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A local-search heuristic for finding high-quality solutions for many hard optimization problems is explored. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of selforganized criticality, a concept introduced to describe emergent complexity in physical systems. This method, called extremal 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 emerge dynamically. These enable the search to 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 as simulated annealing. This method is very general 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 10 5 variables, such as bipartitioning, coloring, and spin glasses. Analysis of a model problem predicts the only free parameter of the method in accordance with all experimental results. © 2003 Wiley Periodicals, Inc.* Key Words: extremal optimization; criticality; simulated annealing; punctuated equilibrium Many natural systems have, without any centralized

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 of self-organized criticality, a concept introduced to describe emergent complexity in physical systems. This method, called extremal 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 as simulated annealing. It may be but one example of applying new insights into non-equilibrium phenomena systematically 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 10 5 variables, 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.

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 some uniform distributions for generating initial solutions. Particularly, Extremal Optimization is a recent meta-heuristic 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 (MAX SAT). 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. 1

We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by "self-organized criticality", a concept introduced to describe emergent complexity in physical systems. In contrast to genetic algorithms, which operate on an entire "gene-pool" of possible solutions, extremal optimization successively replaces extremely undesirable elements of a single sub-optimal solution with new, random ones. Large fluctuations, or "avalanches", ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements heuristics inspired by equilibrium statistical physics, such as simulated annealing. With only one adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Phase transitions are found in many combinatorial optimization problems, and have been co...

We describe the recently introduced extremal optimization algorithm and apply it to target detection and association problems arising in pre-processing for multi-target tracking. Extremal optimization is based on the concept of self-organized criticality, and has been used successfully for a wide variety of hard combinatorial optimization problems. It is an approximate local search algorithm that achieves its success by utilizing avalanches of local changes that allow it to explore a large part of the search space. It is somewhat similar to genetic algorithms, but works by selecting and changing bad chromosomes of a bit-representation of a candidate solution. The algorithm is based on processes of selforganization found in nature. The simplest version of it has no free parameters, while the most widely used and most efficient version has one parameter. For extreme values of this parameter, the methods reduces to hill-climbing and random walk searches, respectively. Here we consider the problem of pre-processing for multiple target tracking when the number of sensor reports received is very large and arrives in large bursts. In this case, it is sometimes necessary to pre-process reports before sending them to tracking modules in the fusion system. The pre-processing step associates reports to known tracks (or initializes new tracks for reports on objects that have not been seen before). It could also be used as a pre-process step before clustering, e.g., in order to test how many clusters to use. The pre-processing is done by solving an approximate version of the original problem. In this approximation, not all pair-wise conflicts are calculated. The approximation relies on knowing how many such pair-wise conflicts that are necessary to compute. To determine this, results on phase-transitions occurring when coloring (or clustering) large random instances of a particular graph ensemble are used. 1.

Abstract: The MAXimum propositional SATisfiability problem (MAXSAT) is a well known NP-hard optimization problem with many theoretical and practical applications in artificial intelligence and mathematical logic. Heuristic local search algorithms are widely recognized as the most effective approaches used to solve them. However, their performance depends both on their complexity and their tuning parameters which are controlled experimentally and remain a difficult task. Extremal Optimization (EO) is one of the simplest heuristic methods with only one free parameter, which has proved competitive with the more elaborate general-purpose method on graph partitioning and coloring. It is inspired by the dynamics of physical systems with emergent complexity and their ability to self-organize to reach an optimal adaptation state. In this paper, we propose an extremal optimization procedure for MAXSAT and consider its effectiveness by computational experiments on a benchmark of random instances. Comparative tests showed that this procedure improves significantly previous results obtained on the same benchmark with other modern local search methods like WSAT, simulated annealing and Tabu Search (TS).

Abstract—Pairwise testing, which requires that every combination of valid values of each pair of system factors be covered by at lease one test case, plays an important role in software testing since many faults are caused by unexpected 2-way interactions among system factors. Although meta-heuristic strategies like simulated annealing can generally discover smaller pairwise test suite, they may cost more time to perform search, compared with greedy algorithms. We propose a new method, improved Extremal Optimization (EO) based on the Bak-Sneppen (BS) model of biological evolution, for constructing pairwise test suites and define fitness function according to the requirement of improved EO. Experimental results show that improved EO gives similar size of resulting pairwise test suite and yields an 85 % reduction in solution time over SA.

(Under the direction of Walter D. Potter) Extremal Optimization (EO) is a relatively new single search-point optimization heuristic based on self-organized criticality. Unlike many traditional optimization heuristics, EO focuses on removing poor characteristics of a solution instead of preserving the good ones. This thesis will examine the physical and biological inspirations behind EO, and will explore the application of EO on four unique search problems in planning, diagnosis, path-finding, and scheduling. Some of the pros and cons of EO will be discussed, and it will be shown that, in many cases, EO can perform as well as or better than many standard search methods. Finally, this thesis will conclude with a survey of the state of the art of EO, mentioning several variations of the algorithm and the benefits of using such modifications. Index words: Extremal optimization, Snake in the box, Forest planning problem,

Nowadays, various imitations of natural processes are used to solve challenging optimization problems faster and more accurately. Spin glass based optimization, specifically, has shown strong local search capability and parallel processing. However, generally, spin glasses have a low rate of convergence, since they use Monte Carlo simulation techniques such as simulated annealing (SA). Here, we investigate a new hybrid local search method based on spin glass for using adaptive distributed system capability, extremal optimization (EO) for using evolutionary locally search algorithm and SA for escaping from local optimum states. As shown in this paper, this strategy can lead to faster rate of convergence and improved performance than conventional SA and EO algorithm. The resulting are then used to solve the portfolio selection problem that is a non-deterministic polynomial complete (NPC) problem. This is confirmed by test results of five of the world's major stock markets, reliability test and phase transition diagram.