# Continuous fitness landscape analysis using a chaos-based random walk algorithm

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## Abstract

Extensive research on heuristic algorithms has proved their potential in solving complex optimization problems. However, it is not easy to choose the best heuristic technique for solving a particular problem. Fitness landscape analysis is used for understanding the problem characteristics based on which the best-suited algorithm for the problem can be chosen. Compared to the literature on discrete search spaces, only a few significant works have been undertaken on landscape analysis in continuous search spaces. Random walk (RW) algorithm has been used for generating sample points in the search space, and fitness landscape is created based on the relative fitness of the neighboring sample points. This paper proposes a chaos-based random walk algorithm, called as the chaotic random walk (CRW), applied in continuous search space to generate the landscape structure for a problem. The chaotic map is used to generate the chaotic pseudorandom numbers for determining variable scaled step size and direction of the proposed RW algorithm. Histogram analysis demonstrates better coverage of search space by the CRW algorithm compared to the simple and progressive random walk algorithms. In addition, we test the efficiency of the proposed method by quantifying the ruggedness and deception of a problem using entropy and fitness distance correlation measures. Experiments are conducted on the IEEE Congers on Evolutionary Computing 2013 benchmark functions in continuous search space having different levels of complexity. Extensive experiments indicate the capability for generating landscape structure on the continuous search space and efficiency of the proposed method to investigate the structural features of fitness landscapes.

## Keywords

Random walk algorithm Fitness landscape analysis Continuous random walk algorithm Chaotic map Entropy measure Fitness distance correlation## Notes

### Compliance with ethical standards

#### Conflict of interest

No potential conflict of interest to be declared.

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