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, optimization problems are often not adequately suitable to be solved using classical point-by-point methodologies. Evolutionary optimization procedures use a population of solutions and stochastic update operators in an iteration in a manner so as to 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 optimization 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 that reported in an existing simulated annealing based optimization procedure on a 24-variable version of the problem and new solutions are found to dominate the solutions of the existing study. Importantly, solutions found by our approach are found to satisfy theoretical Kuhn-Tucker optimality conditions by using the subdifferentials to handle non-differentiable objectives. This systematic and detail study demonstrates that evolutionary optimization procedures are not only flexible and scalable to large-scale optimization problems, but are also potentially efficient in finding theoretical optimal solutions for difficult real-world optimization problems.