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Meta-heuristics perform differently depending on the problem instance they are solving, meaning that manually choosing an algorithm is not trivial and an automatic selection is desirable. This task can be addressed using a meta-learning approach, which relates the characteristics of the problem instances to the performance of a set of solving algorithms. Therefore, the success of such approach is based on the quality of the extracted set of features. Some studies have proposed the use of features based on Fitness Landscape Analysis (FLA) to characterize optimization problems. However, extracting measures based on FLA usually requires a high computational effort. In a previous work, we have employed meta-heuristic selection on the Quadratic Assignment Problem (QAP) using some FLA measures. This research extends our study by including additional FLA meta-features, by using a less costly extraction method, and by considering more QAP instances. In total, we built five multi-label datasets, each composed of meta-features that were extracted by different sampling sizes, and then we used them to train Random Forest classifiers. Besides presenting satisfactory classification performance, and a decrease in time consumption in relation to our previous work, this selection approach was able to achieve better solution costs over the set of QAP instances if compared to running the meta-heuristics individually.

We commence an algorithmic study of Bulk-Robustness, a new model of robustness in combinatorial optimization. Unlike most existing models, Bulk-Robust combinatorial optimization features a highly nonuniform failure model. Instead of an interdiction budget, Bulk-Robust counterparts provide an explicit list of interdiction sets, comprising the admissible set of scenarios, thus allowing to model correlations between failures of different components in the system, interdiction sets of variable cardinality and more. The resulting model is suitable for capturing failures of complex structures in the system. We provide complexity results and approximation algorithms for Bulk-Robust counterparts of the Minimum Matroid Basis problems and the Shortest Path problem. Our results rely on various techniques, and outline the rich and heterogeneous combinatorial structure of Bulk-Robust optimization., Mathematical Programming, 149 (1-2), ISSN:0025-5610, ISSN:1436-4646

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.

Majority of chapters of this book show usefulness of greedy like algorithms for solving various combinatorial optimization problems. The aim of this chapter is to warn the reader that not always a greedy like approach is a good option and, in certain cases, it is a very bad option being sometimes among the worst possible options. Our message is not a discouragement from using greedy like algorithms altogether; we think that for every combinatorial optimization problem of importance, researchers and practitioners should simply investigate the appropriateness of greedy like algorithms and the existence of better alternatives to them (considering both quality of solution and running time). In many cases, especially when the running time must be very short, the conclusion may still be that the most practical of known approaches is a greedy like algorithm. The Traveling Salesman and Multidimensional Assignment Problems are optimization problems for which greedy like approaches are usually not very successful. We demonstrate this by providing both theoretical and experimental results on greedy like algorithms as well as on some other algorithms that produce (in theory and/or in experiments) much better results without spending significantly more time. There are some general theoretical results that indicate that there are, in fact, many combinatorial optimization problems for which greedy like algorithms are not the best option even among fast construction heuristics, see, e.g., [3, 5, 17]. We will not consider these general results in order to avoid most mathematical details that are not necessary for understanding the results of this chapter. For this reason we will not give proofs here apart from two simple proofs: that of Theorem 8 which shows that some instances on which the greedy algorithm fails are not exotic in a sense and that of Theorem 11 since Theorem 11 is a new result. It is not a trivial question whether a certain algorithm is greedy like or not. In the next section we define an independence system and give the classic definition of the greedy algorithm for such a system. We extend this definition to so-called greedy type algorithms that include such well-known algorithms as the Prim’s algorithm for the minimum spanning tree problem and the nearest neighbor algorithm for the traveling salesman problem. We use the term ‘greedy like’ in an informal way and we include in this class simple and fast construction heuristics that seem to us to be of greedy nature. O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

