scholarly journals Review on the Methods to Solve Combinatorial Optimization Problems Particularly: Quadratic Assignment Model

2018 ◽  
Vol 7 (3.20) ◽  
pp. 15
Author(s):  
Asaad Shakir Hameed ◽  
Burhanuddin Mohd Aboobaider ◽  
Ngo Hea Choon ◽  
Modhi Lafta Mutar ◽  
Wassim Habib Bilal
Keyword(s):  
Combinatorial Optimization ◽  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Location Theory ◽  
Quadratic Assignment ◽  
Combinatorial Optimization Problems ◽  
Assignment Model ◽  
Facilities Location ◽  
Basic Characteristics

The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problem (COPs) in the branch of optimization or operation research in mathematics, from the category of the Facilities Location Problems (FLPs).  The quadratic assignment problem (QAP) be appropriate to the group of NP-hard issues and is measured as a challenging problem of the combinatorial optimization. QAP in Location Theory considers one of the problems of facilities tracing which the rate of locating a facility be determined by the spaces between facilities as well as the communication among the further facilities. QAP was presented in 1957 by Beckman and Koopmans as they were attempting to model a problem of facilities location. To survey the researcher’s works for QAP and applied, the mapped research landscape outlines literature into a logical classification and discovers this field basic characteristics represented on the motivation to use the quadratic assignment problem applied in hospital layout and campus planning. This survey achieved a concentrated each QAP article search in three key databases: Web of Science, Science Direct, and IEEE Xplore. Those databases are regarded extensive adequate in covering QAP and the methods utilized in solving 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.

scholarly journals A Methodology to Find the Elementary Landscape Decomposition of Combinatorial Optimization Problems

2011 ◽  
Vol 19 (4) ◽  
pp. 597-637 ◽  
Author(s):  
Francisco Chicano ◽  
L. Darrell Whitley ◽  
Enrique Alba
Keyword(s):  
Combinatorial Optimization ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Combinatorial Optimization Problem ◽  
Quadratic Assignment ◽  
Neighborhood Structure ◽  
Combinatorial Optimization Problems ◽  
Elementary Landscape

A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes.

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 ITERATED TABU SEARCH: AN IMPROVEMENT TO STANDARD TABU SEARCH

2006 ◽  
Vol 35 (3) ◽  
Author(s):  
Alfonsas Misevicius ◽  
Antanas Lenkevicius ◽  
Dalius Rubliauskas
Keyword(s):  
Combinatorial Optimization ◽  
Tabu Search ◽  
High Efficiency ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Special Kind ◽  
Quadratic Assignment ◽  
Combinatorial Optimization Problems ◽  
Diversification Mechanism ◽  
Iterated Tabu Search

The goal of this paper is to discuss the tabu search (TS) meta-heuristic and its enhancement for combinatorial optimization problems. Firstly, the issues related to the principles and specific features of the standard TS are concerned. Further, a promising extension to the classical tabu search scheme is introduced. The most important component of this extension is a special kind of diversification mechanism. We give the paradigm of this new improved TS strategy, which is called an iterated tabu search (ITS). ITS was applied to the difficult combinatorial optimization problems, the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). The results of the experiments with the TSP and QAP show the high efficiency of the ITS strategy. The outstanding performance of ITS is also demonstrated by the fact that the new record-breaking solutions were found for the hard QAP instances - tai80a and tai100a.

scholarly journals Algorithms for exact solutions to combinatorial optimization problems

2013 ◽  
Author(s):  
Θεόδωρος Γκεβεζές
Keyword(s):  
Integer Programming ◽  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment ◽  
Search Procedure ◽  
Np Hard ◽  
Adaptive Search ◽  
Programming Formulation ◽  
Combinatorial Optimization Problems

