Soft Comput (2019) 23:1257–1281 https://doi.org/10.1007/s00500-017-2846-6 METHODOLOGIES AND APPLICATION Minimization of reliability indices and cost of power distribution systems in urban areas using an efficient hybrid meta-heuristic algorithm Avishek Banerjee 1 · Samiran Chattopadhyay 2 · Grigoras Gheorghe 3 · Mihai Gavrilas 3 Published online: 4 October 2017 © Springer-Verlag GmbH Germany 2017 Abstract Power distribution systems (PDS) in urban areas suffer from different types of problems. One such major problem is accidental or scheduled interruption. In electri- cal networks, effects of interruptions are usually quantified using a set of reliability indices, namely the System Aver- age Interruption Frequency Index and the System Average Interruption Duration Index. Installation cost (fixed cost) and cost due to temporary and/or permanent faults during interruptions (variable cost) are also major issues to be con- sidered while achieving a cost efficient, fault-tolerant PDS. Formalization of an optimization problem that jointly mini- mizes the afore-mentioned reliability indices as well as the cost of a PDS by optimal allocation of different protective devices and switches has always been a challenging task. This paper presents a hybrid single as well as joint-objective func- tion optimization technique to minimize different reliability indices (mixed integer minimization problems), as well as the operational cost of a PDS in urban areas. In the proposed technique, two well-known meta-heuristic search techniques, namely genetic algorithms (GA) and ant colony optimiza- tion (ACO), have been hybridized after modifying different participating operators. The effectiveness of the proposed algorithm is examined, and each PDS is tested in a differ- ent environment of constrained optimization. In addition, the presented simulation results are compared with existing approaches that solve this problem. The simulation results Communicated by V. Loia. B Avishek Banerjee avishekbanerji@gmail.com 1 Asansol Engineering College, Asansol, West Bengal, India 2 Jadavpur University, Kolkata, West Bengal, India 3 Technical University of IASI, Iasi, Romania show the superiority of the proposed hybrid GA–ACO model, as compared to other established heuristic approaches. Keywords Power distribution system · Hybrid algorithms · Constrained optimization · Genetic algorithm · Ant colony optimization · Reliability indices 1 Introduction 1.1 The problem domain Electric power distribution systems (PDS) are one of the most complex systems created by mankind. These systems include hundreds of thousands of components: transformers, distri- bution lines, generators, controls, protective equipment etc. In such a complex system, operation and planning conditions continuously vary. Constantly changing weather conditions (e.g., temperature wind speed), uncertainties and random factors make it extremely difficult to take correct decisions for smooth operation and planning of such systems. Wrong decisions cannot be corrected fast and they may result in sub- stantial financial losses (Cartina et al. 2009). Many aspects of operation and planning of a PDS can be mathematically modeled as joint-objective optimization problems in which undesirable metrics such as costs, energy losses, errors etc. are to be minimized and desirable metrics such as profit, quality, reliability, energy efficiency etc. are to be maximized Moscal 2015). A PDS is a combination of different electrical devices, such as feeders, reclosers, switches, fuses etc. A feeder line is a route-peripheral in a power distribution network. It is used to connect load points or consumers to the supply sub- stations. Reclosers or Auto-reclosers, act as circuit breakers. When a fault occurs, a recloser causes the circuit to open 123