Multiple hybrid of lambda iteration and bee colony optimization method for solving economic dispatch problem

Abstract

This article presents a solution to the economic dispatch (ED) problem with a new technique, the multiple of hybrid lambda iteration method and bee colony optimization (MHLBCO) with a smooth cost function. The ED limitations include the electrical energy demand and transmission line losses. The main idea of the MHLBCO algorithm is a method of combining lambda iteration and bee colony optimization then increasing its efficiency by adding multiple search mechanisms. It is an adaptation of the lambda iteration algorithm and bee colony optimization algorithm (HLBCO) to find the best solution in sequence, series, and select the best solution. New techniques have been added to the MHLBCO algorithm to improve the search process, for example the hybrid algorithm, multiple adaptive search scopes and multiple searches. 2 case studies were used to test the efficiency of the MHLBCO algorithm, which included 6 power generating units in case study 1 and 15 power generating units in case study 2. The optimized results by MHLBCO are compared with those of HLBCO and traditional method approaches, for instance simulated annealing (SA), bee colony optimization (BCO), particle swarm optimization (PSO), krill herd algorithm (KHA), differential evolution algorithm (DE), modified harmony search algorithm (MHSA), hybrid differential evolution algorithm based on particle swarm optimization (DEPSO) and cuckoo search algorithm (CSA). The results of the two case studies confirm that the concepts contained in the MHLBCO algorithm can achieve higher-quality convergence of speed and solutions. The conclusion is this method is used to solve the economic dispatch problem under the objective function, power balance constraint and generator rating constraint efficiently.