Kılıç, Haydar (Bilecik, Author) Yüzgeç, Uğur (Bilecik, Author) We propose and develop an improved version of antlion optimizer (ALO), namely tournament selection based antlion optimization algorithm for quadratic assignment problem (QAP). ALO algorithm has some handicaps, such as long run time, local optima stagnation and premature convergence for some problems. The literature describes different methods that improve the performance of antlion optimizer, but most of these are about specific optimization problems. In this paper, we introduce the tournament selection method instead of the roulette wheel method on random walking mechanism of ALO and we update some equations used in ALO algorithm. To compare the proposed tournament selection based ALO (TALO) algorithm with classic ALO, we deal with ten benchmark functions from literature. The comparison results are evaluated according to the different metrics, such as mean best, standard deviation, optimality, accuracy, CPU time, number of function evaluations (NFE). The detailed analyzes of the proposed TALO algorithm are performed. These are the convergence analysis, statistical analysis, search history analysis, trajectory analysis, average distance analysis, computational complexity analysis. The proposed TALO algorithm is compared with the other ALO versions (binary ALO and chaotic ALO variants) for same ten benchmark functions. As last, TALO algorithm has been also implemented for the quadratic assignment problem (QAP). The QAP results has been compared with several well-known meta-heuristic algorithms. TALO's performance has been evaluated with those of binary ALO and chaotic ALO variants for same QAP instance. Finally, the solution quality of proposed TALO algorithm has been analyzed for solving QAP using some instances presented in QAPLIB site. The results provide the proposed TALO algorithm has the best performance in comparison with those of the other meta-heuristic algorithms. Due to the performance of TALO algorithm, we expect this version to be applied for different optimization problems. (C) 2018 Karabuk University. Publishing services by Elsevier B.V. WOS:000463211100031 1-s2.0-S2215098618311340 Q1 Q2

Recently, multi-objective evolutionary algorithms (MOEAs) have been extensively used to solve multi-objective optimization problems (MOPs) since they have the ability to approximate a set of non-dominated solutions in reasonable CPU times. In this paper, we consider the bi-objective quadratic assignment problem (bQAP), which is a variant of the classical QAP, which has been extensively investigated to solve several real-life problems. The bQAP can be defined as having many input flows with the same distances between the facilities, causing multiple cost functions that must be optimized simultaneously. In this study, we propose a memetic algorithm with effective local search and mutation operators to solve the bQAP. Local search is based on swap neighborhood structure whereas the mutation operator is based on ruin and recreate procedure. The experimental results show that our bi-objective memetic algorithm (BOMA) substantially outperforms all the island-based variants of the PASMOQAP algorithm proposed very recently in the literature.

Levy flight Shuffle Frog Leaping Algorithm (LSFLA) is a SFLA variant and enhances the performance of SFLA largely, however, it still has some defects, such as poor convergence and low efficiency. So an improved LSFLA, namely, LSFLA based on Differential perturbation and Quasi-Newton search (DQLSFLA), is proposed in this paper. Firstly, the way of updating only one solution which is the worst one at every sub-iteration in LSFLA is replaced with an all-solution updating way in the subgroup to improve the probability of obtaining the best solution, to omit one sorting step at every sub-iteration and the sub-iteration number parameter setting, to reduce the computational complexity and to enhance the optimization efficiency. Secondly, a random differential perturbation approach and an improved Levy flight updating one are created and used in the subgroup updating to form DLSFLA, that is, the first half frogs in the subgroup use the random differential perturbation updating approach to improve the global search ability, and the last half adopt the improved Levy flight updating method to keep the advantage of the Levy flight updating method and overcome its defects. Finally, quasi-Newton local search is integrated into DLSFLA near the end of the algorithm to improve the convergence speed. Experimental results on the complex functions from CEC-2014 show that DQLSFLA's convergence quality and optimization efficiency are much better than LSFLA's and that compared with quite a few other state-of-the-art algorithms, DQLSFLA has better performance. The results on medical image enhancement and Quadratic Assignment Problem (QAP) also show that DQLSFLA can solve the real word optimization problems better than LSFLA can.

