Search results for: Heuristic search

Authors: S. Khanpour, A. Movaghar

Abstract:

The one of best robust search technique on large scale search area is heuristic and meta heuristic approaches. Especially in issue that the exploitation of combinatorial status in the large scale search area prevents the solution of the problem via classical calculating methods, so such problems is NP-complete. in this research, the problem of winner determination in combinatorial auctions have been formulated and by assessing older heuristic functions, we solve the problem by using of genetic algorithm and would show that this new method would result in better performance in comparison to other heuristic function such as simulated annealing greedy approach.

Keywords: Bids, genetic algorithm, heuristic, metaheuristic, simulated annealing greedy.

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Authors: Wahyudin P. Syam, Ibrahim M. Al-Harkan

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This study compares three meta heuristics to minimize makespan (Cmax) for Hybrid Flow Shop (HFS) Scheduling Problem with Parallel Machines. This problem is known to be NP-Hard. This study proposes three algorithms among improvement heuristic searches which are: Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). SA and TS are known as deterministic improvement heuristic search. GA is known as stochastic improvement heuristic search. A comprehensive comparison from these three improvement heuristic searches is presented. The results for the experiments conducted show that TS is effective and efficient to solve HFS scheduling problems.

Keywords: Flow shop, genetic algorithm, simulated annealing, tabu search.

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Authors: Maha Idrissi Aouad, Rene Schott, Olivier Zendra

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Reducing energy consumption of embedded systems requires careful memory management. It has been shown that Scratch- Pad Memories (SPMs) are low size, low cost, efficient (i.e. energy saving) data structures directly managed at the software level. In this paper, the focus is on heuristic methods for SPMs management. A method is efficient if the number of accesses to SPM is as large as possible and if all available space (i.e. bits) is used. A Tabu Search (TS) approach for memory management is proposed which is, to the best of our knowledge, a new original alternative to the best known existing heuristic (BEH). In fact, experimentations performed on benchmarks show that the Tabu Search method is as efficient as BEH (in terms of energy consumption) but BEH requires a sorting which can be computationally expensive for a large amount of data. TS is easy to implement and since no sorting is necessary, unlike BEH, the corresponding sorting time is saved. In addition to that, in a dynamic perspective where the maximum capacity of the SPM is not known in advance, the TS heuristic will perform better than BEH.

Keywords: Energy consumption, memory allocation management, optimization, tabu search heuristic.

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Authors: S. Raja Balachandar, K. Kannan

Abstract:

A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving large size set covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the set covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.

Keywords: Set covering problem, velocity, gravitational force, Newton's law, meta heuristic, combinatorial optimization.

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Authors: S. Raja Balachandar, K.Kannan

Abstract:

A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving vertex covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the vertex covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.

Keywords: Vertex covering Problem, Velocity, Gravitational Force, Newton's Law, Meta Heuristic, Combinatorial optimization.

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Authors: Sufian Ashraf Mazhari, Surendra Kumar

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This paper compares the heuristic Global Search Techniques; Genetic Algorithm, Particle Swarm Optimization, Simulated Annealing, Generalized Pattern Search, genetic algorithm hybridized with Nelder–Mead and Generalized pattern search technique for tuning of fuzzy PID controller for Puma 560. Since the actual control is in joint space ,inverse kinematics is used to generate various joint angles correspoding to desired cartesian space trajectory. Efficient dynamics and kinematics are modeled on Matlab which takes very less simulation time. Performances of all the tuning methods with and without disturbance are compared in terms of ITSE in joint space and ISE in cartesian space for spiral trajectory tracking. Genetic Algorithm hybridized with Generalized Pattern Search is showing best performance.

Keywords: Controller tuning, Fuzzy Control, Genetic Algorithm, Heuristic search, Robot control.

