Solving np hard problem artificial bee colony algorithm

Solving np hard problem artificial bee colony algorithm

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  INTERNATIONALComputer VolumeOF COMPUTERENGINEERING International Journal of Engineering and Technology (IJCET), ISSN 0976- JOURNAL 4, Issue 1, January- February (2013), © IAEME 6367(Print), ISSN 0976 – 6375(Online) & TECHNOLOGY (IJCET) ISSN 0976 – 6367(Print) ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), pp. 171-177 IJCET © IAEME: www.iaeme.com/ijcet.asp Journal Impact Factor (2012): 3.9580 (Calculated by GISI) ©IAEME www.jifactor.com SOLVING NP-HARD PROBLEM USING ARTIFICIAL BEE COLONY ALGORITHM Lalit Kumar1, Dr. Dheerendra Singh2 1 M.Tech Scholar, Department of CSE, SUSCET Tangori, Mohali, India 2 Professor and Head, Department of CSE, SUSCET, Tangori, Mohali, India E-mail: 1lalit.cse@gmail.com, 2professordsingh@gmail.com ABSTRACT In this paper we present a artificial bee colony (ABC) algorithm for NP- Hard problems. This algorithm is considered as one of the newest nature-inspired swarm-based optimization algorithms and has a promising performance. Shortest Common Supersequence is a classical problem in the field of string and it is classified as NP-Hard problem, such as Genetic algorithms, Majority Merge algorithm and Ant Colony Algorithm [1]. This approach obtains better results than the original artificial bee colony algorithm. KEY-WORDS: Artificial Bee Colony, Nature Inspired Algorithm, Shortest Common Supersequence Problem, Swarm Intelligence. 1. INTRODUCTION Several approaches have been proposed for solving optimization problems. In recent years, the research trend focuses more on heuristic methods rather than the traditional methods to solve the optimisation problems. Swarm intelligence for example focuses on the behavior of insects to develop some meta-heuristics which can mimic the insect’s problem- solving. Artificial bee colony (ABC) [2] algorithm is a part of swarm intelligence algorithms that mimics the natural behavior of real honey bees on searching for food sources. The selection of a best element from some set of available alternative referred as optimization problem. In many such problems, exhaustive search is not feasible. It has important application in several fields, including artificial and intelligence, NP-hard problem in combinatorial optimization studied in operations research. For example Shortest Common Supersequence problem and Solving Shortest Common Supersequence Problem. It has 171
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  International Journal ofComputer Engineering and Technology (IJCET), ISSN 0976- 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME several applications, such as planning, logistics, network communication, transportation and manufacture of microchips. SCS states that for one salesman who wants to visit cities and given distance between them. Shortest Common Supersequence has to visit all of them, but he doesn’t to travel very much. Task is to find a sequence of cities to minimize travel distance[1]. Combinatorial optimization problems have attracted much attention of researchers over the years. Many of combinatorial optimization problems are NP-hard [1, 2], which means they cannot be solved to optimality within polynomially-bounded computation times. Several algorithms, including population-based algorithms, have been developed that can find near-optimal solutions within reasonable running times. The swarm-based algorithm introduced in this paper to solve a single machine scheduling problem is a new population- based search algorithm capable of locating good solutions efficiently. The algorithm is inspired by the food foraging behavior of honey bees and could be regarded as an “intelligent” optimization tool [3] Artificial Bee Colony (ABC) algorithm is a branch of newly developed from of artificial intelligence called Swarm Intelligence, which proposed by Karaboga and Basturk in 2006 to solve NP-hard optimization problems [24]. In groups of insects which live in colonies like the ants and bees, an individual only can do simple task on its own, while the cooperative work of colony is the main reason determining the intelligent behavior of them. ABC algorithm inspired of the natural behavior of real honey bees in their search process for the best food sources in case of the nectar quality and the food source position. A colony of honey bees can extend itself over long distances in order to exploit a large number of food sources. In ABC algorithm, a bee colony contains of three kinds of bees: employed, scout and onlooker bees [25]. The