Flower pollination algorithm is a new nature-inspired algorithm, based on the characteristics of flowering plants. In this paper, a new method is developed based on the flower pollination algorithm combined with chaos theory (IFPCH) to solve definite integral. The definite integral has wide ranging applications in operation research, computer science, mathematics, mechanics, physics, and civil and mechanical engineering. Definite integral has always been useful in biostatistics to evaluate distribution functions and other quantities. Numerical simulation results show that the algorithm offers an effective way to calculate numerical value of definite integrals, and it has a high convergence rate, high accuracy and robustness.

Bat Algorithm is a recently-developed method in the field of computational intelligence. In this paper is presented an improved version of a Bat Meta-heuristic Algorithm, (IBACH), for solving integer programming problems. The proposed algorithm uses chaotic behaviour to generate a candidate solution in behaviors similar to acoustic monophony. Numerical results show that the IBACH is able to obtain the optimal results in comparison to traditional methods (branch and bound), particle swarm optimization algorithm (PSO), standard Bat algorithm and other harmony search algorithms. However, the benefits of this proposed algorithm is in its ability to obtain the optimal solution within less computation, which save time in comparison with the branch and bound algorithm (exact solution method).

In this paper, an Improved Firefly Algorithm with Chaos (IFCH) is presented for solving definite integral. The IFCH satisfies the question of parallel calculating numerical integration in engineering and those segmentation points are adaptive. Several numerical simulation results show that the algorithm offers an efficient way to calculate the numerical value of definite integrals, and has a high convergence rate, high accuracy and robustness.

This paper presents an improved version of a harmony meta-heuristic algorithm, (IHSCH), for solving the linear assignment problem. The proposed algorithm uses chaotic behavior to generation a candidate solution in a behavior similar to acoustic monophony. Numerical results show that the IHSCH is able to obtain the optimal results in comparison with traditional methods (the Hungarian method). However, the benefit of the proposed algorithm is its ability to obtain the optimal solution within less computation in comparison with the Hungarian method.

Flower Pollination algorithm (FPA) is a new nature-inspired algorithm, based on the characteristics of flowering plants.In this paper, a new hybrid optimization method called improved Flower Pollination Algorithm with Chaotic Harmony Search (FPCHS) is proposed. The method combines the standard Flower Pollination algorithm (FPA) with the chaotic Harmony Search (HS) algorithm to improve the searching accuracy. The FPCHS algorithm is used to solve Sudoku puzzles. Numerical results show that the FPCHS is accurate and efficient in comparison with standard Harmony Search, (HS) algorithm.