Extremal optimization

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

Guiding constructive search with statistical instance-base learning

Abstract: Several real world applications involve solving combinatorial optimization problems. Commonly, existing heuristic approaches are designed to address specific difficulties of the underlying problem and are applicable only within its framework. We suspect, however, that search spaces of combinatorial problems are rich in intuitive statistical and numerical information, which could be exploited heuristically in a generic manner, towards achievement of optimized solutions. Our work presents such a heuristic methodology, which can be adequately configured for several types of optimization problems. Experimental results are discussed, concerning two widely used problem models, namely the Set Partitioning and the Kanpsack problems. It is shown that, by gathering statistical information upon previously found solutions to the problems, the heuristic is able to incrementally adapt its behaviour and reach high quality solutions, exceeding the ones obtained by commonly used greedy heuristics.

A Comparison of Extremal Optimization, Differential Evolution and Particle Swarm Optimization Methods for Well Placement Design in Groundwater Management

Abstract: When designing a well field for efficiently extracting groundwater or petroleum, it is common for designers to rely on computational optimization methods to determine the optimal placement of wells. The goal of these methods is to find a well-field solution that maximizes the value of a defined objective function, and to do so while utilizing the least amount of computational effort. To achieve this, researchers have developed algorithms based on a wide range of heuristics. Within groundwater management, popular methods include particle swarm optimization (PSO) and genetic algorithms such as differential evolution (DE). This study seeks to investigate a recently developed method called Extremal Optimization for Well Placement Problems (EO-WPP), and to compare its performance with established methods like PSO and DE. EO-WPP is an optimization method based on the extremal optimization (EO) algorithm. EO optimizes by iteratively identifying and modifying the least effective components of a solution. By following this heuristic, the EO algorithm has the potential to quickly find optimal solutions while requiring minimal computational effort. To test this, the performance of DE, PSO and EO-WPP was compared on four benchmark problems. Two of these are the Rastrigin and the Rosenbrock benchmark functions. These functions were used because of their quick evaluation and their popularity in optimization literature. The third benchmark is a synthetic groundwater model, built to test the methods under the context of groundwater management. The final benchmark is a field problem using the Aberdeen groundwater model in South Dakota. The results reveal that EO-WPP was able to outperform DE and PSO on all tested benchmarks. EO-WPP is an effective and efficient optimization tool for well placement design in groundwater management.

An opposition-based self-adaptive differential evolution with decomposition for solving the multiobjective multiple salesman problem

Abstract: The multiple Traveling Salesman Problem (mTSP) is a complex combinatorial optimization problem, which is a generalization of the well-known Traveling Salesman Problem (TSP), where one or more salesmen can be used in the solution. In this paper, we propose a novel differential evolution algorithm called D-OSADE to solve the Multi-objective Multiple Salesman Problem. For the algorithm, an opposition-based self-adaptive differential evolution variant is incorporated into the decomposition-based framework, and then hybridized with the multipoint evolutionary gradient search (EGS) as a form of local search to enhance the search behaviour. The proposed algorithm is used to solve a multi-objective mTSP with different number of objectives, salesmen and problem sizes. Through the experimental results that are presented by employing the Inverted Generational Distance (IGD) performance indicator, the effectiveness and efficiency of the proposed algorithm can be observed and is seen to be able to achieve competitive performance when benchmarked against several state-of-the-art multi-objective evolutionary algorithms in this study.

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.

Improved Ant Colony Optimization with Particle Swarm Optimization Operator Solving Continuous Optimization Problems

Abstract: Ant Colony Optimization (ACO) has the disadvantages such as easily relapsing into local optima and. Aimed at improving this problem existed in ACO, several new betterments are proposed and evaluated. In particular, pheromone mutation and Particle Swarm Optimization operator were inducted. Then an improved Ant Colony Optimization with Particle Swarm Optimization operator was put forward. It was tested by a set of benchmark continuous function optimization problems. And the results of the examples show that it can not easily run into the local optimum and can converge at the global optimum.