employed bees carry with them information about the food sources that they found them, consist of the direction of food sources, and the nectar amount of them. The scout bees are searching the environment surrounding the nest for finding the new better food sources. And onlookers waiting in the hive and finding the optimal food source through the shared information by the employed bees[4]. In ABC, a food source position represents a possible solution for the optimization problem. Therefore, at the initialization step, a set of food source positions are randomly considered. The nectar amount of a food source corresponds to the quality of the solution represented by that source searched by the bee. So the nectar amounts of the food source existing at the initial positions are determined. On the other hand , the quality values of the initial solutions are calculated. Each employed bee is moved onto her food source area for determining a new food source within the neighborhood of the present one by guidance of the scout bee; then its nectar is evaluated. ABC algorithm can be applied to any optimization problem if it is possible to define: • Appropriate problem representation The problem must be described as a space which consists of food sources. • Construction of feasible solutions A mechanism must be in place whereby possible solutions are efficiently created. Each food source represents a feasible solution. • Heuristic desirability of solutions A suitable heuristic measure of the goodness of the found solution must be defined. ABC is an optimization tool which provides a population-based search procedure in which individuals called foods positions are modified by the artificial bees with time and the bee’s aim is to discover the places of food sources with high nectar amount and finally chose source with the highest nectar amount among the other resources [4], see the outline of the ABC algorithm. 172
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  International Journal ofComputer Engineering and Technology (IJCET), ISSN 0976- 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME Step 1: Initialize the population of solutions xi, i= 1, . . . , SN Step 2: Evaluate the population Step 3: cycle = 1 Step 4: repeat Step 5: Produce new solutions vi for the employed bees and evaluate them Step 6: Apply the greedy selection process for the employed bees Step 7: Calculate the probability values pi for Solutions xi Step 8: Produce the new solutions vi for the onlookers from the solutions xi selected depending on pi and evaluate them Step 9: Apply the greedy selection process for the Onlooker bees Step 10: Determine the abandoned solution for the scout bee, if exists, and replace it with a new randomly produced solution xi Step 11: Memorize the best solution achieved so far Step 12: cycle = cycle + 1 Step 13: until cycle = MCN 2. SHORTEST COMMON SUPERSEQUENCE PROBLEM SOLVERS Shortest Common Supersequence problem (SCS) is a classical NP-Hard problem and has applications in many areas. Pervious researches proposed different algorithms to solve Shortest Common Supersequence problem[1]. The Alphabet algorithm used to solve SCS and has an approximation ratio of q = |∑| with time complexity (qn), in practice the algorithm doesn’t perform when the alphabet is not fixed [3]. Another solution by using Majority- Merge algorithm (MM) and it does not have any worst-case approximation ratio and performs very well in practice with time complexity O(qkn) [13]. Greedy and Tournament algorithms used to solve SCS and have O(k2n2) time complexity and O(kn+n2) space complexity [10]. Genetic Algorithm (GA), On the other hand, was very hard to apply for many reasons for example: Changing a good solution slightly will yield an invalid string and most possible strings with reasonable length are invalid. Three versions of GA were proposed to solve SCS: G0, G1/||L||, G1, after testing, it turned out there is no basic value which performs best for all test instances, which led to propose another version of GA called Gv . The later allows the basic value to vary between 0 and [14]. Ant Colony Algorithm (ACO) algorithm developed by Michel & Middendorf for the SCS problem they called it (AS-SCSP) showed promising results when compared to the results of other approaches[21]. 3. PROPOSED APPROACH This section briefly describes the Artificial Bee Colony algorithm and its modified adaptation for solving the SCS. String S is called a Supersequence of a string T if S can be obtained from T by inserting zero or more symbols. Calculating the number alphabet and their frequency for all of the strings (L) to direct the random generation toward the used alphabets & most frequent alphabet. Checking the generated SCS compatibility with each string and give value for it. Our approach first, calculates the frequency of each alphabet used in L, and then store frequency for each character occurred in L in Array 1. After that we convert the frequencies to characters in Array 2. Example: L = {APLY, DUHA, LADP}, ∑ = {A,D,H,L,P,U,Y}, we store frequency for each character occurred in L in Array 1 (denote the 173