The Quadratic Assignment Problem (QAP) is a combinatorial NP-hard optimization problem that is not solvable in a polynomial time. It has a large number of real-world applications in diverse fields (e.g. facility arrangement in a hospital). The Whale Optimization Algorithm is a new meta-heuristic that achieves a great success in solving the continuous problems. In this paper, we propose a memetic algorithm using the Whale optimization Algorithm (WA) Integrated with a Tabu Search (WAITS) for solving QAP. In fact, this work employs Tabu Search to improve the quality of solution obtained by WA for QAP problem as a local search algorithm. This is an attempt to improve the convergence speed and local search of WA as its main drawbacks. Due to the combinatorial nature of QAP, the continuous values generated from the standard WA were converted to discrete values by the largest real value mapping. The WAITS algorithm is enhanced by a local search that defines a set of neighborhood solutions to improve the accuracy of the obtained solutions. Fourteen different case studies including 122 test problems are employed for analyzing the performance of the proposed WAITS. The results show that the proposed memetic algorithm finds near-optimal solutions with an acceptable computational time. WAITS is compared to several algorithms in the literature. The results show that the proposed algorithm outperforms similar algorithms in the literature.

The Reformulation Linearization Technique (RLT) of Sherali and Adams (Manag Sci 32(10):1274–1290, 1986; SIAM J Discrete Math 3(3):411–430, 1990), when applied to a pure 0–1 quadratic optimization problem with linear constraints (P), constructs a hierarchy of LP (i.e., continuous and linear) models of increasing sizes. These provide monotonically improving continuous bounds on the optimal value of (P) as the level, i.e., the stage in the process, increases. When the level reaches the dimension of the original solution space, the last model provides an LP bound equal to the IP optimum. In practice, unfortunately, the problem size increases so rapidly that for large instances, even computing bounds for RLT models of level k (called RLTk) for small k may be challenging. Their size and their complexity increase drastically with k. To our knowledge, only results for bounds of levels 1, 2, and 3 have been reported in the literature. We are proposing, for certain quadratic problem types, a way of producing stronger bounds than continuous RLT1 bounds in a fraction of the time it would take to compute continuous RLT2 bounds. The approach consists in applying a specific decomposable Lagrangean relaxation to a specially constructed RLT1-type linear 0–1 model. If the overall Lagrangean problem does not have the integrality property, and if it can be solved as a 0–1 rather than a continuous problem, one may be able to obtain 0–1 RLT1 bounds of roughly the same quality as standard continuous RLT2 bounds, but in a fraction of the time and with much smaller storage requirements. If one actually decomposes the Lagrangean relaxation model, this two-step procedure, reformulation plus decomposed Lagrangean relaxation, will produce linear 0–1 Lagrangean subproblems with a dimension no larger than that of the original model. We first present numerical results for the Crossdock Door Assignment Problem, a special case of the Generalized Quadratic Assignment Problem. These show that just solving one Lagrangean relaxation problem in 0–1 variables produces a bound close to or better than the standard continuous RLT2 bound (when available) but much faster, especially for larger instances, even if one does not actually decompose the Lagrangean problem. We then present numerical results for the 0–1 quadratic knapsack problem, for which no RLT2 bounds are available to our knowledge, but we show that solving an initial Lagrangean relaxation of a specific 0–1 RLT1 decomposable model drastically improves the quality of the bounds. In both cases, solving the fully decomposed rather than the decomposable Lagrangean problem to optimality will make it feasible to compute such bounds for instances much too large for computing the standard continuous RLT2 bounds.

Theoretical Computer Science, 745, ISSN:0304-3975

We benchmark the 5000+ qubit system Advantage 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 Advantage 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 DW2000Q sometimes produce more favourable results if they can solve the problems., open-source code available at https://jugit.fz-juelich.de/qip/garden-optimization-problem.git

We present frequent pattern-based search (FPBS) that combines data mining and optimization. FPBS is a general-purpose method that unifies data mining and optimization within the population-based search framework. The method emphasizes the relevance of a modular- and component-based approach, making it applicable to optimization problems by instantiating the underlying components. To illustrate its potential for solving difficult combinatorial optimization problems, we apply the method to the well-known and challenging quadratic assignment problem. We show the computational results and comparisons on the hardest QAPLIB benchmark instances. This work reinforces the recent trend toward closer cooperations between the optimization methods and machine learning or data mining techniques.

