International Journal of Computer Applications (0975 – 8887) Volume 85 – No 9, January 2014 19 A Novel Soft–Computing Algorithm for Channel Allocation in WDM Systems Shonak Bansal Department of Electronics and Communication Engineering, Institute of Science and Technology, Klawad, Haryana, INDIA Kuldeep Singh Department of Electronics and Communication Engineering, Institute of Science and Technology, Klawad, Haryana, INDIA ABSTRACT Nature–inspired algorithms are the most powerful algorithms for optimization problems. This paper presents a novel optimization channel allocation algorithm inspired by the flash pattern of fireflies that allows suppression of the four– wave mixing (FWM) crosstalk while maintaining channel bandwidth. It is composed of a fractional bandwidth channel allocation algorithm by using the concept of Optimal Golomb ruler (OGR) sequences. The simulation results conclude that the proposed novel optimization algorithm outperforms the other two existing conventional algorithms i.e. Extended Quadratic Congruence (EQC) and Search Algorithm (SA) in terms of the total optical bandwidth. General Terms Four wave mixing, Conventional and Soft computing, Nature–inspired, Optimization. Keywords Channel Spacing, Optimal Golomb ruler, Firefly Algorithm, Equally and Unequally spaced channel allocation. 1. INTRODUCTION FWM crosstalk is an optical Kerr effect and is one of the major limiting sources of performance degradation in all optical wave length division multiplexing (WDM) systems. FWM crosstalk is due to the interaction of two or more channels which results in ghost channels. These ghost channels can coincide with other channels resulting in distortion. The performance of WDM systems can be substantially improved if the generation of FWM crosstalk signal at the channel frequencies is avoided. It is therefore important to develop algorithms to allocate the channel frequencies in order to suppress the FWM crosstalk. The efficiency of FWM crosstalk signals depends on both the channel spacing and fiber dispersion [1]–[3]. To suppress the crosstalk due to FWM signals the frequency separation of any two channels of an optical WDM system is kept different from that of any other pair of channels [4]–[7]. In literature [1], [8]–[14], to suppress the FWM crosstalk in optical WDM systems, several unequally spaced channel allocation (USCA) algorithms have been proposed. An optimum–USCA (O–USCA) algorithm ensures if the frequency separation of any two channels is different from any other pair of channels no FWM crosstalk will ever be generated at any of the channel frequencies [11]. However, the algorithms [8]–[14] have the drawback of increased optical bandwidth requirement compared to equally spaced channel allocation (ESCA). This paper proposes, a fractional bandwidth channel allocation algorithm taking into consideration the concept of Optimal Golomb ruler sequences [7], [15]–[17]. This method for USCA achieves suppression in FWM crosstalk with the optical WDM systems without inducing additional cost in terms of total optical channel bandwidth. Golomb rulers represent a class of problems known as NP– complete [18]. Unlike the traveling salesman problem (TSP), which may be classified as a complete ordered set, the Golomb ruler may be classified as an incomplete ordered set. For higher order models, the exhaustive search [19], [20] of such NP–complete problems is impossible. As another mark is added to the ruler, the time required to search the permutations and to test the ruler becomes exponentially larger. Several different algorithms to tackle the Golomb ruler problem such as exact methods [19], [20], constraint programming [21], local searches [22] and exhaustive parallel search [23] have been studied. The success of soft computing algorithms such as Genetic Algorithms (GAs) [24]–[27] and Biogeography Based Optimization (BBO) [28]–[30] and Big Bang–Big Crunch (BB–BC) evolution theory [31], [32] in finding relatively good solutions to such NP–complete problems provides a good starting point for algorithms of finding OGR sequences. Hence, soft computing based algorithms seem to be very effective solutions for such problems. No doubt, these algorithms do not give the best/exact solutions but reasonably good solutions are available at given cost. This paper introduces a novel algorithm of generating OGR sequences for various marks making use of Firefly Algorithm (FA) and its comparison with two existing conventional/classical algorithms i.e. Extended Quadratic Congruence and Search Algorithm. The generated OGR sequences can be used as a bandwidth allocation algorithm in WDM systems. The remainder of this paper is organized as follows: Section II introduces the concept of Golomb rulers. Section III presents the problem formulation using FA. Section IV describes a brief account of FA optimization algorithm. Section V provides simulation results comparing with conventional/classical algorithms of generating unequal channel spacing. Section VI presents some concluding remarks. 2. GOLOMB RULERS The concept of Golomb rulers was first introduced by W. C. Babcock [7], and further described by Professor Solomon W. Golomb [15]. According to Colannino [33] and Dimitromanolakis [34], W. C. Babcock was first who discovered Golomb ruler’s upto 10–marks, while analyzing positioning of radio channels in the frequency spectrum to suppress the third and fifth order distortion. According to William T. Rankin [35], all of rulers’ upto eight are optimum, the nine and ten mark rulers that were presented by W. C. Babcock are near–to–optimum. Golomb ruler refers to a set of positive integers such that no distinct pairs of numbers from the set have the same difference [36], [37]. These numbers are referred to as marks