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The Quadratic Assignment Problem (QAP) is a difficult and important problem studied in the domain of combinatorial optimisation. It is possible to solve QAP instances with 10--20 facilities using exhaustive parallel algorithms within a few days on a cluster machine. However, large QAP instances with more than 100 facilities are not solvable using exhaustive techniques. We have explored a variety of Genetic Algorithm crossover operators for this problem and verified its performance experimentally using well-known instances from the QAPLIB library. By increasing the number of processors, generations and population sizes we have been able to find solutions that are the same as (or very close to) the best reported solutions for large QAP instances in QAPLIB. In order to parallelise the Genetic Algorithm we generate and evolve separate solution pools on each cluster processor, using an island model. This model exchanges 10% of each processor’s solutions at the initial stages of optimisation. We show experiment...

The Generalised MAchine Layout Problem (GMALP) is a generalisation of the integrated machine and layout problem, which is an extension of the machine layout problem. More specifically, the GMALP is the designing of a facility layout by defining the product mix, selecting the number of machines to be used, assigning these machines to the plant floor, and assigning products to machines such that total profit is maximised. Moreover, the GMALP integrates the quadratic assignment problem with a multicommodity flow problem. Therefore, the GMALP is a computationally intractable problem. Consequently, a mixed-integer nonlinear programming model was developed and used to solve small problem instances. Also, two simple construction algorithms and a tabu search (TS) heuristic were developed for solving large GMALP instances in acceptable computation times. In addition, a test dataset was used to evaluate the performances of the TS heuristic using the different construction algorithms. The results show that the TS he...

This paper addresses two real-life assignment problems. In both cases, the number of employees to whom tasks should be assigned is significantly greater than the number of tasks. In the simple job ...