We present an exact partial enumerative algorithm for the maximum clique problem. The pruning device used is derived from graph colorings. Pruning of the search tree is accomplished not only by the number of colors used to color a tree subproblem but also by using information gained in the process of coloring. This leads to increased pruning which translates into improved computational performance. Experimental results on test problems are presented.

An exact algorithm for the maximum clique problem with accelerated pruning

In recent years the unconstrained binary quadratic program (UBQP) has grown in importance in the field of combinatorial optimization due to its application potential and its computational challenge. Research on UBQP has generated a wide range of solution techniques for this basic model that encompasses a rich collection of problem types. In this paper we survey the literature on this important model, providing an overview of the applications and solution methods.

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The unconstrained binary quadratic programming problem: a survey

https://hal.univ-angers.fr/hal-02709508/document

A review on algorithms for maximum clique problems

Quantum Bridge Analytics relates generally to methods and systems for hybrid classical-quantum computing, and more particularly is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the first of a two-part tutorial that surveys key elements of Quantum Bridge Analytics and its applications, with an emphasis on supplementing models with numerical illustrations. In Part 1 (the present paper) we focus on the Quadratic Unconstrained Binary Optimization model which is presently the most widely applied optimization model in the quantum computing area, and which unifies a rich variety of combinatorial optimization problems.

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

Currently, vibration analysis has been widely considered as an effective way to fulfill the fault diagnosis task of gearboxes in wind turbines (WTs) However, vibration signals are usually with abundant noise and characterized as nonlinearity and nonstationarity Therefore, it is quite challenging to extract robust and useful fault features from complex vibration signals to achieve an accurate and reliable diagnosis This paper proposes a novel feature representation learning approach, named stacked multilevel-denoising autoencoders (SMLDAEs), with the aim to learn robust and discriminative fault feature representations through a deep network architecture for diagnosis accuracy improvement In our proposed approach, we design an MLD training scheme, which uses multiple noise levels to train AEs It enables to learn more general and detailed fault feature patterns simultaneously at different scales from the complex frequency spectra of the raw vibration data, and therefore helps enhance the feature learning and fault diagnosis capability Furthermore, SMLDAE-based fault diagnosis is performed with an unsupervised representation learning procedure followed by a supervised fine-tuning process with label information for classification Our approach is evaluated by using the field vibration data collected from a self-designed WT gearbox test rig The results show that our proposed approach learned more robust and discriminative fault feature representations and achieved the best diagnosis accuracy compared with the traditional approaches

Stacked Multilevel-Denoising Autoencoders: A New Representation Learning Approach for Wind Turbine Gearbox Fault Diagnosis

Path relinking for unconstrained binary quadratic programming

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for solving high-dimensional expensive problems. The basic idea of SAEAs is the integration of nature-inspired searching ability of evolutionary algorithms and prediction ability of surrogate models. This paper proposes a novel evolutionary sampling assisted optimization (ESAO) method which combines the two abilities to consider global exploration and local exploitation. Differential evolution is employed to generate offspring using mutation and crossover operators. A global radial basis functions surrogate model is built for prescreening of the offspring’s objective function values and identifying the best one, which will be evaluated with the true function. The best offspring will replace its parent’s position in the population if its function value is smaller than that of its parent. A local surrogate model is then built with selected current best solutions. An optimizer is applied to find the optimum of the local model. The optimal solution is then evaluated with the true function. Besides, a better point found in the local search will be added into the population in the global search. Global and local searches will alternate if one search cannot lead to a better solution. Comprehensive analysis is conducted to study the mechanism of ESAO and insights are gained on different local surrogates. The proposed algorithm is compared with two state-of-the-art SAEAs on a series of high-dimensional problems and results show that ESAO behaves better both in effectiveness and robustness on most of the test problems. Besides, ESAO is applied to an airfoil optimization problem to show its effectiveness.

A Novel Evolutionary Sampling Assisted Optimization Method for High-Dimensional Expensive Problems

https://leeds-faculty.colorado.edu/glover/445%20-%20xQx%20-%20Probabilistic%20GRASP-Tabu%20Search%20w%20YW,%20ZL%20%26%20J-K%20%20CORWang2011.pdf

Probabilistic GRASP-Tabu Search algorithms for the UBQP problem

https://leeds-faculty.colorado.edu/glover/446%20-%20tabu%20search%20based%20memetic%20alg%20for%20max%20diversity.pdf

Yang Wang

Papers

The unconstrained binary quadratic programming problem: a survey

Path relinking for unconstrained binary quadratic programming

A Novel Evolutionary Sampling Assisted Optimization Method for High-Dimensional Expensive Problems

Probabilistic GRASP-Tabu Search algorithms for the UBQP problem

A tabu search based memetic algorithm for the maximum diversity problem