Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3321-3328 3321 www.etasr.com Marouani et al.: A Modified Artificial Bee Colony for the Non-Smooth Dynamic … A Modified Artificial Bee Colony for the Non- Smooth Dynamic Economic/Environmental Dispatch I. Marouani National School of Engineering of Sfax (ENIS), University of Sfax, Sfax, Tunisia ismailmarouani@yahoo.fr A. Boudjemline University of Hail, Hail, Saudi Arabia a.boudjemline@uoh.edu.sa T. Guesmi College of Engineering, University of Hail, Hail, Saudi Arabia tawfiq.guesmi@gmail.com H. H. Abdallah National School of Engineering of Sfax (ENIS), University of Sfax, Sfax, Tunisia Hsan.Hadj@enis.rnu.tn Abstract—This paper presents an improved artificial bee colony (ABC) technique for solving the dynamic economic emission dispatch (DEED) problem. Ramp rate limits, valve-point loading effects and prohibited operating zones (POZs) have been considered. The proposed technique integrates the grenade explosion method and Cauchy operator in the original ABC algorithm, to avoid random search mechanism. However, the DEED is a multi-objective optimization problem with two conflicting criteria which need to be minimized simultaneously. Thus, it is recommended to provide the best solution for the decision-makers. Shannon’s entropy-based method is used for the first time within the context of the on-line planning of generator outputs to extract the best compromise solution among the Pareto set. The robustness of the proposed technique is verified on six- unit and ten-unit system tests. Results proved that the proposed algorithm gives better optimum solutions in comparison with more than ten metaheuristic techniques. Keywords-evolutionary computation; power generation dispatch; optimal scheduling; decision making; cost function I. INTRODUCTION Emission dispatch aims at minimizing emission of harmful gases, caused by fossil-fueled thermal units, such as CO, CO 2 , NO x and SO 2 [1-2]. The combination of the above problems is called the economic emission dispatch (EED) problem. However, due to the dynamic nature of today’s network loads, it is required to schedule the thermal unit outputs in real time according to the variation of power demands during a certain time period [3]. To solve this modified EED problem, known as dynamic economic emission dispatch (DEED), several mathematical formulations have been suggested [3-6]. Usually the DEED problem is considered as a dynamic optimization problem having the same objectives as the EED over a time- period of one day, subdivided into definite time intervals of one hour with respect to the constraints imposed by the generator ramp-rate limits (RRL) [3]. Therefore, the operational decision at an hour may be influenced by the one taken at a previous hour. Other constraints such as prohibited operating zones (POZ) and valve-point loading effects (VPLE) have been considered [7-8]. However, incorporating VPLE in the fuel cost function introduces ripples in the latter and the problem will be with multiple minima. On the other hand, POZ constraints due to physical operation limitation like vibrations in the shaft bearing [9] create discontinuities in the objective functions. Therefore, the DEED becomes a highly nonlinear problem with non-convex and discontinuous fitness functions. Classical methods like, dynamic programming [10] and linear programming [11], have been used to solve the static EED. However, these techniques are iterative and require an initialization step, which can cause the convergence of the search process into local optima. Moreover, they may fail to solve the dynamic case including the above constraints. Recently, metaheuristic search algorithms have demonstrated good performance and high efficiency when applied to complex optimization problems. These optimization procedures are classified into various groups in terms of the optimization methodology. Swarm intelligence-based evolutionary algorithms are the most used algorithms. Among metaheuristic-based optimization techniques, genetic algorithm [12], particle swarm optimization [13], simulated annealing [14], artificial bee colony (ABC) [7], tabu search [15], differential evolution [4] and bacterial foraging [5] have been suggested for solving the EED problem. Despite the fact that these techniques have been proven to have a clear edge over traditional methods, they have been criticized [16] because their efficiencies are sensitive to the form of problem constraints and number of units. Most of the above-mentioned works have concentrated only on the static EED problem. Only a few considered the multi-objective DEED problem. In addition, RRL and POZ constraints were not considered during the transition from the last hour of the current day to the first hour of the next day. ABC algorithms attracted much attention for EED problems [9]. ABC algorithm [17] simulates the foraging behavior of a real bee colony for maximizing the nectar amount stocked in the hive. Compared to several population-based techniques like, PSO and GA, the ABC algorithm is simple in concept with a few setting parameters, easy for combination with other optimization approaches and more effective. Unfortunately, like other evolutionary algorithms, the ABC method has also been criticized for its poor convergence rate and premature convergence due to the unbalanced exploration-exploitation processes [16]. Exploration corresponds to the capability to avoid convergence toward local optima by expanding the search into new areas, while exploitation is the capability to