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Extremal optimization

About: Extremal optimization is a research topic. Over the lifetime, 1168 publications have been published within this topic receiving 104943 citations.


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01 Jan 2004
TL;DR: Almost every combinatorial optimization problem has since been either proved to be polynomial-time solvable or NP-complete — and none of the problems have been proving to be both.
Abstract: Combinatorial optimization searches for an optimum object in a finite collection of objects. Typically, the collection has a concise representation (like a graph), while the number of objects is huge — more precisely, grows exponentially in the size of the representation (like all matchings or all Hamiltonian circuits). So scanning all objects one by one and selecting the best one is not an option. More efficient methods should be found. In the 1960s, Edmonds advocated the idea to call a method efficient if its running time is bounded by a polynomial in the size of the representation. Since then, this criterion has won broad acceptance, also because Edmonds found polynomial-time algorithms for several important combinatorial optimization problems (like the matching problem). The class of polynomial-time solvable problems is denoted by P. Further relief in the landscape of combinatorial optimization was discovered around 1970 when Cook and Karp found out that several other prominent combinatorial optimization problems (including the traveling salesman problem) are the hardest in a large natural class of problems, the class NP. The class NP includes most combinatorial optimization problems. Any problem in NP can be reduced to such ‘NP-complete’ problems. All NP-complete problems are equivalent in the sense that the polynomial-time solvability of one of them implies the same for all of them. Almost every combinatorial optimization problem has since been either proved to be polynomial-time solvable or NP-complete — and none of the problems have been proved to be both. This spotlights the big mystery: are the two properties disjoint (equivalently, P6=NP), or do they coincide (P=NP)? Polyhedral and linear programming techniques have turned out to be essential in solving combinatorial optimization problems and studying their complexity. Often a polynomial-time algorithm yields, as a by-product, a description (in terms of inequalities) of an associated polyhedron. Conversely, an appropriate description of the polyhedron often implies the polynomial-time solvability of the

3 citations

Proceedings ArticleDOI
19 Mar 2015
TL;DR: Two different kinds of Ant Colony algorithms named as Ant System and the improved version of Ant system known as Max-Min Ant System performed in MATLAB to solve travelling Salesman Problem and their respective results are shown by using graphical implementation.
Abstract: Travelling Salesman Problem is well — known and extensively studied problem which plays an important role in combinatorial optimization and in context of ACO. Ant Colony Optimization is heuristic Algorithm which was initially applied on TSP and is an advance technique applied on various other optimization problems. In the research we study two different kinds of Ant Colony algorithms named as Ant System and the improved version of Ant system known as Max-Min Ant System performed in MATLAB to solve travelling Salesman Problem and their respective results are shown by using graphical implementation. In this paper both systems are analyzed by solving the same example of TSP and depict which system solve the problem efficiently with respect to cost and time.

3 citations

Posted Content
TL;DR: This paper reviews nature-inspired metaheuristics, then it introduces a framework named Competitive Ant Colony Optimization inspired by the chemical communications among insects, and a case study is presented to investigate the proposed framework for large-scale global optimization.
Abstract: Large-scale problems are nonlinear problems that need metaheuristics, or global optimization algorithms. This paper reviews nature-inspired metaheuristics, then it introduces a framework named Competitive Ant Colony Optimization inspired by the chemical communications among insects. Then a case study is presented to investigate the proposed framework for large-scale global optimization.

3 citations

Proceedings ArticleDOI
13 Dec 2012
TL;DR: A way to improve DE is presented by combining DE with DSM DE and the application of the new method to the problem of finding the optimum path in the physical travelling salesman problem.
Abstract: Differential Evolution (DE) is a simple and efficient evolutionary algorithm for optimization problems over continuous space. A variant of DE is the Down-hill Simplex method based on Differential Evolution (DSM DE) which has the advantage of converging faster than DE. However, the problem with DSM DE is that it doesn't guarantee to converge to a global optimum. In this paper, we present a way to improve DE by combining DE with DSM DE and the application of the new method to the problem of finding the optimum path in the physical travelling salesman problem.

3 citations

13 Jun 2013
TL;DR: In this article, the authors proposed an enhanced ACS algorithm that integrates a new heuristic function that can reflect the new information discovered by the ants to generate shorter tours within reasonable times by using accumulated values from pheromones and heuristics.
Abstract: Ant Colony System (ACS) is one of the best algorithms to solve NP-hard problems. However, ACS suffers from pheromone stagnation problem when all ants converge quickly on one sub-optimal solution. ACS algorithm utilizes the value between nodes as heuristic values to calculate the probability of choosing the next node. However, one part of the algorithm, called heuristic function, is not updated at any time throughout the process to reflect the new information discovered by the ants. This paper proposes an Enhanced Ant Colony System algorithm for solving the Travelling Salesman Problem. The enhanced algorithm is able to generate shorter tours within reasonable times by using accumulated values from pheromones and heuristics. The proposed enhanced ACS algorithm integrates a new heuristic function that can reflect the new information discovered by the ants. Experiments conducted have used eight data sets from TSPLIB with different numbers of cities. The proposed algorithm shows promising results when compared to classical ACS in term of best, average, and standard deviation of the best tour length.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
202213
20217
20209
201922
201815