RAIRO-Oper. Res. 54 (2020) 1269–1289 RAIRO Operations Research https://doi.org/10.1051/ro/2019043 www.rairo-ro.org A NON-LINEAR-THRESHOLD-ACCEPTING FUNCTION BASED ALGORITHM FOR THE SOLUTION OF ECONOMIC DISPATCH PROBLEM Nabil Nahas 1 , Mohamed Noomane Darghouth 1,∗ and Mohammed Abouheaf 2,3 Abstract. This article introduces a novel heuristic algorithm based on Non-Linear Threshold Accept- ing Function to solve the challenging non-convex economic dispatch problem. Economic dispatch is a power system management tool; it is used to allocate the total power generation to the generating units to meet the active load demand. The power systems are highly nonlinear due to the physical and opera- tional constraints. The complexity of the resulting non-convex objective cost function led to inabilities to solve the problem by using analytical approaches, especially in the case of large-scale problems. Optimization techniques based on heuristics are used to overcome these difficulties. The Non-Linear Threshold Accepting Algorithm has demonstrated efficiency in solving various instances of static and dynamic allocation and scheduling problems but has never been applied to solve the economic dispatch problem. Existing benchmark systems are used to evaluate the performance of the proposed heuristic. Additional random instances with different sizes are generated to compare the adopted heuristic to the Harmony Search and the Whale Optimization Algorithms. The obtained results showed the superiority of the proposed algorithm in finding, for all considered instances, a high-quality solution in minimum computational time. Mathematics Subject Classification. 49-02. Received March 3, 2018. Accepted April 20, 2019. 1. Introduction The decrease in the non-renewable energies reserves, along with the increase in the power consumption, has motivated researchers to focus on the Economic Dispatch (ED) problem. The ED problem ensures economical based allocation of the active load demand to a number of committed or online generating units while sustaining the units’ physical and economic constraints [13, 26]. The high non-linearity of the power systems and the massive amount of calculations needed to efficiently allocate the generating sources have made the ED problem hard to solve. The nonlinear physical constraints (spinning reserve, transmission losses, ramp rate limits, multiple fuel options, etc.) result in non-convex cost functions. The conventional approaches used to solve the ED problem are Keywords. Economic dispatch, non-convex optimization, constraints optimization, meta-heuristics. 1 Systems Engineering Department, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Saudi Arabia. 2 School of Electrical Engineering and Computer Science, Ottawa University, K1N 6N5 Ottawa, Canada. 3 College of Energy Engineering, Aswan University, Aswan, Egypt. * Corresponding author: darghouth@kfupm.edu.sa Article published by EDP Sciences c  EDP Sciences, ROADEF, SMAI 2020