© 2020, CIMNE, Barcelona, Spain. Many optimization problems encountered in the real-world have more than two objectives. To address such optimization problems, a number of evolutionary many-objective optimization algorithms were developed recently. In this paper, we tested 18 evolutionary many-objective algorithms against well-known combinatorial optimization problems, including knapsack problem (MOKP), traveling salesman problem (MOTSP), and quadratic assignment problem (mQAP), all up to 10 objectives. Results show that some of the dominance and reference-based algorithms such as non-dominated sort genetic algorithm (NSGA-III), strength Pareto-based evolutionary algorithm based on reference direction (SPEA/R), and Grid-based evolutionary algorithm (GrEA) are promising algorithms to tackle MOKP and MOTSP with 5 and 10 while increasing the number of objectives. Also, the dominance-based algorithms such as MaOEA-DDFC as well as the indicator-based algorithms such as HypE are promising to solve mQAP with 5 and 10 objectives. In contrast, decomposition based algorithms present the best on almost problems at saving time. For example, t-DEA displayed superior performance on MOTSP for up to 10 objectives.

Quantum annealing and D-Wave quantum annealer attracted considerable attention for their ability to solve combinatorial optimization problems. In order to solve other type of optimization problems, it is necessary to apply certain kinds of mathematical transformations. However, linear constraints reduce the size of problems that can be represented in quantum annealers, owing to the sparseness of connections between qubits. For example, the quadratic assignment problem (QAP) with linear equality constraints can be solved only up to size 12 in the quantum annealer D-Wave Advantage, which has 5640 qubits. To overcome this obstacle, Ohzeki developed a method for relaxing the linear equality constraints and numerically verified the effectiveness of this method with some target problems, but others remain unsolvable. In particular, it is difficult to obtain feasible solutions to problems with hard constraints, such as the QAP. We therefore propose a method for solving the QAP with quantum annealing by applying a post-processing bit-flip heuristic algorithm to solutions obtained by the Ohzeki method. In a numerical experiment, we solved a sparse QAP by the proposed method. This sparse QAP has been used in areas such as item listing on an E-commerce website. We successfully solved a QAP of size 19 with high accuracy for the first time using D-Wave Advantage. We also confirmed that the bit-flip heuristic algorithm moves infeasible solutions to nearby feasible solutions in terms of Hamming distance with good computational efficiency., Comment: 11 pages. The first page includes the initial screen displaying IEEE-copyrighted material

This paper aims to highlight the motivations for investigating genetic algorithms to solve the DNA Fragments Assembly problem (DNA_FA). DNA_FA is an optimization problem that attempts to reconstruct the original DNA sequence by finding the shortest DNA sequence from a given set of fragments. We showed that the DNA_FA optimization problem is a special case of the two well-known optimization problems: The Traveling Salesman Problem (TSP) and the Quadratic Assignment Problem (QAP). TSP and QAP are important problems in the field of combinatorial optimization and for which there exists an abundant literature. Genetic Algorithms (GA) applied to these problems have led to very satisfactory results in practice. In the perspective of designing efficient genetic algorithms to solve DNA_FA we showed the existence of a polynomial-time reduction of DNA-FA into TSP and QAP enabling us to point out some technical similarities in terms of solutions and search space complexity. We then conceptually designed a genetic algorithm platform for solving the DNA-FA problem inspired from the existing efficient genetic algorithms in the literature solving TSP and QAP problems. This platform offers several ingredients enabling us to create several variants of GA solvers for the DNA assembly optimization problems.

This paper studies a specific class of multiobjective combinatorial optimization problems (MOCOPs), namely the permutation-based MOCOPs. Many commonly seen MOCOPs, e.g., multiobjective traveling salesman problem (MOTSP), multiobjective project scheduling problem (MOPSP), belong to this problem class and they can be very different. However, as the permutation-based MOCOPs share the inherent similarity that the structure of their search space is usually in the shape of a permutation tree, this paper proposes a generic multiobjective set-based particle swarm optimization methodology based on decomposition, termed MS-PSO/D. In order to coordinate with the property of permutation-based MOCOPs, MS-PSO/D utilizes an element-based representation and a constructive approach. Through this, feasible solutions under constraints can be generated step by step following the permutation-tree-shaped structure. And problem-related heuristic information is introduced in the constructive approach for efficiency. In order to address the multiobjective optimization issues, the decomposition strategy is employed, in which the problem is converted into multiple single-objective subproblems according to a set of weight vectors. Besides, a flexible mechanism for diversity control is provided in MS-PSO/D. Extensive experiments have been conducted to study MS-PSO/D on two permutation-based MOCOPs, namely the MOTSP and the MOPSP. Experimental results validate that the proposed methodology is promising.

