Abstract
Hyperheuristics rise as powerful techniques that get good results in less computational time than exact methods like dynamic programming or branch and bound. These exact methods promise the global best solution, but with a high computational time. In this matter, hyperheuristics do not promise the global best solution, but they promise a good solution in a lot less computational time. On the contrary, fuzzy logic provides the tools to model complex problems in a more natural way. With this in mind, this paper proposes a fuzzy hyperheuristic approach, which is a combination of a fuzzy inference system with a selection hyperheuristic. The fuzzy system needs the optimization of its fuzzy rules due to the lack of expert knowledge; indeed, traditional hyperheuristics also need an optimization of their rules. The fuzzy rules are optimized by genetic algorithms, and for the rules of the traditional methods, we use particle swarm optimization. The genetic algorithm will also reduce the number of fuzzy rules, in order to find the best minimal fuzzy rules, whereas traditional methods already use very few rules. Experimental results show the advantage of using our approach instead of a traditional selection hyperheuristic in 3200 instances of the 0/1 knapsack problem.
Highlights
Hyperheuristics are high-level methods created to solve problems by either selecting among different solvers [1] or by generating new ones based on the components of others [2]. ese solvers are usually referred to as low-level heuristics
We are including the coefficient of variation as a percentage in the standard deviation of the results, to see the differences between the fuzzy approach and the traditional selection hyperheuristics
Our proposed fuzzy hyperheuristic approach helps in getting better quality results when is included in the inner working of a selection hyperheuristic. e fuzzy approach gets better results with an increase in computational time, slower than a selection hyperheuristic with 4 rules, but at the same level than the others with 6 or 8 rules. e proposed approach gets better results in a controlled environment, and when it is applied to different instances, it helps to improve the quality of the results
Summary
Hyperheuristics are high-level methods created to solve problems by either selecting among different solvers [1] or by generating new ones based on the components of others [2]. ese solvers are usually referred to as low-level heuristics (or heuristics). Hyperheuristics are high-level methods created to solve problems by either selecting among different solvers [1] or by generating new ones based on the components of others [2]. Ese solvers are usually referred to as low-level heuristics (or heuristics). Since heuristics are approximation methods, they have the advantage of being fast to execute, but they cannot guarantee to find the optimal solution. En, hyperheuristics attempt to choose the best heuristic for each type of problem to improve the quality of the solutions. Burke et al [3] refer to hyperheuristics as “high-level heuristics,” and classify them into two broad categories: selection and generation. Selection hyperheuristics decide which is the best heuristic to apply in different states of the problem. One heuristic is likely to be better than the others for some specific instances
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