A comparison of nature inspired algorithms for the quadratic assignment problem

Abstract

Abstract. This paper presents an application of the ant algorithm and bees algorithm in optimization of QAP problem as an example of NPhard optimization problem. The experiments with two types of algorithms: the bees algorithm and the ant algorithm were performed for the test instances of the quadratic assignment problem from QAPLIB, designed by Burkard, Karisch and Rendl. On the basis of the experiments results, an influence of particular elements of algorithms, including neighbourhood size and neighbourhood search method, will be determined. The QAP is an NP-hard problem and this difficulty is not restricted only to finding the optimal solution. Sahni and Gonzalez [4] proved that even finding an ɛ-approximation solution for QAP is a hard problem in this sense that the existence of a ɛ-approximation algorithm implies P = NP.Finding an optimal solution to QAP is a difficult task not only in case of looking for the best solution among all the feasible ones. It might appear that finding an optimal solution in the subset of the feasible solutions can be easier. For QAP it was proven that finding an optimal solution in case of the local search is a difficult problem too. Johnson and Papadimitriou in [6] created the base for the complexity theory in the local search case, where a special structure of neighbourhood is introduced. They define the PLS-problems (polynomial-time local search problem) as a set for which a locally optimal solution can be found in polynomial time. Next, they introduce a PLS-complete decision problem as an analogy of NP-complete one, which are the most difficult problems in PLS.Murthy, Pardalos and Li [7] proposed a neighbourhood structure for QAP problem and proved that the corresponding local search problem is PLS-complete. The proposed structure is similar to that proposed by Kernighan and Lin [8] for the graph partitioning problem called K-L type neighbourhood structure N K-L . As the problem of finding QAP optimal solution in N K-L (called (QAP, N K-L )) is PLS-complete, then in the

Solving quadratic assignment problem by symbiotic organisms search algorithm

“…Test problems both from the literature (Kennedy and Eberhart, 1942;Durkota, 2011;Riffi and Bouzidi, 2014;Chmiel et al, 2017;Riffi et al, 2017) and randomly generated are used in the computational experiments. Problems from the literature provide a benchmark to measure the performance of the proposed algorithm relative to other existing methods.…”

“…Four sets of test problems from the literature were used. One set was provided by Kennedy and Eberhart (1942), Riffi and Bouzidi (2014), Miranda et al (2005), one set was formed by Chmiel et al (2017), one set was tested by Burkard et al (1991), Riffi et al (2017), Ahmed (2015aAhmed ( , 2014 and the other set was tested by Mamaghani and Meybodi (2012). The table shows for each problem the best known solution obtained from QAPLIB, average error from the best knew solution, the number of times the best known solution was found by our proposed algorithm out of the 20 runs (no.…”

A Swarm-Based Approach to Generate Challenging Mazes

“…The paper [ 32 ] presents an automated guided vehicle (AGV) control system, using the Wireless Sensor Network technology so that the vehicles can operate as mobile robots, using the swarm intelligence to coordinate vehicle operation. The algorithms based on swarm intelligence are also applied in solving the Quadratic Assignment Problem (QAP), modelling a number of such issues as the travelling salesman problem, generalised problem of graph subdivision, or the problem of finding a maximum clique [ 33 ]. Certain studies also concerned the application of swarm algorithms to tune PID controllers [ 34 , 35 , 36 , 37 ].…”

Quantum-Inspired Evolutionary Approach for the Quadratic Assignment Problem

“…Due to the computational complexity of the QAPs, exact methods can solve relatively small-sized instances from the QAP benchmark library (QAPLIB) with up to 30 locations. Therefore, to obtain near-optimal solutions, various heuristic and metaheuristic approaches have been developed, such as tabu search [ 5 , 6 , 7 ], simulated annealing [ 8 , 9 ], scatter search or swarm algorithms including ant colony optimization [ 10 ], particle swarm optimization [ 11 , 12 ] and bees algorithm [ 13 , 14 ]. One of the initiatives followed by many researchers is using evolutionary algorithms for solving quadratic assignment problems [ 3 , 15 , 16 , 17 , 18 ].…”