Bandit-Inspired Memetic Algorithms for Solving Quadratic Assignment Problems

In this paper we propose a novel algorithm called the Bandit-Inspired Memetic Algorithm (BIMA) and we have applied it to solve different large instances of the Quadratic Assignment Problem (QAP). Like other memetic algorithms, BIMA makes use of local search and a population of solutions. The novelty lies in the use of multi-armed bandit algorithms and assignment matrices for generating novel solutions, which will then be brought to a local minimum by local search. We have compared BIMA to multi-start local search (MLS) and iterated local search (ILS) on five QAP instances, and the results show that BIMA significantly outperforms these competitor

A GPU-based Iterated Tabu Search for Solving the Quadratic 3-dimensional Assignment Problem

International audienceThe quadratic 3-dimensional assignment problem (Q3AP) is an extension of the well-known NP-hard quadratic assignment problem. It has been proved to be one of the most difficult combinatorial optimization problems. Local search (LS) algorithms are a class of heuristics which have been successfully applied to solve such hard optimization problem. These methods handle with a single solution iteratively improved by exploring its neighborhood in the solution space. In this paper, we propose an iterated tabu search for solving the Q3AP. The design of this algorithm is essentially based on a new large neighborhood structure. Indeed, in LS heuristics, designing operators to explore large promising regions of the search space may improve the quality of the obtained solutions. However, designing such neighborhood is at the expense of a highly computationally process. Therefore, the use of graphics processing units (GPUs) provides an efficient complementary way to speed up the search. The proposed GPU-based iterated tabu search has been experimented on 5 different Q3AP instances. The obtained results are convincing both in terms of efficiency, quality and robustness of the provided solutions at run time

Information flow and Laplacian dynamics on local optima networks

We propose a new way of looking at local optima networks (LONs). LONs represent fitness landscapes; the nodes are local optima, and the edges are search transitions between them. Many metrics computed on LONs have been proposed and shown to be linked to metaheuristic search difficulty. These have typically considered LONs as describing static structures. In contrast to this, Laplacian dynamics (LD) is an approach to consider the information flow across a network as a dynamical process. We adapt and apply LD to the context of LONs. As a testbed, we consider instances from the quadratic assignment problem (QAP) library. Metrics related to LD are proposed and these are compared with existing LON metrics. The results show that certain LD metrics are strong predictors of metaheuristic performance for iterated local search and tabu search

Clarifying the Difference in Local Optima Network Sampling Algorithms

We conduct the first ever statistical comparison between two Local Optima Network (LON) sampling algorithms. These methodologies attempt to capture the connectivity in the local optima space of a fitness landscape. One sampling algorithm is based on a random-walk snowballing procedure, while the other is centred around multiple traced runs of an Iterated Local Search. Both of these are proposed for the Quadratic Assignment Problem (QAP), making this the focus of our study. It is important to note the sampling algorithm frameworks could easily be modified for other domains. In our study descriptive statistics for the obtained search space samples are contrasted and commented on. The LON features are also used in linear mixed models and random forest regression for predicting heuristic optimisation performance of two prominent heuristics for the QAP on the underlying combinatorial problems. The model results are then used to make deductions about the sampling algorithms’ utility. We also propose a specific set of LON metrics for use in future predictive models alongside previously-proposed network metrics, demonstrating the payoff in doing so

Comparing Communities of Optima with Funnels in Combinatorial Fitness Landscapes

The existence of sub-optimal funnels in combinatorial fitness landscapes has been linked to search difficulty. The exact nature of these structures — and how commonly they appear — is not yet fully understood. Improving our understanding of funnels could help with designing effective diversification mechanisms for a ‘smoothing’ effect, making optimisation easier. We model fitness landscapes as local optima networks. The relationship between communities of local optima found by network clustering algorithms and funnels is explored. Funnels are identified using the notion of monotonic sequences from the study of energy landscapes in theoretical chemistry. NK Landscapes and the Quadratic Assignment Problem are used as case studies. Our results show that communities are linked to funnels. The analysis exhibits relationships between these landscape structures and the performance of trajectory-based metaheuristics such as Simulated Annealing (SA) and Iterated Local Search (ILS). In particular, ILS gets trapped in funnels, and modular communities of optima slow it down. The funnels contribute to lower success for SA. We show that increasing the strength of ILS perturbation helps to ‘smooth’ the funnels and improves performance in multi-funnel landscapes.Authors listed as ECOM Trac

Comparative Performance of Tabu Search and Simulated Annealing Heuristics for the Quadratic Assignment Problem

For almost two decades the question of whether tabu search (TS) or simulated annealing (SA) performs better for the quadratic assignment problem has been unresolved. To answer this question satisfactorily, we compare performance at various values of targeted solution quality, running each heuristic at its optimal number of iterations for each target. We find that for a number of varied problem instances, SA performs better for higher quality targets while TS performs better for lower quality targets