Multi-objective optimization of short-term hydrothermal scheduling using non-dominated sorting gravitational search algorithm with chaotic mutation

This paper proposes a non-dominated sorting gravitational search algorithm with chaotic mutation (NSGSA-CM) to solve short-term economic/environmental hydrothermal scheduling (SEEHTS) problem. The SEEHTS problem is formulated as a multi-objective optimization problem with many equality and inequality constraints. By introducing the concept of non-dominated sorting and crowding distance, NSGSA-CM can optimize two objectives of fuel cost and pollutant emission simultaneously and obtain a set of Pareto optimal solutions in one trial. In order to improve the performance of NSGSA-CM, the paper introduces particle memory character and population social information in velocity update process. And a chaotic mutation is adopted to prevent the premature convergence. Furthermore, NSGSA-CM utilizes an elitism strategy which selects better solutions in parent and offspring populations based on their non-domination rank and crowding distance to update new generations. When dealing with the constraints of the SEEHTS, new strategies without penalty factors are proposed. In order to handle the water dynamic balance and system load balance constraints, this paper uses a combined strategy which adjusts the violation averagely to each decision variable at first and adjusts the rest violation randomly later. Meanwhile, a new symmetrical adjustment strategy by modifying the discharges at current and later interval without breaking water dynamic balance is adopted to handle reservoir storage constraints. To test the performance of the proposed NSGSA-CM, simulation results are compared with other methods reported in literatures. The results verify that the proposed NSGSA-CM is feasible and efficient for solving SEEHTS problem.