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Authors: Adel Bouchakhchoukha, Hakim Akeb

Abstract:

In this work, we propose a hybrid heuristic in order to solve the Team Orienteering Problem (TOP). Given a set of points (or customers), each with associated score (profit or benefit), and a team that has a fixed number of members, the problem to solve is to visit a subset of points in order to maximize the total collected score. Each member performs a tour starting at the start point, visiting distinct customers and the tour terminates at the arrival point. In addition, each point is visited at most once, and the total time in each tour cannot be greater than a given value. The proposed heuristic combines beam search and a local optimization strategy. The algorithm was tested on several sets of instances and encouraging results were obtained.

Keywords: Team Orienteering Problem, Vehicle Routing, Beam Search, Local Search.

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Authors: S. Balaji

Abstract:

An edge based local search algorithm, called ELS, is proposed for the maximum clique problem (MCP), a well-known combinatorial optimization problem. ELS is a two phased local search method effectively £nds the near optimal solutions for the MCP. A parameter ’support’ of vertices de£ned in the ELS greatly reduces the more number of random selections among vertices and also the number of iterations and running times. Computational results on BHOSLIB and DIMACS benchmark graphs indicate that ELS is capable of achieving state-of-the-art-performance for the maximum clique with reasonable average running times.

Keywords: Maximum clique, local search, heuristic, NP-complete.

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Authors: S. B. Liu, K. M. Ng, H. L. Ong

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This paper presents a new heuristic algorithm for the classical symmetric traveling salesman problem (TSP). The idea of the algorithm is to cut a TSP tour into overlapped blocks and then each block is improved separately. It is conjectured that the chance of improving a good solution by moving a node to a position far away from its original one is small. By doing intensive search in each block, it is possible to further improve a TSP tour that cannot be improved by other local search methods. To test the performance of the proposed algorithm, computational experiments are carried out based on benchmark problem instances. The computational results show that algorithm proposed in this paper is efficient for solving the TSPs.

Keywords: Local search, overlapped neighborhood, travelingsalesman problem.

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Authors: Ayed Salman, Fawaz Al-Anzi, Aseel Al-Minayes

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Heuristics-based search methodologies normally work on searching a problem space of possible solutions toward finding a “satisfactory" solution based on “hints" estimated from the problem-specific knowledge. Research communities use different types of methodologies. Unfortunately, most of the times, these hints are immature and can lead toward hindering these methodologies by a premature convergence. This is due to a decrease of diversity in search space that leads to a total implosion and ultimately fitness stagnation of the population. In this paper, a novel Decision Maturity framework (DMF) is introduced as a solution to this problem. The framework simply improves the decision on the direction of the search by materializing hints enough before using them. Ideas from this framework are injected into the particle swarm optimization methodology. Results were obtained under both static and dynamic environment. The results show that decision maturity prevents premature converges to a high degree.

Keywords: Heuristic Search, hints, Particle Swarm Optimization, Decision Maturity Framework.

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Authors: M. Saravanan, J. Raja Murugadoss, V. Jayanthi

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Optimal design of structure has a main role in reduction of material usage which leads to deduction in the final cost of construction projects. Evolutionary approaches are found to be more successful techniques for solving size and shape structural optimization problem since it uses a stochastic random search instead of a gradient search. By reviewing the recent literature works the problem found was the optimization of weight. A new meta-heuristic algorithm called as Cuckoo Search (CS) Algorithm has used for the optimization of the total weight of the truss structures. This paper has used set of 10 bars and 25 bars trusses for the testing purpose. The main objective of this work is to reduce the number of iterations, weight and the total time consumption. In order to demonstrate the effectiveness of the present method, minimum weight design of truss structures is performed and the results of the CS are compared with other algorithms.

Keywords: Cuckoo search algorithm, levy’s flight, meta-heuristic, optimal weight.

