Cuckoo Search for Optimization and Computational Intelligence

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Introduction

In almost all applications in engineering and industry, we are always trying to optimize something -- whether to minimize the cost and energy consumption, or to maximize the profit, output, performance and efficiency (Yang, 2010b; Yang & Koziel, 2011). The optimal use of available resources of any sort requires a paradigm shift in scientific thinking, this is because most real-world applications have far more complicated factors and parameters to affect how the system behaves.

Optimization algorithms are the tools and techniques of achieving the optimality of the problem of interest. This search for optimality is complicated further by the fact that uncertainty almost always presents in the real-world systems. Therefore, we seek not only the optimal design but also robust design in engineering and industry. Optimal design solutions, which are not robust enough, are not practical in reality. Suboptimal solutions or good robust solutions are often the choice in such cases because they are more robust and less sensitive to the uncertainty in the material properties in the real systems.

Optimization problems can be formulated in many ways. For example, the commonly used method of least-squares is a special case of maximum-likelihood formulations. By far the most widely formulation is to write a nonlinear optimization problem as

(1) subject to the constraints (2) (3) where and are in general nonlinear functions. Here the design vectorcan be continuous, discrete or mixed in a d-dimensional space. The functions are called objectives or cost functions, and when , the optimization problem is multiobjective or multicriteria (Yang, 2008, 2010a; Yang, 2010b). It is possible to combine different objectives into a single objective, though multiobjective optimization can give far more information and options to the decision-makers with more insight into the problem. It is worth pointing out that here we write the problem as a minimization problem, it can also be written as a maximization problem by simply replacing by .

When all functions are nonlinear, we are dealing with nonlinear constrained problems. In some special cases when are linear, the problem becomes linear, and we can use the widely used linear programming techniques such as the simplex method. When some design variables can only take discrete values (often integers), while other variables are real continuous, the problem is of mixed type, which is often difficult to solve, especially for large-scale optimization problems. A very special class of optimization is the convex optimization, which has guaranteed global optimality. Any optimal solution is also the global optimum, and most importantly, there are efficient algorithms of polynomial time to solve such problems.