A modified artificial bee colony algorithm based on a non-dominated sorting genetic approach for combined economic-emission load dispatch problem

The multi-objective optimization algorithms (MOO) are used to obtain the best compromising solutions when two or more objective functions need to be optimized simultaneously. The convergence and diversity are critical factors to consider while solving the MOO problems because they determine the possibility of obtaining an evenly distributed Pareto front. This paper proposes a hybrid optimization algorithm to solve a multi-objective economic emission dispatch (MOEED) problem of electrical power systems. The electrical power generated by consuming fossil fuels is very costly and also burning of these fuels contributes to global warming. Hence, electrical power is generated at the least cost and emission. The MOEED problems have been solved in the past by using swarm intelligence and evolutionary algorithms. However, the solutions reported in the literature, are either inferior or the constraints are violated. The algorithm proposed in this paper is an integration of an Artificial Bee Colony optimization algorithm and a Non-Dominated Sorting Genetic Algorithm-II. The effectiveness of the proposed algorithm is evaluated by applying it to three test systems having 6, 10, and 40 coal-based generators. Additionally, various multi-criteria decision-making algorithms are used to identify the best non-dominated solutions obtained by the proposed algorithm and compared with previously reported results. The best fuel costs obtained by the proposed approach, for a 6-unit test system with and without transmission losses are found to be 605.9983 and 600.11140 $/h respectively. While the best emission values, for this test system, with and without transmission losses are found to be 0.1941 and 0.1942 tons/h. Moreover, the best fuel costs obtained by the proposed approach, for 10 and 40-unit test systems are found to be 111181.9871 and 121369.0838 $/h respectively. Furthermore, the best emission values for these test systems are found to be 3932.24322 and 176682.264 tons/h respectively. All these results are obtained without constraint violations and within 10–600 iterations.