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Shuffled frog leaping (SFL) algorithm is one of the heuristic algorithms which is classified in swarm intelligence area. The standard version of the SFL and the improved versions of the algorithm operate in continuous space and is being researched and utilised in different subjects by researches around the world. The results obtained show that the improved versions of the algorithm perform well. But many optimisation problems are set in discrete space and there is no binary version of SFL to deal with these problems. Thus, an SFL algorithm is presented for optimising binary encoded problems called as binary SFL (BSFL). To show the effectiveness of the proposed algorithm, BSFL is tested on unit commitment problem, which is one of the most important problems to be solved in the operation and planning of a power system. The results obtained by the proposed algorithm are compared with the previous approaches reported in the literature. The results show that the proposed algorithm produces optimal solution for the study system.

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This paper presents nonlinear and linear models for the losses of Plug in Hybrid Electric Vehicle (PHEV). An accurate model to calculate the PHEV losses for just one vehicle is not remarkable. However, in the case of including thousands of vehicles, even a slight error for each vehicle leads to significant total losses which decreases the vehicles' owner profit. In previous works, the losses of PHEV charging and discharging mode are equally considered as a percentage of PHEV rating power. However, the charging and discharging mode losses are neither equal nor constant. Therefore, a nonlinear model of PHEV losses is presented for different parts of PHEV structure, i.e., AC/DC inverter, DC/DC converter and battery. After that, a simplified linear model for PHEV losses is presented to decrease the computation burden in the case of participating large number of PHEVs in the energy market. In the case study, the proposed losses formulation is used to obtain optimal charging and discharging time of PHEV. The profit of the PHEV owner is also maximized considering energy price in the energy market. V C 2013 AIP Publishing LLC. [http://dx.

Two previously proposed heuristic algorithms for solving penalized regression‐based clustering model (PRClust) are (a) an algorithm that combines the difference‐of‐convex programming with a coordinate‐wise descent (DC‐CD) algorithm and (b) an algorithm that combines DC with the alternating direction method of multipliers (DC‐ADMM). In this paper, a faster method is proposed for solving PRClust. DC‐CD uses p × n × (n − 1)/2 slack variables to solve PRClust, where n is the number of data and p is the number of their features. In each iteration of DC‐CD, these slack variable and cluster centres are updated using a second‐order cone programming (SOCP). DC‐ADMM uses p × n × (n − 1) slack variables. In each iteration of DC‐ADMM, these slack variables and cluster centres are updated using ADMM. In this paper, PRClust is reformulated into an equivalent model to be solved using alternating optimization. Our proposed algorithm needs only n × (n − 1)/2 slack variables, which is much less than that of DC‐CD and DC‐ADMM and updates them analytically using a simple equation in each iteration of the algorithm. Our proposed algorithm updates only cluster centres using an SOCP. Therefore, our proposed SOCP is much smaller than that of DC‐CD, which is used to update both cluster centres and slack variables. Experimental results on real datasets confirm that our proposed method is faster and much faster than DC‐ADMM and DC‐CD, respectively.