Το Shortest Superstring Problem (SSP) είναι ένα πρόβλημα συνδυαστικής βελτιστοποίησης που έχει προσελκύσει το ενδιαφέρων πολλών ερευνητών, λόγω των εφαρμογών του. Μπορεί να χρησιμοποιηθεί σε προβλήματα Υπολογιστικής Μοριακής Βιολογίας όπως η αλληλούχιση του DNA και σε προβλήματα της επιστήμης υπολογιστών όπως η συμπίεση δεδομένων. Το SSP είναι ένα NP-hard πρόβλημα. Ένα άρθρο ανασκόπησης για το SSP παρουσιάζεται στο πρώτο κεφάλαιο της παρούσας διατριβής με έναν περιεκτικό και σαφή τρόπο, καλύπτοντας ολόκληρη τη σχετική βιβλιογραφία, αναδεικνύοντας την κατακτημένη γνώση και βοηθώντας στην μελλοντική έρευνα.Η μέθοδος GRASP (Greedy Randomized Adaptive Search Procedure) είναι μια επαναληπτική ευρετική μέθοδος για συνδυαστική βελτιστοποίηση. Η μέθοδος Path Relinking (PR) αποτελεί έναν τρόπο ενοποίησης των στρατηγικών εντατικοποίησης και διαφοροποίησης στην αναζήτηση για βέλτιστες λύσεις. Η PR στα πλαίσια του GRASP εισήχθη ως μηχανισμός μνήμης για την αξιοποίηση των δεδομένων από καλές λύσεις που έχουν ήδη βρεθεί. Στο δεύτερο κεφάλαιο, παρουσιάζεται η υλοποίηση της μεθόδου GRASP με PR για το SSP. Η νέα μέθοδος λύνει στιγμιότυπα μεγάλης κλίμακας και υπερτερεί του φυσικού άπληστου αλγόριθμου στη συντριπτική πλειοψηφία των στιγμιοτύπων που δοκιμάστηκαν. Η προτεινόμενη μέθοδος είναι ικανή να παράγει πολλαπλές λύσεις κοντά στο βέλτιστο, γεγονός το οποίο είναι σημαντικό για την πρακτική της αλληλούχισης του DNA και επιτρέπει μια φυσική και εύκολη παράλληλη υλοποίηση. Ένα σύνολο αναφοράς στιγμιοτύπων με γνωστή βέλτιστη λύση κατασκευάστηκε χρησιμοποιώντας μια νέα Διατύπωση Ακέραιου Προγραμματισμού (Integer Programming Formulation) για το SSP.Η οικογένεια των γράφων επικάλυψης αποτελεί ένα κατάλληλο είδος δομής δεδομένων για την περίπτωση του SSP. Έχουν εφαρμογές στην αλληλούχιση γονιδιώματος, στην συμπίεση ακολουθιών και στον χρονοπρογραμματισμό μηχανών. Ένας κατευθυνόμενος γράφος με βάρη είναι γράφος επικάλυψης αν υπάρχει ένα σύνολο από ακολουθίες, οι οποίες βρίσκονται σε ένα προς ένα αντιστοιχία με τις κορυφές του γράφου, έτσι ώστε κάθε βάρος του γράφου να ισούται με την επικάλυψη μεταξύ των αντίστοιχων ακολουθιών. Στο τρίτο κεφάλαιο της παρούσας διατριβής, παρουσιάζεται ένα θεώρημα χαρακτηρισμού των γράφων επικάλυψης και ο αντίστοιχος αλγόριθμος αναγνώρισής τους.Το Quadratic Assignment Problem (QAP) είναι ένα από τα δυσκολότερα προβλήματα συνδυαστικής βελτιστοποίησης. Το QAP είναι ένα NP-hard πρόβλημα, ενώ η εύρεση ενός ε-προσεγγιστικού αλγόριθμου για αυτό είναι επίσης δύσκολη. Ο κλασικός άπληστος αλγόριθμος για διακριτά προβλήματα βελτιστοποίησης όπου η βέλτιστη λύση είναι ένα μεγιστοτικό ανεξάρτητο υποσύνολο ενός πεπερασμένου συνόλου βάσης με στοιχεία με βάρη, μπορεί να οριστεί με δύο διαφορετικούς τρόπους που είναι δυϊκοί ο ένας προς το άλλο. Τον άπληστο-εισαγωγής (greedy-in) αλγόριθμο, όπου μια λύση κατασκευάζεται από ένα κενό σύνολο με την εισαγωγή του επόμενου καλύτερου στοιχείου, ενός κάθε φορά, μέχρι να προκύψει μια μη εφικτή λύση και τον άπληστο-εξαγωγής (greedy-out) αλγόριθμο, όπου ξεκινώντας από το σύνολο βάσης, διαγράφεται το επόμενο χειρότερο στοιχείο, ένα κάθε φορά, μέχρι να προκύψει κάποια εφικτή λύση. Έχει αποδειχτεί ότι ενώ ο πρώτος αλγόριθμος παρέχει έναν παράγοντα προσέγγισης για τα προβλήματα μεγιστοποίησης, η απόδοσή του στην χειρότερη περίπτωση δεν είναι φραγμένη για τα προβλήματα ελαχιστοποίησης και το αντίστροφο για τον δεύτερο αλγόριθμο. Στο τέταρτο κεφάλαιο αυτής της διατριβής, παρουσιάζεται ο άπληστος-εξαγωγής αλγόριθμος για το QAP, αφότου αναπτύσσεται ένας συνδυαστικός χαρακτηρισμός των λύσεων του προβλήματος.

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.

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.

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