Social networks are regarded as a specific type of social interactions which include activities such as making somebody’s acquaintance, making friends, cooperating, sharing photos, beliefs, and emotions among individuals or groups of people. Cliques are a certain type of groups that include complete communications among all of its members. The issue of identifying the largest clique in the network is regarded as one of the notable challenges in this domain of study. Up to now, several studies have been conducted in this area and some methods have been proposed for solving the problem. Nevertheless, due to the NP-hard nature of the problem, the solutions proposed by the majority of different methods regarding large networks are not sufficiently desirable. In this paper, using a meta-heuristic method based on Artificial Bee Colony (ABC) optimization, a novel method for finding the largest clique in a given social network is proposed and simulated in Matlab on two dataset groups. The former group consists of 17 standard samples adopted from the literature whit know global optimal solutions, and the latter group includes 6 larger instances adopted from the Facebook social network. The simulation results of the first group indicated that the proposed algorithm managed to find optimal solutions in 16 out of 17 standard test cases. Furthermore, comparison of the results of the proposed method with Ant Colony Optimization (ACO) and the hybrid PS-ACO method on the second group revealed that the proposed algorithm was able to outperform these methods as the network size increases.  The evaluation of five DIMACS benchmark instances reveals the high performance in obtaining best-known solutions.

The Rubik’s cube is 3D puzzle with 6 different colored faces. The classis puzzle is a 3x3x3 cube with 43 quintillion possible permutations having a complexity of NP-Hard. In this paper, new metaheuristic approaches based on Simulated Annealing (SA) and Genetic Algorithm (GA) are proposed for solving the cube. The proposed algorithms are simulated in Matlab software and tested for 100 random test cases. The simulation results show that the GA approach is more effective in finding shorter sequence of movements than SA, but the convergence speed and computation time of the SA method is considerably less than GA. Besides, the simulation of GA confirms the claim that the cube can be solved with maximum 22 numbers of movements.

In the current industrial world, Time and cost are two the most important concepts affecting whole our planning, activities and scheduling. Effective use of these factors, will lead to increasing performance and profit. Solving the parallel-machine problem is one of the basic and important problems in industrial and service delivery systems. In this paper, a new mathematical multi-objective linear programming model is proposed for scheduling the parallel machines to minimize the total make-span and total machines cost. The proposed model is implemented in Matlab using the NSGA-II approach and the results are compared with MOPSO approach. The computational results show the effectiveness and superiority of the proposed model.

The process scheduling, is one of the most important tasks of the operating system. One of the most common scheduling algorithms used by the most operating systems is the Round Robin method in which, the ready processes waiting in ready queue, seize the processor for a short period of time known as the quantum (or time slice) circularly. In this paper, a non-linear programming mathematical model is developed to determine the optimum value of the time quantum, in order to minimize the average waiting time of the processes. The model is implemented and solved by Lingo 8.0 software on four selected problems from the literature.