Combinatorial optimization problems arise from various real life situations and the quadratic assignment problem (QAP) to model a facility layout problem or a plant location problem is such an example. While examining the facility layout of a semi-automated bus body manufacturing unit, a bi-objective facility layout optimization problem is identified in which the solution space of the second objective function depends and changes upon the feasible solutions of the first objective function. In this paper, the said problem is first defined in the form of a bi-objective quadratic dependent location assignment problem (bi-d-QAP), a heuristic solution approach is then provided, and finally, a modified artificial bee colony algorithm is proposed while combining both the genetic and neighborhood search algorithms to solve the considered bi-d-QAP. The data obtained from the above-mentioned manufacturing unit are utilized to show how the proposed algorithm performs better in comparison to some of the popular state-of-the-art optimization algorithms.

Advances in Pareto optimization techniques have encouraged the study of their application to solve single-objective optimization problems. The motive is that the Pareto concept can be an effective approach to reduce the impacts of local optima. The most challenging task in developing such an approach is the reformulation of the target single-objective to multiple objectives. This paper proposes a new multi-objectivization approach by introducing an additional helper objective that is to be optimized with the primary objective simultaneously using Pareto local search. As a key feature, the additional objective is formulated as a function of the primary objective and penalties associated to solution features. The penalties are dynamically updated during the search, with the hope to guide the search to avoid non-promising features for the primary objective. Computational results on the traveling salesman problem and the quadratic assignment problem confirm the effectiveness of the proposed approach in comparison to other multi-objectivization approaches and state-of-the-art methods on these benchmarks.

The Quadratic assignment problem (QAP) is to assign a set of facilities to a set of locations with given distances between the locations and given flows between the facilities such that the sum of the products between flows and distances is minimized, which is a notoriously difficult NP-hard combinatorial optimization problem. A lot of heuristics have been proposed for the QAP problem, and some of them have proved to be efficient approximation algorithms for this problem. Ant colony optimization (ACO) is a general-purpose heuristic and usually considered as an approximation algorithms for NP-hard optimization problems. However, we know little about the performance of ACO for QAP from a theoretical perspective. This paper contributes to a theoretical understanding of ACO on the QAP problem. The worst-case bound on a simple ACO algorithm called (1+1) Max-min ant algorithm ((1+1) MMAA) for the QAP problem is presented. It is shown that a degenerate (1+1) MMAA finds an approximate solution on the QAP problem. Finally, we reveal that ACO can outperform the 2-exchange local search algorithm on an instance of the QAP problem.

This paper applies four population-based classical meta-heuristic algorithms to solve a pick-and-place optimization problem for a surface mounter in a PCB assembly environment. A mathematical model of this optimization problem is formulated as an integrated problem of the capacitated vehicle routing problem and the quadratic assignment problem, which are well-known NP-hard problems. A brief description of each method is presented and special operators for the integer encoded solutions are developed. Ten real-world PCB samples are tested and optimized using all the four algorithms. The experiment results show that the genetic algorithm has better performance than the others in terms of solution quality, especially the deviation of results from multiple trials, and computation time.

The bat algorithm is one of the recent nature-inspired algorithms, which has been emerged as a powerful search method for solving continuous as well as discrete problems. The quadratic assignment problem is a well-known NP-hard problem in combinatorial optimization. The goal of this problem is to assign n facilities to n locations in such a way as to minimize the assignment cost. For that purpose, this paper introduces a novel discrete variant of bat algorithm to deal with this combinatorial optimization problem. The proposed algorithm was evaluated on a set of benchmark instances from the QAPLIB library and the performance was compared to other algorithms. The empirical results of exhaustive experiments were promising and illustrated the efficacy of the suggested approach.

