Multi-objective Quadratic Assignment Problem Research Articles

A New Multi-Objective Ant Colony Optimisation Algorithm for Solving the Quadratic Assignment Problem

The multi-objective quadratic assignment problem (mQAP) is an NP-hard combinatorial optimisation problem. Real world problems are concerned with multi-objective problems which optimise more objective functions simultaneously. Moreover, QAP models many real-world optimisation problems, such as network design problems, communication problems, layout problems, etc. One of its major applications is the facility location, which is to find an assignment of all facilities to all locations in the way their total is minimised. The multi-objective QAP considers multiple types of flows between two facilities. Over the last few decades several meta-heuristic algorithms have been proposed to solve the multi-objective QAP, such as genetic algorithms, Tabu search, simulated annealing, and ant colony optimisation. This paper presents a new ant colony optimisation algorithm for solving multiple objective optimisation problems, and it is named as the random weight-based ant colony optimisation algorithm (RWACO). The proposed algorithm is applied to the bi-objective quadratic assignment problem and evaluates the performance by comparing with some recently developed multiobjective ant colony optimisation algorithms. The experimental results have shown that the proposed algorithm performs better than the other multi-objective ACO algorithms considered in this study. Keywords: ACO, multi-objective problem, QAP, travelling salesman problem

Random walk’s correlation function for multi-objective NK landscapes and quadratic assignment problem

The random walk’ correlation matrix of multi-objective combinatorial optimization problems utilizes both local structure and general statistics of the objective functions. Reckoning time of correlation, or the random walk of lag 0, is quadratic in problem size L and number of objectives D. The computational complexity of the correlation coefficients of mNK is $$O(D^2 K^2 L)$$ , and of mQAP is $$O(D^2 L^2)$$ , where K is the number of interacting bits. To compute the random walk of a lag larger than 0, we employ a weighted graph Laplacian that associates a mutation operator with the difference in the objective function. We calculate the expected objective vector of a neighbourhood function and the eigenvalues of the corresponding transition matrix. The computational complexity of random walk’s correlation coefficients is polynomial with the problem size L and the number of objectives D. The computational effort of the random walks correlation coefficients of mNK is $$O(2^K L D^2)$$ , whereas of mQAP is $$O(L^6 D^2)$$ . Numerical examples demonstrate the utilization of these techniques.

The Collaborative Local Search Based on Dynamic-Constrained Decomposition With Grids for Combinatorial Multiobjective Optimization.

The decomposition-based algorithms [e.g., multiobjective evolutionary algorithm based on decomposition (MOEA/D)] transform a multiobjective optimization problem (MOP) into a number of single-objective optimization subproblems and solve them in a collaborative manner. It is a natural framework for using single-objective local search (LS) to solve combinatorial MOPs. However, commonly used decomposition methods, such as weighted sum (WS), Tchebycheff (TCH), and penalty-based boundary intersection (PBI) may not be good at maintaining the population diversity while providing diverse initial solutions for different LS procedures in a collaborative way. Based on our previous work on the constrained decomposition with grids (CDG), this article proposes a dynamic CDG (DCDG) framework used to design a multiobjective memetic algorithm (DCDG-MOMA). DCDG uses grids for maintaining diversity, supporting the collaborative LS. In addition, DCDG dynamically increases the number of grids for obtaining more nondominated solutions as well as the better collaborative search among them. DCDG-MOMA has been compared with several classical and state-of-the-art algorithms on multiobjective traveling salesman problem (MOTSP), multiobjective quadratic assignment problem (MOQAP), and multiobjective capacitated arc routing problem (MOCARP).

Hypervolume-based multi-objective local search

This paper presents a multi-objective local search, where the selection is realized according to the hypervolume contribution of solutions. The HBMOLS algorithm proposed is inspired from the IBEA algorithm, an indicator-based multi-objective evolutionary algorithm proposed by Zitzler and Kunzli in 2004, where the opti- mization goal is defined in terms of a binary indicator defining the selection operator. In this paper, we use the indicator optimization principle, and we apply it to an iterated local search algorithm, using hypervolume contri- bution indicator as selection mechanism. The methodology proposed here has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on the multi-objective flow shop problem and the multi-objective quadratic assignment problem, using the hypervolume contribution selection as well as two different binary indicators which were initially proposed in the IBEA algorithm. Experi- mental results indicate that the HBMOLS algorithm is highly effective in comparison with the algorithms based on binary indicators.