scholarly journals Garden optimization problems for benchmarking quantum annealers

2021 ◽  
Vol 20 (9) ◽  
Author(s):  
Carlos D. Gonzalez Calaza ◽  
Dennis Willsch ◽  
Kristel Michielsen
Keyword(s):  
Real World ◽  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment ◽  
New Class ◽  
Qubit System ◽  
Hybrid Solver ◽  
Qubo Formulation ◽  
D Wave

AbstractWe 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.

scholarly journals ANALYSIS OF THE 2-SUM PROBLEM AND THE SPECTRAL ALGORITHM

2014 ◽  
pp. 139-148
Author(s):  
Alexander Kolomiychuk
Keyword(s):  
Real World ◽  
Assignment Problem ◽  
Quadratic Assignment Problem ◽  
Sparse Matrices ◽  
Approximate Solutions ◽  
Upper Bounds ◽  
Quadratic Assignment ◽  
Euclidian Space ◽  
Real World Applications ◽  
Spectral Algorithm

This paper presents the analysis of the 2-sum problem and the spectral algorithm. The spectral algorithm was proposed by Barnard, Pothen and Simon in [1]; its heuristic properties have been advocated by George and Pothen in [4] by formulation of the 2-sum problem as a Quadratic Assignment Problem. In contrast to that analysis another approach is proposed: permutations are considered as vectors of Euclidian space. This approach enables one to prove the bound results originally obtained in [4] in an easier way. The geometry of permutations is considered in order to explain what are ‘good’ and ‘pathological’ situations for the spectral algorithm. Upper bounds for approximate solutions generated by the spectral algorithm are proved. The results of numerical computations on (graphs of) large sparse matrices from real-world applications are presented to support the obtained results and illustrate considerations related to the ‘pathological’ cases.

scholarly journals Solving the Quadratic Assignment Problem using the Swallow Swarm Optimization Problem

2019 ◽  
Vol 8 (6) ◽  
pp. 3116-3120
Keyword(s):  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Combinatorial Problems ◽  
Computational Method ◽  
Quadratic Assignment ◽  
Swarm Optimization ◽  
Natural Behavior ◽  
Combinatorial Optimization Problems ◽  
Benchmark Instances

In recent years, there is a growing interest in swarm intelligent algorithms inspired by the observation of the natural behavior of swarm to define a computational method, which may resolve the hardest combinatorial optimization problems. The Quadratic Assignment Problem is one of the well-known combinatorial problems, which simulate with the assignment problem in several domains such as the industrial domain. This paper proposes an adaptation of a recent algorithm called the swallow swarm optimization to solve the Quadratic Assignment Problem; this algorithm is characterized by a hierarchy of search who allow it to search in a totality of research space. The obtained results in solving some benchmark instances from QAPLIB are compared with those obtained from other know metaheuristics in other to evaluate the performance of the proposed adaptation.

scholarly journals Heuristic Approaches to Stochastic Quadratic Assignment Problem: VaR and CVar Cases

MENDEL ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Radomil Matousek ◽  
Pavel Popela ◽  
Jakub Kudela
Keyword(s):  
At Risk ◽  
Assignment Problem ◽  
Value At Risk ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Risk Measures ◽  
Conditional Value At Risk ◽  
Quadratic Assignment ◽  
Heuristic Approaches ◽  
Combinatorial Optimization Problems

The goal of this paper is to continue our investigation of the heuristic approaches of solving thestochastic quadratic assignment problem (StoQAP) and provide additional insight into the behavior of di erentformulations that arise through the stochastic nature of the problem. The deterministic Quadratic AssignmentProblem (QAP) belongs to a class of well-known hard combinatorial optimization problems. Working with severalreal-world applications we have found that their QAP parameters can (and should) be considered as stochasticones. Thus, we review the StoQAP as a stochastic program and discuss its suitable deterministic reformulations.The two formulations we are going to investigate include two of the most used risk measures - Value at Risk(VaR) and Conditional Value at Risk (CVaR). The focus is on VaR and CVaR formulations and results of testcomputations for various instances of StoQAP solved by a genetic algorithm, which are presented and discussed.

scholarly journals A Hybrid Ant Colony Algorithm for Quadratic Assignment Problem

2013 ◽  
Vol 7 (1) ◽  
pp. 51-54 ◽  
Author(s):  
Guo Hong
Keyword(s):  
Ant Colony Optimization ◽  
Assignment Problem ◽  
Large Scale ◽  
Ant Colony Algorithm ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Ant Colony ◽  
Quadratic Assignment ◽  
Optimal Solutions ◽  
Combinatorial Optimization Problems

Quadratic assignment problem (QAP) is one of fundamental combinatorial optimization problems in many fields. Many real world applications such as backboard wiring, typewriter keyboard design and scheduling can be formulated as QAPs. Ant colony algorithm is a multi-agent system inspired by behaviors of real ant colonies to solve optimization problems. Ant colony optimization (ACO) is one of new bionic optimization algorithms and it has some characteristics such as parallel, positive feedback and better performances. ACO has achieved in solving quadratic assignment problems. However, its solution quality and its computation performance need be improved for a large scale QAP. In this paper, a hybrid ant colony optimization (HACO) has been proposed based on ACO and particle swarm optimization (PSO) for a large scale QAP. PSO algorithm is combined with ACO algorithm to improve the quality of optimal solutions. Simulation experiments on QAP standard test data show that optimal solutions of HACO are better than those of ACO for QAP.

