ABSTRACT
If y = f(X), where X represents a set of variables (x1, x2, x3, …xn), a search for a set of X for which y is optimum (maximum or minimum as per requirement) is called an optimisation problem. Many real-world and theoretical problems can be placed in this framework. The variable X has upper and lower boundaries for all of its members (called constraints in the case of conventional optimisation) and the ‘feasible solutions’ need to be searched without violating these limits. All possible y generated using the X within the limits comprise the ‘search space’. The function f is called an objective function, a loss function or cost function or fitness function and so forth. The feasible solution that gives the optimum y is called the ‘optimal solution’. In addition to the boundaries of X, there may exist several other constraints in the form of g(X) = p (equality constraints) or h(X) ≥ q (inequality constraints), which need to be satisfied simultaneously during the process of searching the optimal solution. This type of optimisation is called constrained optimisation (Rao 1996).