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Authors: Bin Cai, Shilong Wang, Haibo Hu

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The job shop scheduling problem (JSSP) is well known as one of the most difficult combinatorial optimization problems. This paper presents a hybrid genetic algorithm for the JSSP with the objective of minimizing makespan. The efficiency of the genetic algorithm is enhanced by integrating it with a local search method. The chromosome representation of the problem is based on operations. Schedules are constructed using a procedure that generates full active schedules. In each generation, a local search heuristic based on Nowicki and Smutnicki-s neighborhood is applied to improve the solutions. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Genetic algorithm, Job shop scheduling problem, Local search, Meta-heuristic algorithm

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Authors: K. Krishna Veni, S. Raja Balachandar

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This paper presents a heuristic to solve large size 0-1 Multi constrained Knapsack problem (01MKP) which is NP-hard. Many researchers are used heuristic operator to identify the redundant constraints of Linear Programming Problem before applying the regular procedure to solve it. We use the intercept matrix to identify the zero valued variables of 01MKP which is known as redundant variables. In this heuristic, first the dominance property of the intercept matrix of constraints is exploited to reduce the search space to find the optimal or near optimal solutions of 01MKP, second, we improve the solution by using the pseudo-utility ratio based on surrogate constraint of 01MKP. This heuristic is tested for benchmark problems of sizes upto 2500, taken from literature and the results are compared with optimum solutions. Space and computational complexity of solving 01MKP using this approach are also presented. The encouraging results especially for relatively large size test problems indicate that this heuristic can successfully be used for finding good solutions for highly constrained NP-hard problems.

Keywords: 0-1 Multi constrained Knapsack problem, heuristic, computational complexity, NP-Hard problems.

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Authors: Pichet Sriyanyong

Abstract:

This paper presents the application of an enhanced Particle Swarm Optimization (EPSO) combined with Gaussian Mutation (GM) for solving the Dynamic Economic Dispatch (DED) problem considering the operating constraints of generators. The EPSO consists of the standard PSO and a modified heuristic search approaches. Namely, the ability of the traditional PSO is enhanced by applying the modified heuristic search approach to prevent the solutions from violating the constraints. In addition, Gaussian Mutation is aimed at increasing the diversity of global search, whilst it also prevents being trapped in suboptimal points during search. To illustrate its efficiency and effectiveness, the developed EPSO-GM approach is tested on the 3-unit and 10-unit 24-hour systems considering valve-point effect. From the experimental results, it can be concluded that the proposed EPSO-GM provides, the accurate solution, the efficiency, and the feature of robust computation compared with other algorithms under consideration.

Keywords: Particle Swarm Optimization (PSO), GaussianMutation (GM), Dynamic Economic Dispatch (DED).

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Authors: Hakim Akeb, Mhand Hifi

Abstract:

In this paper, the use of beam search and look-ahead strategies for solving the strip packing problem (SPP) is investigated. Given a strip of fixed width W, unlimited length L, and a set of n circular pieces of known radii, the objective is to determine the minimum length of the initial strip that packs all the pieces. An augmented algorithm which combines beam search and a look-ahead strategies is proposed. The look-ahead is used in order to evaluate the nodes at each level of the tree search. The best nodes are then retained for branching. The computational investigation showed that the proposed augmented algorithm is able to improve the best known solutions of the literature on most instances used.

Keywords: Combinatorial optimization, cutting and packing, beam search, heuristic, look-ahead strategy.

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Authors: Stephen C. H. Leung, Defu Zhang

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This paper addresses a stock-cutting problem with rotation of items and without the guillotine cutting constraint. In order to solve the large-scale problem effectively and efficiently, we propose a simple but fast heuristic algorithm. It is shown that this heuristic outperforms the latest published algorithms for large-scale problem instances.

Keywords: Combinatorial optimization, heuristic, large-scale, stock-cutting.

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Authors: Ellips Masehian, Davoud Sedighizadeh

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This paper reviews the major contributions to the Motion Planning (MP) field throughout a 35-year period, from classic approaches to heuristic algorithms. Due to the NP-Hardness of the MP problem, heuristic methods have outperformed the classic approaches and have gained wide popularity. After surveying around 1400 papers in the field, the amount of existing works for each method is identified and classified. Especially, the history and applications of numerous heuristic methods in MP is investigated. The paper concludes with comparative tables and graphs demonstrating the frequency of each MP method's application, and so can be used as a guideline for MP researchers.

