In this study we present a discrete artificial bee colony (DABC) algorithm to solve the economic lot scheduling problem (ELSP) under extended basic period (EBP) approach and power-of-two (PoT) policy. In specific, our algorithm provides a cyclic production schedule of n items to be produced on a single machine such that the production cycle of each item is an integer multiple of a fundamental cycle. All the integer multipliers are in the form of power-of-two, and under EBP approach feasibility is guaranteed with a constraint that checks if the items assigned in each period can be produced within the length of the period. For this problem, which is NP-hard, our DABC algorithm employs a multi-chromosome solution representation to encode power-of-two multipliers and the production positions separately. Both feasible and infeasible solutions are maintained in the population through the use of some sophisticated constraint handling methods. A variable neighborhood search (VNS) algorithm is also fused into DABC algorithm to further enhance the solution quality. The experimental results show that the proposed algorithm is very competitive to the best performing algorithms from the existing literature under the EBP and PoT policy.