Modified and Ensemble Intelligent Water Drop Algorithms and Their Applications

Abstract

1.1 Introduction Optimization is a process that concerns with finding the best solution of a given problem from among the possible solutions within an affordable time and cost (Weise et al., 2009). The first step in the optimization process is formulating the optimization problem through an objective function and a set of constrains that encompass the problem search space (ie, regions of feasible solutions). Every alternative (ie, solution) is represented by a set of decision variables. Each decision variable has a domain, which is a representation of the set of all possible values that the decision variable can take. The second step in optimization starts by utilizing an optimization method (ie, search method) to find the best candidate solutions. Candidate solution has a configuration of decision variables that satisfies the set of problem constrains, and that maximizes or minimizes the objective function (Boussaid et al., 2013). It converges to the optimal solution (ie, local or global optimal solution) by reaching the optimal values of the decision variables. Figure 1.1 depicts a 3D-fitness landscape of an optimization problem. It shows the concept of the local and global optima, where the local optimal solution is not necessarily the same as the global one (Weise et al., 2009). Optimization can be applied to many real-world problems in various domains. As an example, mathematicians apply optimization methods to identify the best outcome pertaining to some mathematical functions within a range of variables (Vesterstrom and Thomsen, 2004). In the presence of conflicting criteria, engineers use optimization methods to