Ant Foraging Behavior, Combinatorial Optimization, and Routing in Communications Networks

1999 ◽  
Author(s):  
Eric Bonabeau ◽  
Marco Dorigo ◽  
Guy Theraulaz
Keyword(s):  
Combinatorial Optimization ◽  
Assignment Problem ◽  
Food Source ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment ◽  
Time Varying ◽  
Communications Networks ◽  
Combinatorial Optimization Problems ◽  
Stochastic Time

This chapter is dedicated to the description of the collective foraging behavior of ants and to the discussion of several computational models inspired by that behavior—ant-based algorithms or ant colony optimization (AGO) algorithms. In the first part of the chapter, several examples of cooperative foraging in ants are described and modeled. In particular, in some species a colony self-organizes to find and exploit the food source that is closest to the nest. A set of conveniently defined artificial ants, the behavior of which is designed after that of their real counterparts, can be used to solve combinatorial optimization problems. A detailed introduction to ant-based algorithms is given by using the traveling salesman problem (TSP) as an application problem. Ant-based algorithms have been applied to other combinatorial optimization problems such as the quadratic assignment problem, graph coloring, job-shop scheduling, sequential ordering, and vehicle routing. Results obtained with ant-based algorithms are often as good as those obtained with other general-purpose heuristics. Application to the quadratic assignment problem is described in detail. Coupling ant-based algorithms with local optimizers obtains, in some cases, world-class results. Parallels are drawn between ant-based optimization algorithms and other nature-inspired optimization techniques, such as neural nets and evolutionary computation. All the combinatorial problems mentioned above are static, that is, their characteristics do not change over time. In the last part of the chapter, the application of ant-based algorithms to a class of stochastic time-varying problems is investigated: routing in telecommunications networks. Given the adaptive capabilities built into the ant-based algorithms, they may be more competitive in stochastic time-varying domains, in which solutions must be adapted online to changing conditions, than in static problems. The performance of AntNet, an ant-based algorithm designed to adaptively build routing tables in packet-switching communications networks, is the best of a number of state-of-the-art algorithms compared on an extensive set of experimental conditions. Many ant species have trail-laying trail-following behavior when foraging: individual ants deposit a chemical substance called pheromone as they move from a food source to their nest, and foragers follow such pheromone trails.

A TISSUE P SYSTEM BASED SOLUTION TO QUADRATIC ASSIGNMENT PROBLEM

2012 ◽  
Vol 23 (07) ◽  
pp. 1511-1522 ◽  
Author(s):  
YUNYUN NIU ◽  
K. G. SUBRAMANIAN ◽  
IBRAHIM VENKAT ◽  
ROSNI ABDULLAH
Keyword(s):  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Real Life ◽  
Computation Time ◽  
Polynomial Time Algorithm ◽  
P Systems ◽  
Quadratic Assignment ◽  
P System ◽  
Combinatorial Optimization Problems

The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems, which models many real-life problems. However, it is considered as one of the most difficult NP-hard problems, which means that no polynomial-time algorithm is known to solve this intractable problem effectively. Even small instances of QAP may require vast computation time. In this work, a uniform cellular solution to QAP is proposed in the framework of membrane computing by using a family of recognizer tissue P systems with cell division. In the design of the solution, we encode the given instances in binary notations. The paper can be considered as a contribution to the study of considering a binary encoding of the information in P systems.

scholarly journals Artificial Bee Colony for Quadratic Assignment Problem: A Hospital Case Study

2016 ◽  
Vol 2 (3) ◽  
pp. 502
Author(s):  
Jalal A. Sultan ◽  
Daham A. Matrood ◽  
Zaidoun M. Khaleel
Keyword(s):  
Assignment Problem ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment ◽  
Position Operator ◽  
Abc Algorithm ◽  
Combinatorial Optimization Problems ◽  
Total Distance ◽  
Bee Colony

The problem of locating hospital departments so as to minimize the total distance travelled by patients can be formulated as a Quadratic Assignment Problem (QAP).In general, (QAP) is one of the Combinatorial Optimization Problems and always high dimensional. Therefore, the use of meta-heuristics that generates good solutions in reasonable computer time becomes an attractive alternative. In this paper, a proposed artificial bee colony (ABC) algorithm is used to optimize QAP. The main idea is to use different crossover techniques for employee and onlooker bee stages and use exchange position operator for scout bee stage. The results of ABC algorithm show the efficiency and capabilities of proposed algorithm in finding the optimum solutions, compared with results of GA and SA in all test problems. The purpose of this paper is to apply the QAP in Azadi hospital in Kirkuk city to minimize the total distance travelled by patients. The application involves determine the flow matrix and the distance matrix to solve the problem. The results related that QAP model was presented suitable framework for clinics allocation and optimum use.

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

2022 ◽  
Vol 13 (2) ◽  
pp. 151-164 ◽  
Author(s):  
Radomil Matousek ◽  
Ladislav Dobrovsky ◽  
Jakub Kudela
Keyword(s):  
Lower Bounds ◽  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Computation Time ◽  
Quadratic Assignment ◽  
Combinatorial Optimization Problems ◽  
Lower Bounding ◽  
Programming Techniques

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.

scholarly journals A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Wee Loon Lim ◽  
Antoni Wibowo ◽  
Mohammad Ishak Desa ◽  
Habibollah Haron
Keyword(s):  
Tabu Search ◽  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Optimization Technique ◽  
Quadratic Assignment ◽  
Hybrid Technique ◽  
Mutation Operator ◽  
Migration Strategy ◽  
Benchmark Instances

The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them.

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