Alan Crispin

Quantum annealing of the graph coloring problem

Quantum annealing extends simulated annealing by introducing artificial quantum fluctuations. The path-integral Monte Carlo version chosen is population-based and designed to be implemented on a classical computer. Its first application to the graph coloring problem is presented in this paper. It is shown by experiments that quantum annealing can outperform classical thermal simulated annealing for this particular problem. Moreover, quantum annealing proved competitive when compared with the best algorithms on most of the difficult instances from the DIMACS benchmarks. The quantum annealing algorithm has even found that the well-known benchmark graph dsjc1000.9 has a chromatic number of at most 222. This is an improvement on its best upper-bound from a large body of literature.

Genetic Algorithm Coding Methods for Leather Nesting

The problem of placing a number of specific shapes in order to minimise waste is commonly encountered in the sheet metal, clothing and shoe-making industries. The paper presents genetic algorithm coding methodologies for the leather nesting problem which involves cutting shoe upper components from hides so as to maximise material utilisation. Algorithmic methods for computer-aided nesting can be either packing or connectivity driven. The paper discusses approaches to how both types of method can be realised using a local placement strategy whereby one shape at a time is placed on the surface. In each case the underlying coding method is based on the use of the no-fit polygon (NFP) that allows the genetic algorithm to evolve non-overlapping configurations. The packing approach requires that a local space utilisation measure is developed. The connectivity approach is based on an adaptive graph method. Coding techniques for dealing with some of the more intractable aspects of the leather nesting problem such as directionality constraints and surface grading quality constraints are also discussed. The benefits and drawbacks of the two approaches are presented.

Graph coloring with a distributed hybrid quantum annealing algorithm

Quantum simulated annealing is analogous to a population of agents cooperating to optimize a shared cost function defined as the total energy between them. A hybridization of quantum annealing with mainstream evolutionary techniques is introduced to obtain an effective solver for the graph coloring problem. The state of the art is advanced by the description of a highly scalable distributed version of the algorithm. Most practical simulated annealing algorithms require the reduction of a control parameter over time to achieve convergence. The algorithm presented is able to keep all its parameters fixed at their initial value throughout the annealing schedule, and still achieve convergence to a global optimum in reasonable time. Competitive results are obtained on challenging problems from the standard DIMACS benchmarks. Furthermore, for some of the graphs, the distributed hybrid quantum annealing algorithm finds better results than those of any known algorithm.

Parameter tuning patterns for random graph coloring with quantum annealing

Quantum annealing is a combinatorial optimization technique inspired by quantum mechanics. Here we show that a spin model for the k-coloring of large dense random graphs can be field tuned so that its acceptance ratio diverges during Monte Carlo quantum annealing, until a ground state is reached. We also find that simulations exhibiting such a diverging acceptance ratio are generally more effective than those tuned to the more conventional pattern of a declining and/or stagnating acceptance ratio. This observation facilitates the discovery of solutions to several well-known benchmark k-coloring instances, some of which have been open for almost two decades.

Genetic algorithms applied to leather lay plan material utilization

Abstract This paper presents a genetic algorithm method for the leather-nesting problem that involves cutting shoe upper components from hides so as to maximize material utilization. A significant proportion of the manufacturing cost of a pair of shoes is invested in the natural raw material, and so the efficient utilization of this resource is of prime importance. Consequently, the part nesting and cutting process is one of the most important stages in the manufacture of leather shoes. The genetic algorithm method presented for leather lay-planning is capable of handling some of the more intractable aspects of the problem, namely multiple non-convex shapes, irregularly shaped hides, directionality constraints and surface grading quality issues. The underlying encoding method is based on the use of the no-fit polygon (NFP), lay angles and directionality angle constraints. The NFP allows the genetic algorithm to evolve non-overlapping configurations. Lay-plan results are presented using standard shoe component shapes and scanned hide input data conforming to a grading scale commonly used in shoemaking.