Keywords: Robot motion planning, Heuristic algorithms.

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3ⁿ enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3ⁿ integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Keywords: Constrained integer problems, enumerative search algorithm, Heuristic algorithm, tunneling algorithm.

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Authors: Mejía M. Paula, Ramírez L. Leonardo, Puerta A. Gabriel

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In telemedicine, the image repository service is important to increase the accuracy of diagnostic support of medical personnel. This study makes comparison between two routing algorithms regarding the quality of service (QoS), to be able to analyze the optimal performance at the time of loading and/or downloading of medical images. This study focused on comparing the performance of Tabu Search with other heuristic and metaheuristic algorithms that improve QoS in telemedicine services in Colombia. For this, Tabu Search and Simulated Annealing heuristic algorithms are chosen for their high usability in this type of applications; the QoS is measured taking into account the following metrics: Delay, Throughput, Jitter and Latency. In addition, routing tests were carried out on ten images in digital image and communication in medicine (DICOM) format of 40 MB. These tests were carried out for ten minutes with different traffic conditions, reaching a total of 25 tests, from a server of Universidad Militar Nueva Granada (UMNG) in Bogotá-Colombia to a remote user in Universidad de Santiago de Chile (USACH) - Chile. The results show that Tabu search presents a better QoS performance compared to Simulated Annealing, managing to optimize the routing of medical images, a basic requirement to offer diagnostic images services in telemedicine.

Keywords: Medical image, QoS, simulated annealing, Tabu search, telemedicine.

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Authors: Tripatjot S. Panag, J. S. Dhillon

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The lifetime of a wireless sensor network can be effectively increased by using scheduling operations. Once the sensors are randomly deployed, the task at hand is to find the largest number of disjoint sets of sensors such that every sensor set provides complete coverage of the target area. At any instant, only one of these disjoint sets is switched on, while all other are switched off. This paper proposes a heuristic search method to find the maximum number of disjoint sets that completely cover the region. A population of randomly initialized members is made to explore the solution space. A set of heuristics has been applied to guide the members to a possible solution in their neighborhood. The heuristics escalate the convergence of the algorithm. The best solution explored by the population is recorded and is continuously updated. The proposed algorithm has been tested for applications which require sensing of multiple target points, referred to as point coverage applications. Results show that the proposed algorithm outclasses the existing algorithms. It always finds the optimum solution, and that too by making fewer number of fitness function evaluations than the existing approaches.

Keywords: Coverage, disjoint sets, heuristic, lifetime, scheduling, wireless sensor networks, WSN.

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Authors: M. Fathi, M. J. Alvarez, V. Rodríguez

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Assembly line balancing is a very important issue in mass production systems due to production cost. Although many studies have been done on this topic, but because assembly line balancing problems are so complex they are categorized as NP-hard problems and researchers strongly recommend using heuristic methods. This paper presents a new heuristic approach called the critical task method (CTM) for solving U-shape assembly line balancing problems. The performance of the proposed heuristic method is tested by solving a number of test problems and comparing them with 12 other heuristics available in the literature to confirm the superior performance of the proposed heuristic. Furthermore, to prove the efficiency of the proposed CTM, the objectives are increased to minimize the number of workstation (or equivalently maximize line efficiency), and minimizing the smoothness index. Finally, it is proven that the proposed heuristic is more efficient than the others to solve the U-shape assembly line balancing problem.

Keywords: Critical task method, Heuristic, Line balancingproblem, U-shape

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Authors: Muhammad Naeem, Syed Ismail Shah, Habibullah Jamal

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In this paper, a simple heuristic genetic algorithm is used for Multistage Multiuser detection in fast fading environments. Multipath channels, multiple access interference (MAI) and near far effect cause the performance of the conventional detector to degrade. Heuristic Genetic algorithms, a rapidly growing area of artificial intelligence, uses evolutionary programming for initial search, which not only helps to converge the solution towards near optimal performance efficiently but also at a very low complexity as compared with optimal detector. This holds true for Additive White Gaussian Noise (AWGN) and multipath fading channels. Experimental results are presented to show the superior performance of the proposed techque over the existing methods.

