“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 (TS) algorithms have been proven to be extremely efficient for solving combinatorial optimization problems. In this paper, we discuss new variants of the tabu search for the well-known combinatorial problem, the quadratic assignment problem (QAP). In particular, a so-called stagnation-protected tabu search (SPTS) strategy is proposed. The goal is to fight against the chaotic behaviour and stagnation phenomenon, especially at long runs of TS. SPTS seems to be quite useful for the unstructured (random) quadratic assignment problems. These problems, which resemble a "needle-in-a-haystack" problem, are hardly solvable by the ordinary heuristic algorithms and still remain a challenge for the QAP community. The results obtained from the experiments with SPTS on the unstructured QAPs taken from the QAP library QAPLIB demonstrate that this new strategy is superior to other tabu search algorithms.

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Stagnation-protected tabu search variants for unstructured quadratic assignment problems

One of the most important improvements for the Traveling Salesman Problem (TSP) heuristics is usage of limited size candidate sets, also known as candidate lists (CLs). CLs help to effectively reduce the search space and appropriately sorted biases the search in a more gainful direction. Besides the best known nearest-neighbor, quadrant, Delaunay or leading Helsgaun’s alpha CLs, other effective CLs can be constructed. We revise tour merging technique proposed by Applegate et al. and using multi-random-start procedure with incorporated fast 3-opt and simplified Lin-Kernighan-Helsgaun (LKH) algorithm modifications, generate tour union CLs and analyze them by comparing with the most common alternatives. In addition, we propose a criteria indicating when merging procedure should be terminated to form high quality CLs. Finally, we show a high potential of such CLs by performing the experiments with our modified LKH variant.

Generating High Quality Candidate Sets by Tour Merging for the Traveling Salesman Problem

The purpose of this paper is to compare the efficiency of three different evolutionary programming techniques – Genetic Programming, Grammatical Evolution and Gene Expression Programming. These algorithms were applied to different type test problems with the same set of parameters. The results of the experiments and some insights on similar experiments of the other authors are provided.

Comparison of Genetic Programming, Grammatical Evolution and Gene Expression Programming Techniques

In this paper we compare two new binary linear formulations to a standard quadratic binary program for the gray pattern problem and solved all three by the Gurobi solver. One formulation performed significantly better and obtained seven optimal solutions that were not proven optimal before. It is interesting that the formulation that performed best is based on significantly more variables and constraints.

Finding optimal solutions to several gray pattern instances

In this paper, we investigate some modified local search (LS) heuristics for the solution of symmetric traveling salesman problems (TSPs). These modifications are mainly due to the use of extended neighborhood structures. In addition, we are concerned with several new sets of the moves (transitions of solutions) based on the extended configurations of edge exchanges. We are also examining the performance of these extensions being used in an iterated local search (ILS) paradigm. The results from the experiments with the benchmark TSP instances from the TSP library (TSPLIB) demonstrate that the introduced improvements enable to seek solutions of higher quality without substantially increasing computational complexity. DOI: http://dx.doi.org/10.5755/j01.itc.42.3.1301

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Alfonsas Misevičius

Papers

Stagnation-protected tabu search variants for unstructured quadratic assignment problems

Generating High Quality Candidate Sets by Tour Merging for the Traveling Salesman Problem

Comparison of Genetic Programming, Grammatical Evolution and Gene Expression Programming Techniques

Finding optimal solutions to several gray pattern instances

Modified Local Search Heuristics for the Symmetric Traveling Salesman Problem