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  International Journal ofComputer Engineering and Technology (IJCET), ISSN 0976- 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME alphabet 26 characters) then we convert the frequencies to character in Array 2 (illustrated in Figure 1). These two steps are to ensure the best way of random string generation. Figure 1 generating string from alphabet used Each worker bee xi generate candidate SCS by randomly choosing characters from Array 2 in random length and we can see that the most frequent alphabet will be choosing more than less frequent alphabet. Then the onlooker bee calculate fitness value fi for each candidate SCS by checking each candidate SCS with L one string at a time by checking how much alphabet with the same ordering in L that the candidate SCS have, the more fi the more the candidate SCS is fitted to be SCS for L. We had modified the Merge Algorithm to calculate fi for the candidate SCS the approach assigns fitness value for each candidate SCS using equation (1) described below: ∑ Merge(Si,T1….Tn) (1) Fitness (Si) = ∑ Fitness (S1….. Sm) • n: number of entered strings • m: number of generated strings • S: generated string • T: entered string After assigning final fitness value fi for each worker bee, the onlooker bee needs to calculate Average to determine whether the generated string’s fitness is good or not. The measure is simply calculated by finding the average of the finesses of the generated strings over the number of the entered strings, see equation (2). Average = ∑ Fitness (S1…..Sn) (2) n Example: Figure 3 shows that there are 5 worker bees have different fitness values resulted by comparing the generated SCS with entered string “ABCABAA” using heuristic (1) mentioned before, when we calculate the Average if worker bees fitness values the result is 5.6, so we check the fitness values for worker bees and we found that worker bees 1 & 5 have fitness values below average. So in the next cycle the worker bees number 1 & 5 regenerate SCS and compute fitness values. 174
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  International Journal ofComputer Engineering and Technology (IJCET), ISSN 0976- 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME Figure 2 the results of the 1st cycle of the execution of the Program Figure 3 shows worker bees in the 2nd cycle of the program execution Figure 3 the results of the 2nd cycle of the execution of the Program Here, we present the Artificial Bee Colony Shortest Common Supersequence problem Solver Step 1: Read Entered Strings Step 2: Calculate alphabet number & frequencies Step 3: Random generation new solution for each worker bee Step 4: for (cycle = 0, cycle < MCN, cycle++) Step 5: for-each ES (Entered String) Step 6: Calculate the fi for the solutions produced by worker bees Step 7: Calculate Average Step 8: if fi < Average Step 9: then Step 10: Generate new string and calculate fi Step 11: Store the solution with the highest fi and shortest length 4. ABC-SCS PERFORMANCE We compared the results of ABC-SCS and the optimal solution to check the performance of ABC-SCS. Table 1 shows the results of ABC-SCS implementation with respect of L & ∑. 175
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  International Journal ofComputer Engineering and Technology (IJCET), ISSN 0976- 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME Table 1 comparing the results of ABC-SCS with optimal solutions L ∑ SCS Length Optical Solution 1 1 4 4 2 2 8.5 8 5 5 13.25 12 10 10 33 26 20 20 54 46 5. CONCLUSION It can be concluded from the results that proposed Artificial Bee Colony Algorithm as a solver for the shortest Common Super sequence problem. We compare the results obtained by applying Artificial Bee Colony Algorithm with the results obtained from applying other approaches that were proposed for solving the Shortest Common Super sequence problem. We can also use our proposed algorithm ABC with SCS rule to solve various NP-Hard problems. 