Migrating Birds Optimization: A new metaheuristic approach and its performance on quadratic assignment problem

Abstract

We propose a new nature inspired metaheuristic approach based on the V flight formation of the migrating birds which is proven to be an effective formation in energy saving. Its performance is tested on quadratic assignment problem instances arising from a real life problem and very good results are obtained. The quality of the solutions we report are better than simulated annealing, tabu search, genetic algorithm, scatter search, particle swarm optimization, differential evolution and guided evolutionary simulated annealing approaches. The proposed method is also tested on a number of benchmark problems obtained from the QAPLIB and in most cases it was able to obtain the best known solutions. These results indicate that our new metaheuristic approach could be an important player in metaheuristic based optimization.

Introduction

Solving large scale combinatorial optimization problems optimally is often intractable and one usually has to be content with near optimal solutions. Near optimal solutions are found by heuristic algorithms which can broadly be classified as constructive and improvement algorithms. Constructive algorithms start from scratch and build a solution gradually whereas improvement algorithms start with a complete solution and try to improve it. Heuristic algorithms are usually developed to solve a specific problem in hand. There is also a class of heuristic algorithms that can be used to solve a large class of problems, either directly or with minor modifications, called metaheuristics [20].

Most metaheuristic algorithms can also be named as neighborhood (or, local) search procedures. These are a wide class of improvement algorithms where at each iteration an improving solution is found by searching the “neighborhood” of the current solution. A critical issue in the design of a neighborhood search algorithm is the choice of the neighborhood structure, that is, the manner in which the neighborhood is defined [2].

So far many metaheuristics have been proposed by researchers. Among these the genetic algorithm proposed by Holland [24], the simulated annealing proposed by Kirkpatrick et al. [28], the tabu search proposed by Glover [19], the ant colony optimization proposed by Dorigo [11] and the particle swarm optimization proposed by Eberhart and Kennedy [15] are the most popular ones. The harmony search algorithm [18], the artificial bee colony algorithm [27], the monkey search algorithm [36], the differential evolution [46] and the firefly algorithm [52] are examples of other competitive metaheuristics proposed recently. Most of these metaheuristics are inspired by nature. This is an indication that although we the mankind are the most intelligent creature in the world, we have lessons to learn from the perfectness of nature.

Metaheuristics have been successfully applied to many different areas and problems from manufacturing [26] to services [33], from scheduling [30] to transportation [6], from health [42] to sports [23], from justice [17] to entertainment [53], from data mining [34] to curve fitting [50], from robotics [8] to timetabling [1] and from geology [4] to astronomy [9]. It is possible to find thousands of similar studies in the literature. Here we can only name just a few of them.

The application domain we focus on is the quadratic assignment problem (QAP) due to our prior work and familiarity. The QAP is best described as the plant layout problem, where a number of departments are to be located on a number of locations so that the transportation cost among the departments is minimized. Typically, the number of departments and locations are taken as equal to each other [32]. The QAP is an NP-Hard problem and it is very difficult to solve it optimally once the number of departments exceeds 15 [14]. Parallel to its complexity the research work on the QAP is still diverging and many researchers still report their new research in leading journals. Some of the recent studies regarding QAP can be listed as follows.

Duman and Or [14] addressed the QAP in the context of specific assembly machines. Ramkumar et al. [41] proposed a new iterated fast local search heuristic for solving QAP in facility layout design. Drezner [12] and Misevicius and Rubliauskas [35] tried to solve QAP with hybrid genetic algorithms wheras, Ravindra et al. [43] proposed a greedy genetic algorithm for the QAP. There is also a recent survey of the metaheuristics applied to QAP [37]. A recent study considered effective formulation reductions for the QAP [54]. Another recent example is self controlling tabu search algorithm where the application is held on QAP instances [16]. Robust tabu search is another important contribution for solving the quadratic assignment problem with less complexity and fewer parameters and it is still being improved [40], [47], [48].

We name our new nature inspired metaheuristic algorithm as the Migrating Birds Optimization (MBO) algorithm since it is inspired from the V formation flight of the migrating birds which is a very effective formation in energy minimization [31]. To test the performance of the MBO algorithm the studies of Duman and Or [14] and Kiyicigi et al. [29] are taken as the benchmarks. In [14] a number of heuristic algorithms including 2-opt, 3-opt and their combinations and the metaheuristics tabu search, simulated annealing and guided evolutionary simulated annealing are implemented and compared for the solution of the quadratic assignment problem. Then in [29] this comparison is extended to cover genetic algorithms and scatter search also. In this study, the MBO algorithm is compared with the best performing procedure in those studies and two additional metaheuristics which are implemented now and better solutions are obtained in all test problems. Similar to other metaheuristics the MBO is also a parametric procedure and its performance may depend on how effectively its parameters are settled. In addition to this, the MBO is also applied to standard benchmark problems in QAPLIB and very successful results are obtained.

The outline of the study is as follows. In the next section we give some information on how birds fly and what benefits they can obtain in using the V flight formation. Based on the birds’ story, the MBO algorithm is detailed in Section 3. The results obtained with the initial set of parameters are given in Section 4. Detailed parameter fine tuning experiments are discussed in Section 5 where the results obtained by the best set of parameters are also given. Section 6 discusses the results obtained on a number of standard QAP instances available in QAPLIB. Section 7 concludes by providing a summary of the study and directions for further study.