Solution representation is an important aspect of the development of a meta-heuristic. However, most meta-heuristics focus on the algorithm aspect rather than the solution representation. As the scale of the optimization problem under study rises, the solution representation becomes ever more crucial because the computational performance tends to deteriorate for three reasons: (1) increased landscape complexity, (2) exponential growth of search space, and (3) costly function evaluation. In this study, data compression of solution representation is explored to improve the performance of meta-heuristics in terms of compression efficiency and solution quality. A proposed new data compression scheme – variable-length solution representation compression for meta-heuristics – is developed and tested against benchmarked problem instances from the quadratic assignment problem library (QAPLIB) and additional large problem instances. The analyzed results indicate that the compressed solution representation scheme under a meta-heuristic framework performs well against the QAPLIB and large problem instances with less space complexity and computation time.

This paper addresses the problem of joint power management and radar assignment to detect multiple targets in surveillance region for a distributed mono-static radar network while a low probability of interception (LPI) has been attained. Based on detection probabilities and target location estimates, the targeted problem is formulated as a combinatorial non-convex optimization problem which needs exhaustive search through all assignment schemes to reach optimal solution. Due to NP-hardness and non-convexity of the problem, some relaxations are proposed to transform the problem to a more tractable form. The main problem can be considered from two viewpoints, without information fusion and with information fusion. As another relaxation, we separated power allocation from radar assignments through two sub-problems in which first, the optimum power allocation is obtained for each assignment scheme and second, the target assignment schemes are selected based on the allocated powers. Simulation results show that our proposed algorithms not only guarantee detection performances but also considerably improve LPI specification in comparison with benchmark algorithms.

The pipeline task of scheduling theory (flow shop) with the standard constraints, the variables of which are the times of the beginning of processing of each of the tasks on the corresponding device are investigated. Tasks of this type belong to the NP-complex class with the number of processing devices more than two. The number of calculations and the search time for the optimal schedule grow in proportion to n !, where n is the number of jobs. By some transformations the constraints of the pipeline task are reduced to analytical functions of the unknown variables, and the objective function to the linear function of these variables. The number of functions, the constraints of the optimization problem, depends polynomially on the number of tasks of the original pipeline task. Then, using the method of exact quadratic regularization (EQR), let’s pass to the problem of convex optimization. Since the number of constraints depends polynomially on the number of jobs, the search time of the optimal schedule will grow polynomially for a fixed accuracy of the solution. Thus, the NP-complex problem of scheduling theory is transformed to the problem of convex optimization with a linear objective function. It is shown that any pipeline problem of scheduling theory reduces to the problem of a minimum of a linear function with a set of linear and quadratic constraints, that is, to a problem of convex optimization. A model example is considered and an optimal schedule with a given accuracy is obtained by the method of exact quadratic regularization.

Accurate fault detection and isolation requires signal processing of measurement signals which are contaminated with noise. Typically, gas turbine faults are revealed by sharp trend shifts in the signals and these trend shifts should be preserved during signal processing. Linear filters can smooth out the sharp trend shifts while removing noise. However, nonlinear filters such as the weighted recursive median (WRM) filters show good noise reduction while preserving key signal features if their integer weights are determined optimally. We propose the ant colony optimization (ACO) method coupled with local search to calculate the integer weights of WRM filters. It is found that the filter weight optimization problem is mathematically equivalent to the quadratic assignment problem which can be solved by ACO. Optimal parameters for the ACO are found using numerical experiments. The WRM filter is demonstrated for abrupt and gradual faults in gas turbines and is found to yield noise reduction of 52–64% for simulated noisy signals considered in this paper.

