A hyperchaotic map with distance-increasing pairs of coexisting attractors and its application in the pelican optimization algorithm

Abstract

When both an absolute value function and a cosine function are introduced for chaotic sequence generation, coexisting attractors with different polarities and locations could be extracted by the offset boosting of the initial condition, and thus a hyperchaotic map with distance-increasing coexisting attractors is constructed. It is found that this map has two controllers for rescaling the oscillation totally and partially. The digital circuit implementation shows good consistency with numerical simulation. Moreover, the parameter adaptation in the basic Pelican Optimization Algorithm (POA) is improved by the above-mentioned hyperchaotic map. Correspondingly, the Hyperchaotic Pelican Optimization Algorithm (HCPOA) is constructed, where the hyperchaotic sequences are employed as the sampling pool when random numbers are required in the basic POA. Furthermore, the impact of chaos regulation on the performance of HCPOA is investigated, and the indicators of HCPOA are analyzed by employing five benchmark functions, where the single attractor shows better performance than the double-cavity attractor. The methods of HCPOA proposed in this paper bring the chance to improve the quality of solutions and the ability to escape local optima.