Quantum Annealing Algorithm for Vehicle Scheduling

In this paper we propose a new strategy for solving the Capacitated Vehicle Routing Problem using a quantum annealing algorithm. The Capacitated Vehicle Routing Problem is a variant of the Vehicle Routing Problem being characterized by capacitated vehicles which contain goods up to a certain maximum capacity. Quantum annealing is a metaheuristic that uses quantum tunneling in the annealing process. We discuss devising a spin encoding scheme for solving the Capacitated Vehicle Routing Problem with a quantum annealing algorithm and an empirical approach for tuning parameters. We study the effectiveness of quantum annealing in comparison with best known solutions for a range of benchmark instances.

Immune engineering for Elgasir algorithm optimization

Fuzzy regression trees are a generalization of the standard artificial intelligence technique of regression trees. The Elgasir algorithm has previously been used to create fuzzy regression trees in order to improve the performance of crisp regression trees. A weakness of this approach was that no optimisation of tree node membership functions took place. Artificial Immune Systems are an evolutionary methodology, inspired by the principles and processes of the natural immune system. In this paper a novel method based on an optimization version of Artificial Immune Network model (opt-aiNet) is used to optimize the Elgasir algorithm. In order to illustrate the prediction accuracy of the proposed method, two problem datasets from the UCI repository are used to evaluate the approach. Experimental results have shown the effectiveness of using opt-aiNet for optimization Elgasir algorithm by increasing the prediction accuracy and robustness of fuzzy regression trees.

High performance trajectory control using a neural network cross-coupling gain scheduler

Cross-coupling control is an accepted methodology for improving contouring performance in multiaxial motion systems where axis interaction exists. This paper describes a new approach based on the use of neural networks for scheduling optimal cross-coupling gains for linear contours as the angle subtended with the x axis varies. The procedure for obtaining the optimal cross-coupling gains involves finding a minimum in a measured performance index. The experimental results for a biaxial system show that the proposed approach reduces contouring errors at test angles as compared to conventional uncoupled control of the axes. Measured performance indices are compared with and without cross-coupling at representative-angle to indicate the performance improvements that can be obtained with this approach.

An automatic corpus based method for a building Multiple Fuzzy Word Dataset

Fuzzy sentence semantic similarity measures are designed to be applied to real world problems where a computer system is required to assess the similarity between human natural language and words or prototype sentences stored within a knowledge base. Such measures are often developed for a specific corpus/domain where a limited set of words and sentences are evaluated. As new “fuzzy” measures are developed the research challenge is on how to evaluate them. Traditional approaches have involved rigorous and complex human involvement in compiling benchmark datasets and obtaining human similarity measures. Existing datasets often contain limited fuzzy words and do allow the fuzzy measures to be exhaustively tested. This paper presents an automatic method for the generation of a Multiple Fuzzy Word Dataset (MFWD) from a corpus. A Fuzzy Sentence Pairing Algorithm is used to extract and augment high, medium and low similarity sentence pairs with multiple fuzzy words. Human ratings are collected through crowdsourcing and the MFWD is evaluated using both fuzzy and traditional sentence similarity measures. The results indicated that fuzzy measures returned a higher correlation with human ratings compared with traditional measures.

Evolutionary algorithm for PCB inspection

An important inspection task in the automated assembly of printed circuit boards (PCBs) is that of detecting if all components have been placed correctly on the board. This paper describes a constrained evolutionary search based inspection technique for simultaneously detecting multiple component objects in a source image. The approach has the advantage that it does not rely on image alignment (registration) as do conventional optical inspection methods such as image subtraction. It is a template based search method which achieves speed and quality requirements by making use of an evolutionary algorithm and a simultaneous search for multiple objects in a source image using a generalised template. The generalised template matching method defines a template model that takes into account the statistical variations between the grey-level appearances of components. The evolutionary search for specific components is constrained to Canny edges making this a fast method for locating multiple targets. Results are presented for locating multiple surface mount resistors on a PCB so that missing components can be reported.