Bi-level optimization problems (BOPs) are a class of challenging problems with two levels of optimization tasks. The main goal is to optimize the upper level problem which has another optimization problem as a constraint. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the upper level one. Such a requirement makes the optimization problem difficult to solve, and has kept the researchers busy towards devising methodologies, which can efficiently handle the problem. Recently, a new research field, called EBO (Evolutionary Bi-Level Optimization) has appeared thanks to the promising results obtained by the use of EAs (Evolutionary Algorithms) to solve such kind of problems. However, most of these promising results are restricted to the continuous case. The number of existing EBO works for the discrete (combinatorial case) bi-level problems is relatively small when compared to the field of evolutionary continuous BOP. Motivated by this observation, we have recently proposed a Co-evolutionary Decomposition-Based Algorithm (CODBA) to solve combinatorial bi-level problems. The recently proposed approach applies a Genetic Algorithm to handle BOPs. Besides, a new recently proposed meta-heuristic called CRO has been successfully applied to several practical NP-hard problems. To this end, we propose in this work a CODBA-CRO (CODBA with Chemical Reaction Optimization) to solve BOP. The experimental comparisons against other works within this research area on a variety of benchmark problems involving various difficulties show the effectiveness and the efficiency of our proposal.

This paper presents GHOST , a combinatorial optimization framework that a real-time strategy (RTS) AI developer can use to model and solve any problem encoded as a constraint satisfaction/optimization problem (CSP/COP). We show a way to model three different problems as a CSP/COP, using instances from the RTS game StarCraft as test beds. Each problem belongs to a specific level of abstraction (the target selection as reactive control problem, the wall-in as a tactics problem, and the build order planning as a strategy problem). In our experiments, GHOST shows good results computed within some tens of milliseconds. We also show that GHOST outperforms state-of-the-art constraint solvers, matching them on the resources allocation problem, a common combinatorial optimization problem.

We review some complexity results and present a viable heuristic approach based on the Variable Neighborhood Search (VNS) framework for multimode extension of combinatorial optimization problems, such as the the Set Covering Problem (SCP) and the Covering Location Problem (CLP).

Methods of tropical (idempotent) mathematics are applied to the solution of minimax location problems under constraints on the feasible location region. A tropical optimization problem is first considered, formulated in terms of a general semifield with idempotent addition. To solve the optimization problem, a parameter is introduced to represent the minimum value of the objective function, and then the problem is reduced to a parametrized system of inequalities. The parameter is evaluated using existence conditions for solutions of the system, whereas the solutions of the system for the obtained value of the parameter are taken as the solutions of the initial optimization problem. Then, a minimax location problem is formulated to locate a single facility on a line segment in the plane with a rectilinear metric. When no constraints are imposed, this problem, which is also known as the Rawls problem or the messenger boy problem, has known geometric and algebraic solutions. For the location problems, where the location region is restricted to a line segment, a new solution is obtained, based on the representation of the problems in the form of the tropical optimization problem considered above. Explicit solutions of the problems for various positions of the line are given both in terms of tropical mathematics and in the standard form.

International audience; Parallelization is an important paradigm for solving massive optimization problems. Understanding how to fully benefit form the aggregated computing power and what makes a parallel strategy successful is a difficult issue. In this study, we propose a simple parallel iterative tabu search (PITS) and study its effectiveness with respect to different experimental settings. Using the quadratic assignment problem (QAP) as a case study, we first consider different small-and medium-size instances from the literature and then tackle a large-size instance that was rarely considered due the its inherent solving difficulty. In particular, we show that a balance between the number of function evaluations each parallel process is allowed to perform before resuming the search is a critical issue to obtain an improved quality.

For e-commerce websites, deciding the manner in which items are listed on webpages is an important issue because it can dramatically affect item sales. One of the simplest strategies of listing items to improve the overall sales is to do so in a descending order of sales or sales numbers. However, in lists generated using this strategy, items with high similarity are often placed consecutively. In other words, the generated item list might be biased toward a specific preference. Therefore, this study employs penalties for items with high similarity being placed next to each other in the list and transforms the item listing problem to a quadratic assignment problem (QAP). The QAP is well-known as an NP-hard problem that cannot be solved in polynomial time. To solve the QAP, we employ quantum annealing (QA), which exploits the quantum tunneling effect to efficiently solve an optimization problem. In addition, we propose a problem decomposition method based on the structure of the item listing problem because the quantum annealer we use (i.e., D-Wave 2000Q) has a limited number of quantum bits. Our experimental results indicate that we can create an item list that considers both sales and diversity. In addition, we observe that using the problem decomposition method based on a problem structure can lead to a better solution with the quantum annealer in comparison with the existing problem decomposition method.

