Scope of stationary multi-objective evolutionary optimization: a case study on a hydro-thermal power dispatch problem

Many engineering design and developmental activities finally resort to an optimization task which must be solved to get an efficient and often an intelligent solution. Due to various complexities involved with objective functions, constraints, and decision variables, these optimization problems are adequately suitable to be solved by means of classical point-bypoint methodologies. Evolutionary optimization procedures use a population of solutions and stochastic update operators such that they constitute a flexible search procedure thereby demonstrating promise to such difficult and practical problem-solving tasks. In this paper, we illustrate the power of evolutionary algorithms in handling different kinds of optimization tasks on a hydro-thermal power dispatch optimization problem: (i) dealing with non-linear, non-differentiable objectives and constraints, (ii) dealing with more than one objectives and constraints, (iii) dealing with uncertainties in decision variables and other problem parameters, and (iv) dealing with a large number (more than 1,000) variables. The results on the static power dispatch optimization problem are compared with results available by an existing simulated annealing based optimization procedure on a 24-variable version of the problem and new solutions dominating the existing solutions are reported here. Importantly, solutions found by our approach are found to satisfy theoretical Karush-Kuhn-Tucker optimality conditions by using the subdifferentials to handle non-differentiable variables. This systematic and detail study demonstrates that evolutionary optimization procedures are potentially efficient in finding not only theoretically provable near-optimal solutions for difficult optimization problems, but also are scalable to large-scale optimization problems.