We consider the multiple travelling salesman Problem (MTSP) that is one of the generalization of the travelling salesman problem (TSP). For solving this problem genetic algorithms (GAs) based on numerous crossover operators have been described in the literature. Choosing effective crossover operator can give effective GA. Generally, the crossover operators that are developed for the TSP are applied to the MTSP. We propose to develop simple and effective GAs using sequential constructive crossover (SCX), adaptive SCX, greedy SCX, reverse greedy SCX and comprehensive SCX for solving the MTSP. The effectiveness of the crossover operators is demonstrated by comparing among them and with another crossover operator on some instances from TSPLIB of various sizes with different number of salesmen. The experimental study shows the promising results by the crossover operators, especially CSCX, for the MTSP.

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In this paper, we investigate the outage probability, channel capacity and symbol error rate (SER) performance of device-to-device (D2D) communication systems. The D2D communication system is affected by several co-channel interferers. Gamma fading channel is considered for the D2D communication system. The channel for the co-channel interference is assumed to be Nakagami faded. An expression for the probability density function (PDF) of the signal-to-interference ratio (SIR) is presented. The PDF is a function of distances between various devices in the D2D system, path-loss, channel fading conditions and signal powers. Based on the PDF expression, we present the expressions for the outage, channel capacity and SER. With the help of numerical results the performance of D2D communication system is discussed under various conditions of interference, path-loss and channel fading.

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