the performance of the proposed algorithm. The simulation results indicate that the proposed method has higher optimality than the conventional Tabu Search.

A Heuristic for Boolean Optimization Problems

Abstract: A heuristic method is proposed for the solution of a large class of binary optimization problems, which includes weighted versions of the set covering, graph stability, partitioning, maximum satisfiability, and numerous other problems. The reported substantial computational experiments amply demonstrate the efficiency of the proposed method.

Progresses in Ant Colony Optimization Algorithm with Applications

Abstract: The recent research results of Ant Colony Algorithm(ACA)and its applications for combinatorial optimization are overviewedAt first ant colonies foraging behavior and their communication system are briefly introducedThen the basic principle and the main characteristics of artificial ant colony algorithm are presentedThirdly the applications of ACA for the combinatorial optimization problems are described,such as TSP,QAP,JSP,VRP,GCP,SOP and the networks routing problemFinally the problems to be solved and the future works are discussed

The Ant Colony Optimization paradigm for combinatorial optimization

Abstract: Ant Colony Optimization is a paradigm for designing combinatorial optimization metaheuristic algorithms, which construct a solution on the basis of information provided both by some standard constructive heuristic and by previously obtained solutions. In this chapter, we present current results obtained by ACO algorithms on several hard combinatorial optimization problems. Furthermore, we describe in more detail a particular ACO algorithm, the ANTS metaheuristic, presenting its general structure and reporting results obtained on the quadratic and on the frequency assignment problems.

Combining extremal optimization with singular value decomposition for effective point matching

Abstract: Feature point matching is a key step for most problems in computer vision. It is an ill-posed problem and suffers from combinatorial complexity which becomes even more critical with the increase in data and the presence of outliers. The work covered in this paper describes a new framework to solve this problem in order to achieve robust registration of two feature point sets assumed to be available. This framework combines the use of extremal optimization heuristic with a clever startup routine which exploits some properties of singular value decomposition. The role of the latter is to produce an interesting matching configuration whereas the role of the former is to refine the initial matching by generating hypothetical matches and outliers using a far-from-equilibrium based stochastic rule. Experiments on a wide range of real data have shown the effectiveness of the proposed method and its ability to achieve reliable feature point matching.

Optimization and self-organized criticality in a magnetic system

Abstract: We propose a kind of Bak–Sneppen dynamics as a general optimization technique to treat magnetic systems. The resulting dynamics shows self-organized criticality with power-law scaling of the spatial and temporal correlations. An alternative method of the extremal optimization (EO) is also analyzed here. We provided a numerical confirmation that, for any possible value of its free parameter τ, the EO dynamics exhibits a non-critical behavior with an infinite spatial range and exponential decay of the avalanches. Using the chiral clock model as our test system, we compare the efficiency of the two dynamics with regard to their abilities to find the system's ground state.

Dynamic window search of ant colony optimization for complex multi-stage decision problems

Abstract: It is difficult to solve complex multi-stage decision problems with strong non-linearity, high dimensional or complex constraints. In contrast to the limitation of dynamic programming techniques and genetic algorithms, ant colony optimization algorithms represent complex constraints naturally and use the local heuristic information to guide search efficiently. In this paper, a dynamic window ant colony optimization algorithm is proposed for the large-scale complex multistage decision problems. In the algorithm a subset of the feasible decision set at each stage is selected by real-code genetic optimization and mapped to the nodes in one layer of a layered construction graph. Ants find routes through the layered construction graph, and each route corresponds to a solution candidate. Computation complexity analysis and simulation results demonstrate that, in comparison with basic ant colony optimization algorithms and genetic algorithms, the proposed algorithm greatly improves the computational efficiency.

A Comparison of Extremal Optimization with Flat-Histogram and Equal-Hit Dynamics for Finding Spin–Glass Ground States

Abstract: We compare the performance of extremal optimization (EO), flat-histogram and equal-hit algorithms for finding spin–glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of τ=1.15, EO outperforms other methods for small system sizes, but equal-hit algorithm is competitive to EO, particularly for large systems. Flat-histogram and equal-hit algorithms offer additional advantage that they can be used for equilibrium thermodynamic calculations. We also propose a method to turn EO into a useful algorithm for equilibrium calculations.

An accelerated ant colony algorithm for complex nonlinear system optimization

Abstract: Ant colony algorithms as a category of evolutionary computational intelligence can deal with complex optimization problems better than traditional optimization techniques An accelerated ant colony algorithm is proposed in this paper to tackle complex nonlinear system optimization problems by using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates Global optimal solutions can be obtained more efficiently through self-adjusting the path searching behaviors of the artificial ants The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes The simulation results convectively show that, in comparison with traditional optimization approaches and currently used basic ant colony algorithms, the proposed algorithm possess prominent capability in dealing with complex nonlinear system optimization problems with extremely complex solution structures and is applicable in solving complicated nonlinear optimization problems in practice such as network optimization and transportation problems

Optimization and self-organized criticality in a magnetic system

Abstract: We propose a kind of Bak-Sneppen dynamics as a general optimization technique to treat magnetic systems. The resulting dynamics shows self-organized criticality with power law scaling of the spatial and temporal correlations. An alternative method of the extremal optimization is also analyzed here. We provided a numerical confirmation that, for any possible value of its free parameter $\tau$, the extremal optimization dynamics exhibits a non-critical behavior with an infinite spatial range and exponential decay of the avalanches. Using the chiral clock model as our test system, we compare the efficiency of the two dynamics with regard to their abilities to find the system's ground state.

Self-organized criticality, optimization and biodiversity

Abstract: By driving to extinction species that are less or poorly adapted, the Darwinian evolutionary theory is intrinsically an optimization theory. We investigate two optimization algorithms with such evo...

Generalized ant colony optimization algorithm for reactive power optimization in power systems

Abstract: Generalized ant colony optimization (GACO) is a versatile optimization algorithm, which can be used to solve the discontinuous, nonconvex, and nonlinear constrained optimization problems. It was inspired by the behavior of real ant colonies, in particular, by their foraging behavior. It has the characteristics of positive feedback, distributed computation, and the use of constructive greedy heuristic. The application of GACO to reactive power optimization in electric power systems is investigated. The corresponding mathematical model is established. The solution algorithms are developed. And several refined methods are studied. The presented method has been tested in IEEE 6, 14, 30 bus systems, and the results show that these methods are feasible and efficient.