Keywords: Genetic Algorithm (GA), Multiple AccessInterference (MAI), Multistage Detectors (MSD), SuccessiveInterference Cancellation.

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Authors: S. Raja Balachandar, K.Kannan

Abstract:

This paper presents a heuristic approach to solve the Generalized Assignment Problem (GAP) which is NP-hard. It is worth mentioning that many researches used to develop algorithms for identifying the redundant constraints and variables in linear programming model. Some of the algorithms are presented using intercept matrix of the constraints to identify redundant constraints and variables prior to the start of the solution process. Here a new heuristic approach based on the dominance property of the intercept matrix to find optimal or near optimal solution of the GAP is proposed. In this heuristic, redundant variables of the GAP are identified by applying the dominance property of the intercept matrix repeatedly. This heuristic approach is tested for 90 benchmark problems of sizes upto 4000, taken from OR-library and the results are compared with optimum solutions. Computational complexity is proved to be O(mn2) of solving GAP using this approach. The performance of our heuristic is compared with the best state-ofthe- art heuristic algorithms with respect to both the quality of the solutions. The encouraging results especially for relatively large size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems.

Keywords: Combinatorial Optimization Problem, Generalized Assignment Problem, Intercept Matrix, Heuristic, Computational Complexity, NP-Hard Problems.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

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In this paper, a novel associative memory model will be proposed and applied to memory retrievals based on the conventional continuous time model. The conventional model presents memory capacity is very low and retrieval process easily converges to an equilibrium state which is very different from the stored patterns. Genetic Algorithms is well-known with the capability of global optimal search escaping local optimum on progress to reach a global optimum. Based on the well-known idea of Genetic Algorithms, this work proposes a heuristic rule to make a mutation when the state of the network is trapped in a spurious memory. The proposal heuristic associative memory show the stored capacity does not depend on the number of stored patterns and the retrieval ability is up to ~ 1.

Keywords: Artificial Intelligent, Soft Computing, NeuralNetworks, Genetic Algorithms, Hopfield Neural Networks, andAssociative Memories.

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Authors: Salinee Thumronglaohapun

Abstract:

The proper number and appropriate locations of service centers can save cost, raise revenue and gain more satisfaction from customers. Establishing service centers is high-cost and difficult to relocate. In long-term planning periods, several factors may affect the service. One of the most critical factors is uncertain demand of customers. The opened service centers need to be capable of serving customers and making a profit although the demand in each period is changed. In this work, the capacitated location-allocation problem with stochastic demand is considered. A mathematical model is formulated to determine suitable locations of service centers and their allocation to maximize total profit for multiple planning periods. Two heuristic methods, a local search and genetic algorithm, are used to solve this problem. For the local search, five different chances to choose each type of moves are applied. For the genetic algorithm, three different replacement strategies are considered. The results of applying each method to solve numerical examples are compared. Both methods reach to the same best found solution in most examples but the genetic algorithm provides better solutions in some cases.

Keywords: Location-allocation problem, stochastic demand, local search, genetic algorithm.

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Authors: Somayeh Alizadeh, Mehdi Ghazanfari, Mostafa Jafari, Salman Hooshmand

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Fuzzy Cognitive Maps (FCMs) is a causal graph, which shows the relations between essential components in complex systems. Experts who are familiar with the system components and their relations can generate a related FCM. There is a big gap when human experts cannot produce FCM or even there is no expert to produce the related FCM. Therefore, a new mechanism must be used to bridge this gap. In this paper, a novel learning method is proposed to construct causal graph based on historical data and by using metaheuristic such Tabu Search (TS). The efficiency of the proposed method is shown via comparison of its results of some numerical examples with those of some other methods.

Keywords: Fuzzy Cognitive Map (FCM), Learning, Meta heuristic, Genetic Algorithm, Tabu search.

