Extremal optimization

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

Population-Based Extremal Optimization with Adaptive Lévy Mutation for Constrained Optimization

Abstract: Recently, a local-search heuristic algorithm called Extremal Optimization (EO) has been successfully applied in some combinatorial optimization problems. This paper presents the studies on the applications of EO to numerical constrained optimization problems with a set of popular benchmark problems. To enhance and improve the search performance and efficiency of EO, we developed a novel EO strategy with population based search. The newly developed EO algorithm is named population-based EO (PEO). Additionally, we adopted the adaptive Levy mutation, which is more likely to generate an offspring that is farther away from its parent than the commonly employed Gaussian mutation. Compared with three state-of-the-art stochastic search methods with six popular bench-mark problems, it has been shown that our approach is a good alternative to deal with the numerical constrained optimization problems.

Optimization of aircraft structural components by using nature-inspired algorithms and multi-fidelity approximations

Abstract: In this work, a flat pressure bulkhead reinforced by an array of beams is designed using a suite of heuristic optimization methods (Ant Colony Optimization, Genetic Algorithms, Particle Swarm Optimization and LifeCycle Optimization), and the Nelder-Mead simplex direct search method. The compromise between numerical performance and computational cost is addressed, calling for inexpensive, yet accurate analysis procedures. At this point, variable fidelity is proposed as a tradeoff solution. The difference between the low-fidelity and high-fidelity models at several points is used to fit a surrogate that corrects the low-fidelity model at other points. This allows faster linear analyses during the optimization; whilst a reduced set of expensive non-linear analyses are run "off-line," enhancing the linear results according to the physics of the structure. Numerical results report the success of the proposed methodology when applied to aircraft structural components. The main conclusions of the work are (i) the variable fidelity approach enabled the use of intensive computing heuristic optimization techniques; and (ii) this framework succeeded in exploring the design space, providing good initial designs for classical optimization techniques. The final design is obtained when validating the candidate solutions issued from both heuristic and classical optimization. Then, the best design can be chosen by direct comparison of the high-fidelity responses.

Reducing Epistasis in Combinatorial Problems by Expansive Coding

Abstract: This paper describes a new technique for tackling highly epistatic combinatorial optimization problems. Rather than having a simple representation, simple operators, a simple fitness function, but a highly epistatic search space, this technique is intended to spread the problem’s complexity more evenly. Using our new technique, known as expansive coding, the representation, operators and fitness function become more complicated, but the search space becomes less epistatic, and therefore easier for a GA to tackle. In effect, the combinatorial task is changed to a function optimization one. We demonstrate how this technique can be applied in the field of arithmetic algorithm design/electronic circuit simplification. In the design of a multiplier for quaternion numbers, consistently good results are obtained.

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.

Improved Ant Colony Optimization for the Traveling Salesman Problem

Abstract: The traveling salesman problem (TSP) in operations research is a classical problem in discrete or combinatorial optimization. It is a prominent illustration of a class of problems in computational complexity theory which are classified as NP-hard. Ant colony optimization inspired by co-operative food retrieval have been widely applied unexpectedly successful in the combinatorial optimization. This paper presents an improved ant colony optimization algorithm for traveling salesman problem, which adopts a new probability selection mechanism by using Held-Karp lower bound to determine the trade-off between the influence of the heuristic information and the pheromone trail. The experiments showed that it can stably generate better solution for the traveling salesman problem than rank-based ant system and max-min ant colony optimization algorithm.