“Exploration and exploitation are the two cornerstones of problem solving by search.” For more than a decade, Eiben and Schippers' advocacy for balancing between these two antagonistic cornerstones still greatly influences the research directions of evolutionary algorithms (EAs) [1998]. This article revisits nearly 100 existing works and surveys how such works have answered the advocacy. The article introduces a fresh treatment that classifies and discusses existing work within three rational aspects: (1) what and how EA components contribute to exploration and exploitation; (2) when and how exploration and exploitation are controlled; and (3) how balance between exploration and exploitation is achieved. With a more comprehensive and systematic understanding of exploration and exploitation, more research in this direction may be motivated and refined.

Exploration and exploitation in evolutionary algorithms: A survey

Every search algorithm needs to address the exploration and exploitation of a search space. Exploration is the process of visiting entirely new regions of a search space, whilst exploitation is the process of visiting those regions of a search space within the neighborhood of previously visited points. In order to be successful a search algorithm needs to establish a good ratio between exploration and exploitation. In this respect Evolutionary Algorithms (EAs) [De Jong 2002; Eiben and Smith 2008], such as Genetic Algorithms (GAs) [Michalewicz 1996; Goldberg 2008], Evolutionary Strategies (ES) [Back 1996], Evolutionary Programming (EP) [Fogel 1999], and Genetic Programming (GP) [Koza 1992], to name the more well-known instances, are no exception. Herrera and Lozano [1996] emphasized this by saying “The genetic algorithm behaviour is determined by the exploitation and exploration relationship kept throughout the run.” Many researchers believe that EAs are effective because of their good ratio between exploration and exploitation. Michalewicz [1996] stated that “Genetic Algorithms are a

A Exploration and Exploitation in Evolutionary Algorithms: A Survey

A survey for the quadratic assignment problem

We encounter optimization problems in our daily lives and in various research domains. Some of them are so hard that we can, at best, approximate the best solutions with (meta-) heuristic methods. However, the huge number of optimization problems and the small number of generally acknowledged methods mean that more metaheuristics are needed to fill the gap. We propose a new metaheuristic, called chemical reaction optimization (CRO), to solve optimization problems. It mimics the interactions of molecules in a chemical reaction to reach a low energy stable state. We tested the performance of CRO with three nondeterministic polynomial-time hard combinatorial optimization problems. Two of them were traditional benchmark problems and the other was a real-world problem. Simulation results showed that CRO is very competitive with the few existing successful metaheuristics, having outperformed them in some cases, and CRO achieved the best performance in the real-world problem. Moreover, with the No-Free-Lunch theorem, CRO must have equal performance as the others on average, but it can outperform all other metaheuristics when matched to the right problem type. Therefore, it provides a new approach for solving optimization problems. CRO may potentially solve those problems which may not be solvable with the few generally acknowledged approaches.

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Chemical-Reaction-Inspired Metaheuristic for Optimization

The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. Consider the problem of allocating a set of facilities to a set of locations, with the cost being a function of the distance and flow between the facilities, plus costs associated with a facility being placed at a certain location. The objective is to assign each facility to a location such that the total cost is minimized. Specifically, we are given three n x n input matrices with real elements F = (f ij ), D = (d kl ) and B = (b ik ), where f ij is the flow between the facility i and facility j, d kl is the distance between the location k and location l, and b ik is the cost of placing facility i at location k. The Koopmans-Beckmann version of the QAP can be formulated as follows: Let n be the number of facilities and locations and denote by N the set N = {1, 2,..., n}.

Quadratic Assignment Problem.

Tabu search approach based algorithms are among the widest applied to various combinatorial optimization problems. In this paper, we propose a new version of the tabu search algorithm for the well-known problem, the quadratic assignment problem (QAP). One of the most important features of our tabu search implementation is an efficient use of mutations applied to the best solutions found so far. We tested this approach on a number of instances from the library of the QAP instances--QAPLIB. The results obtained from the experiments show that the proposed algorithm belongs to the most efficient heuristics for the QAP. The high efficiency of this algorithm is also demonstrated by the fact that the new best known solutions were found for several QAP instances.

A tabu search algorithm for the quadratic assignment problem

Genetic algorithms (GAs) have been proven to be among the most powerful intelligent techniques in various areas of the computer science, including difficult optimization problems. In this paper, we propose an improved hybrid genetic algorithm (IHGA). It uses a robust local improvement procedure (a limited iterated tabu search (LITS)) as well as an effective restart (diversification) mechanism that is based on so-called “shift mutations”. IHGA has been applied to the well-known combinatorial optimization problem, the quadratic assignment problem (QAP). The results obtained from the numerous experiments on different QAP instances from the instances library QAPLIB show that the proposed algorithm appears to be superior to other modem heuristic approaches that are among the best algorithms for the QAP. The high efficiency of our algorithm is also corroborated by the fact that the new, recordbreaking solutions were obtained for a number of large real-life instances.

An Improved Hybrid Genetic Algorithm: New Results for the Quadratic Assignment Problem

The quadratic assignment problem (QAP) is one of the well-known combinatorial optimization problems and is known for its various applications. In this paper, we propose a modified simulated annealing algorithm for the QAP - M-SA-QAP. The novelty of the proposed algorithm is an advanced formula of calculation of the initial and final temperatures, as well as an original cooling schedule with oscillation, i.e., periodical decreasing and increasing of the temperature. In addition, in order to improve the results obtained, the simulated annealing algorithm is combined with a tabu search approach based algorithm. We tested our algorithm on a number of instances from the library of the QAP instances - QAPLIB. The results obtained from the experiments show that the proposed algorithm appears to be superior to earlier versions of the simulated annealing for the QAP. The power of M-SA-QAP is also corroborated by the fact that the new best known solution was found for the one of the largest QAP instances - THO150.

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A Modified Simulated Annealing Algorithm for the Quadratic Assignment Problem

Genetic algorithms (GAs) are among the widely used in various areas of computer science, including optimization problems In this paper, we propose a GA hybridized with so-called ruin and recreate (R and R) procedure We have applied this new hybrid strategy to the well-known combinatorial optimization problem, the quadratic assignment problem (QAP) The results obtained from the experiments on different QAP instances show that the proposed algorithm belongs to the best heuristics for the QAP The power of this algorithm is also demonstrated by the fact that the new best known solutions were found for several QAP instances

Alfonsas Misevičius

Papers

A tabu search algorithm for the quadratic assignment problem

An Improved Hybrid Genetic Algorithm: New Results for the Quadratic Assignment Problem

A Modified Simulated Annealing Algorithm for the Quadratic Assignment Problem

Genetic algorithm hybridized with ruin and recreate procedure: application to the quadratic assignment problem

Enhancing the performance of hybrid genetic algorithms by differential improvement