6. REFERENCES [1] Singh D., “Solving Real Optimization Problem using Genetic Algorithm with Employed Bee” International Journal of Computer Applications (0975 – 8887) Volume 42– No.11, March 2012. [2] Mohd Afizi Mohd Shukran, “Artificial Bee Colony based Data Mining Algorithms for Classification Tasks” 2011.[3] Mustafa M. Noaman, “Solving Shortest Common Supersequence Problem Using Artificial Bee Colony Algorithm” The Research Bulletin of Jordan ACM, ISSN, Volume II (III) PP-80. [4] Gupta M., “An Efficient Modified Artificial Bee Colony Algorithm for Job Scheduling Problem” International Journal of Soft Computing and Engineering (IJSCE) ISSN: 2231-2307, Volume-1, Issue-6, January 2012 [5] Inova B., “Artificial bee colony algorithm for the capacitated vehicle routing problem” Proceedings of the European Computing Conference 2010. [6] Chang Jianghui, Zhao Yongsheng, Wen Chongzhu, “Research on Optimization of Fuzzy Membership function based on Ant Colony Algorithm,” Proc of the 25th Chinese Control Conference, Harbin, Aug, 2006. [7] Ashita S. Bhagade, “Artificial Bee Colony (ABC) Algorithm for Vehicle Routing Optimization Problem” International Journal of Soft Computing and Engineering (IJSCE ISSN: 2231-2307, Volume-2, Issue-2, May 2012 [8] Malek Alzaqebah, “Artificial bee colony search algorithm for examination timetabling Problems” International Journal of the Physical Sciences Vol. 6(17), pp. 4264-4272, September, 2011 [9] Adil Baykasoglu, “Artificial Bee Colony Algorithm and Its Application to Generalized Assignment Problem” International Conference on Computational Intelligence for Modeling, Control and Automation, Las Vegas. [10] Marco Dorigo and Thomas Stuzzle, Ant Colony Optimization, Eastern Economy Edition, PHI, 2005. 176
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  International Journal ofComputer Engineering and Technology (IJCET), ISSN 0976- 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME [11] Arun Khosla, Shakti Kumar, KK Aggarwal, Jagatpreet Singh,”Particle Swarm Optimizer for fuzzy models IEEE Proc. on Fuzzy Systems, 2007 [12] Marco Dorigo and Thomas Stuzzle, Ant Colony Optimization, Eastern Economy Edition, PHI, 2005. [13] M. Galea and Q. Shen, “Fuzzy Rules from ant-inspired computation,”Proc. IEEE Int’l Conf. Fuzzy Systems, pp 1691-1696, 2004. [14] Bhalla P., “Fuzzy Rule base generation from Numerical Data using Ant colony optimization,” MAIMT-Journal of IT & Management. Vol. 1, No. 1 May-Oct, 2007, pp 33-47. [15] Chia-Feng J, H.J. Huang and C.M. Lu, “Fuzzy Controller Design by ant colony optimization,” IEEE Proc. on Fuzzy Systems, 2007. [16] Kumar S. “Introduction to Fuzzy Logic Based Systems”, Workshop on Intelligent System Engineering (WISE-2010), 2010. [17] Shakti Kumar, P.Bhalla and Amarpartap Singh, “Soft Computing Approaches to Fuzzy System identification:A Survey”, IISN-2009,pp 402-411, 2009. [18] M.S. Abadeh, J. Habibi and E. Soroush, “Induction of Fuzzy classification systems using evolutionary ABC-based algorithms,” Proc. of the First Asia Int’l Conf. on Modeling and Simulation (AMS’07), 2007 [19] Shakti K, P. Bhalla and S.Sharma, “Automatic Fuzzy Rule base Generation for Intersystem Handover using Ant Colony Optimization Algorithm,” International Conference on Intelligent Systems and Networks (IISN-2007), Feb 23-25, 2007, MAIMT, Jagadhri Haryana, India, pp 764-773. [20] Shakti Kumar, “Rule base generation using ant colony optimization,” Proc. Of the one week workshop on applied soft computing (SOCO-2006), Haryana Engineering College, Jagadhri, July 2006. [21] Adil, B., Lale, Ö., and Pınar, T. 2007. Artificial Bee Colony Algorithm and Its Application to Generalized Assignment Problem. I-Tech Education and Publishing, ISBN 978-3-902613 [22] Andreas, W. 2003. The Shortest Common Supersequence Problem. ISBN 978-3- 90232 [23] Barone, P., Bonizzoni P., Vedova, G.D., and Mauri, G. 2001. An approximation algorithm for the shortest common Supersequence symposium on applied computing, 56-60. [24] Dervis, K. 2010. Artificial bee colony algorithm. Scholarpedia. 5(3):6915. [25] Dervis, K., and Bahriye, A. 2009. A comparative study of Artificial Bee Colony algorithm. Applied Mathematics and Computation, 214, 108–132. [26] G.Vasu, J. Nancy Namratha and V.Rambabu, “Large Scale Linear Dynamic System Reduction Using Artificial Bee Colony Optimization Algorithm” International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 1, 2012, pp. 145 - 155, Published by IAEME. [27] S. Kanimozhi Suguna and Dr.S.Uma Maheswari, “Comparative Analysis Of Bee-Ant Colony Optimized Routing (Bacor) With Existing Routing Protocols For Scalable Mobile Ad Hoc Networks (Manets)” International journal of Computer Engineering & Technology (IJCET), Volume 3, Issue 1, 2012, pp. 232 - 240, Published by IAEME 177