How to start a heuristic? Utilizing lower bounds for solving the quadratic assignment problem

The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. The QAP is an NP-hard optimization problem which attracts the use of heuristic or metaheuristic algorithms that can find quality solutions in an acceptable computation time. On the other hand, there is quite a broad spectrum of mathematical programming techniques that were developed for finding the lower bounds for the QAP. This paper presents a fusion of the two approaches whereby the solutions from the computations of the lower bounds are used as the starting points for a metaheuristic, called HC12, which is implemented on a GPU CUDA platform. We perform extensive computational experiments that demonstrate that the use of these lower bounding techniques for the construction of the starting points has a significant impact on the quality of the resulting solutions.

A comprehensive investigation into the performance of genetic algorithm for effective shipyard topological layout

Shipyards have large departments or facilities. It is essential to make an effective topological layout plan since the initial investment cost of these departments is high. Topological layout is an optimization problem and Genetic Algorithm (GA) is generally used in the literature. The selection of effective genetic algorithm approaches and operators are very important to improve the performance of the optimization. This study investigates an effective solution to the shipyard topological layout using a Quadratic Assignment Problem (QAP) model with classic and elitist GA approaches. Besides, genetic operators that have significant effects on exploitation and exploration capabilities are analyzed. Therefore, 126 experiments were run with 13 different operators. The results obtained from the classic and elitist GA approach were evaluated individually and compared with each other. It was observed that the elitist GA approach has a superior performance compared to the classic GA approach. This study is the most comprehensive and practical study on the performance of the GA for topological layout of the shipyard in the literature.

Thompson Sampling in Heuristic Selection for the Quadratic Assignment Problem

Este trabalho propõe uma Hiper-Heurística (HH) de seleção baseada na abordagem Thompson Sampling (TS) para a solução do Problema Quadrático de Alocação (PQA). O PQA tem como objetivo a alocação de instalações em um conjunto de possíveis localidades já conhecidas, a fim de minimizar o custo total de todas as movimentações entre as instalações. A HH proposta é aplicada na configuração automática de um algoritmo memético, atuando na seleção de uma combinação de heurísticas de baixo nível. Cada combinação envolve a seleção de uma heurística de recombinação, de uma estratégia de busca local e de uma heurística de mutação. O algoritmo foi analisado em 15 instâncias do benchmark Nug e o desempenho da HH é superior àquele obtido por qualquer combinação de heurísticas aplicada de forma isolada, demonstrando a sua eficiência na configuração automática do algoritmo. Os experimentos mostram que o desempenho da TS é afetado pela qualidade do conjunto de heurísticas de baixo nível. A melhor versão da HH obtém a solução ótima em 9 instâncias e o desvio médio percentual da solução ótima (gap), considerando todas as 15 instâncias foi de 8,6%, sendo que os maiores gaps foram encontrados para as três maiores instâncias.

Hyperheuristic Based Migrating Birds Optimization Algorithm for a Fairness Oriented Shift Scheduling Problem

The purpose of this paper is twofold. First, it introduces a new hybrid computational intelligence algorithm to the optimization community. This novel hybrid algorithm has hyperheuristic (HH) neighborhood search movements embedded into a recently introduced migrating birds optimization (MBO) algorithm. Therefore, it is called HHMBO. Second, it gives the necessary mathematical model for a shift scheduling problem of a manufacturing company defined by including the fairness perspective, which is typically ignored especially in manufacturing industry. Therefore, we call this complex optimization problem fairness oriented integrated shift scheduling problem (FOSSP). HHMBO is applied on FOSSP and is compared with the well-known simulated annealing, hyperheuristics, and classical MBO algorithms through extended computational experiments on several synthetic datasets. Experiments demonstrate that the new hybrid computational intelligence algorithm is promising especially for large sized instances of the specific problem defined here. HHMBO has a high exploration capability and is a promising technique for all optimization problems. To justify this assertion, we applied HHMBO to the well-known quadratic assignment problem (QAP) instances from the QAPLIB. HHMBO was up to 14.6% better than MBO on converging to the best known solutions for QAP benchmark instances with different densities. We believe that the novel hybrid method and the fairness oriented model presented in this study will give new insights to the decision-makers in the industry as well as to the researchers from several disciplines.

Garden optimization problems for benchmarking quantum annealers

We benchmark the 5000+ qubit system coupled with the Hybrid Solver Service 2 released by D-Wave Systems Inc. in September 2020 by using a new class of optimization problems called garden optimization problems known in companion planting. These problems are scalable to an arbitrarily large number of variables and intuitively find application in real-world scenarios. We derive their QUBO formulation and illustrate their relation to the quadratic assignment problem. We demonstrate that the system and the new hybrid solver can solve larger problems in less time than their predecessors. However, we also show that the solvers based on the 2000+ qubit system sometimes produce more favourable results if they can solve the problems.

The Color Mix Problem

In this paper, we introduce a new combinatorial optimization problem entitled the color mix problem (CMP), which is a more general case of the grey pattern quadratic assignment problem (GP-QAP). Also, we propose an original hybrid genetic-iterated tabu search algorithm for heuristically solving the CMP. In addition, we present both analytical solutions and graphical visualizations of the obtained solutions, which clearly demonstrate the excellent performance of the proposed heuristic algorithm.