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Authors: J. Tospornsampan, I. Kita, M. Ishii, Y. Kitamura

Abstract:

In this paper a combination approach of two heuristic-based algorithms: genetic algorithm and tabu search is proposed. It has been developed to obtain the least cost based on the split-pipe design of looped water distribution network. The proposed combination algorithm has been applied to solve the three well-known water distribution networks taken from the literature. The development of the combination of these two heuristic-based algorithms for optimization is aimed at enhancing their strengths and compensating their weaknesses. Tabu search is rather systematic and deterministic that uses adaptive memory in search process, while genetic algorithm is probabilistic and stochastic optimization technique in which the solution space is explored by generating candidate solutions. Split-pipe design may not be realistic in practice but in optimization purpose, optimal solutions are always achieved with split-pipe design. The solutions obtained in this study have proved that the least cost solutions obtained from the split-pipe design are always better than those obtained from the single pipe design. The results obtained from the combination approach show its ability and effectiveness to solve combinatorial optimization problems. The solutions obtained are very satisfactory and high quality in which the solutions of two networks are found to be the lowest-cost solutions yet presented in the literature. The concept of combination approach proposed in this study is expected to contribute some useful benefits in diverse problems.

Keywords: GAs, Heuristics, Looped network, Least-cost design, Pipe network, Optimization, TS

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Authors: Supriya Arya, Sunita Dhingra

Abstract:

Multiprocessor task scheduling problem for dependent and independent tasks is computationally complex problem. Many methods are proposed to achieve optimal running time. As the multiprocessor task scheduling is NP hard in nature, therefore, many heuristics are proposed which have improved the makespan of the problem. But due to problem specific nature, the heuristic method which provide best results for one problem, might not provide good results for another problem. So, Simulated Annealing which is meta heuristic approach is considered. It can be applied on all types of problems. However, due to many runs, meta heuristic approach takes large computation time. Hence, the hybrid approach is proposed by combining the Duplication Scheduling Heuristic and Simulated Annealing (SA) and the makespan results of Simple Simulated Annealing and Hybrid approach are analyzed.

Keywords: Multiprocessor task scheduling Problem, Makespan, Duplication Scheduling Heuristic, Simulated Annealing, Hybrid Approach.

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Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. This paper presents a hybrid artificial immune system for the JSSP with the objective of minimizing makespan. The proposed approach combines the artificial immune system, which has a powerful global exploration capability, with the local search method, which can exploit the optimal antibody. The antibody coding scheme is based on the operation based representation. The decoding procedure limits the search space to the set of full active schedules. In each generation, a local search heuristic based on the neighborhood structure proposed by Nowicki and Smutnicki is applied to improve the solutions. The approach is tested on 43 benchmark problems taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Artificial immune system, Job shop scheduling problem, Local search, Metaheuristic algorithm

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Authors: Ghada Badr, Manar Hosny, Nuha Bintayyash, Eman Albilali, Souad Larabi Marie-Sainte

Abstract:

The median problem is significantly applied to derive the most reasonable rearrangement phylogenetic tree for many species. More specifically, the problem is concerned with finding a permutation that minimizes the sum of distances between itself and a set of three signed permutations. Genomes with equal number of genes but different order can be represented as permutations. In this paper, an algorithm, namely BeamGA median, is proposed that combines a heuristic search approach (local beam) as an initialization step to generate a number of solutions, and then a Genetic Algorithm (GA) is applied in order to refine the solutions, aiming to achieve a better median with the smallest possible reversal distance from the three original permutations. In this approach, any genome rearrangement distance can be applied. In this paper, we use the reversal distance. To the best of our knowledge, the proposed approach was not applied before for solving the median problem. Our approach considers true biological evolution scenario by applying the concept of common intervals during the GA optimization process. This allows us to imitate a true biological behavior and enhance genetic approach time convergence. We were able to handle permutations with a large number of genes, within an acceptable time performance and with same or better accuracy as compared to existing algorithms.

Keywords: Median problem, phylogenetic tree, permutation, genetic algorithm, beam search, genome rearrangement distance.

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