The idea of k-adaptability in two-stage robust optimization is to calculate a fixed number k of second-stage policies here-and-now. After the actual scenario is revealed, the best of these policies is selected. This idea leads to a min---max---min problem. In this paper, we consider the case where no first stage variables exist and propose to use this approach to solve combinatorial optimization problems with uncertainty in the objective function. We investigate the complexity of this special case for convex uncertainty sets. We first show that the min---max---min problem is as easy as the underlying certain problem if k is greater than the number of variables and if we can optimize a linear function over the uncertainty set in polynomial time. We also provide an exact and practical oracle-based algorithm to solve the latter problem for any underlying combinatorial problem. On the other hand, we prove that the min---max---min problem is NP-hard for every fixed number k, even when the uncertainty set is a polyhedron, given by an inner description. For the case that k is smaller or equal to the number of variables, we finally propose a fast heuristic algorithm and evaluate its performance.

In the classical min-max approach to robust combinatorial optimization, a single feasible solution is computed that optimizes the worst case over a given set of considered scenarios. As is well known, this approach is very conservative, leading to solutions that in the average case are far from being optimal. In this paper, we present a different approach: the objective is to compute k feasible solutions such that the best of these solutions for each given scenario is worst-case optimal, i.e., we model the problem as a min-max-min problem. In practice, these k solutions can be computed once in a preprocessing phase, while choosing the best of the k solutions can be done in real time for each scenario occuring. Using a polynomial-time oracle algorithm, we show that the problem of choosing k min-max-min optimal solutions is as easy as the underlying combinatorial problem if k ≥ n + 1 and if the uncertainty set is a polytope or an ellipsoid. On contrary, in the discrete scenario case, many tractable problems such as the shortest path problem or the minimum spanning tree problem turn NP-hard in the new approach.

The real world problems in the supply-chain domain are generally constrained and combinatorial in nature. Several nature-/bio-/socio-inspired metaheuristic methods have been proposed so far solving such problems. An emerging metaheuristic methodology referred to as Cohort Intelligence (CI) in the socio-inspired optimization domain is applied in order to solve three selected combinatorial optimization problems. The problems considered include a new variant of the assignment problem which has applications in healthcare and inventory management, a sea-cargo mix problem and a cross-border shipper selection problem. In each case, we use two benchmarks for evaluating the effectiveness of the CI method in identifying optimal solutions. To assess the quality of solutions obtained by using CI, we do comparative testing of its performance against solutions generated by using CPLEX. Furthermore, we also compare the performance of the CI method to that of specialized multi-random-start local search optimization methods that can be used to find solutions to these problems. The results are robust with a reasonable computational time and accuracy.

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.

Quadratic Assignment Problems (QAPs) are the hardest of combinatorial optimization problems, with some problems of sizes of the order of 30 still remaining unsolved optimally. Solving these problems with exact optimization methods is cumbersome and hence the use of non-traditional optimization methods is advisable. The discrete version of Particle Swarm Optimization (DPSO) is a widely accepted non-conventional optimization algorithm for combinatorial optimization problems. This paper uses Taguchi's robust design approach to determine the best combination of parameters for discrete particle swarm optimization algorithm for solving quadratic assignment problems.

This paper concerns the design of optimized single-finger keyboard layouts on smartphones. In the literature, the optimization problem associated with assigning characters to keys on a single-finger keyboard is denoted as single-finger keyboard layout problem (SK-QAP), which can be seen as a variant of the quadratic assignment problem (QAP), a classical combinatorial optimization problem. To solve it, we propose a simple yet effective local search-based metaheuristic which is composed of three neighborhood structures. Two of them were previously applied to solve the SK-QAP, whereas the third one consists of an adaptation of a QAP neighborhood and it was introduced in this work. In addition, two perturbation mechanisms were developed as diversification procedures and together with the latter neighborhood structure, they revealed to be highly beneficial for improving the performance of the algorithm. Computational experiments were carried out on benchmark instances for English, French, Italian and Spanish. The results obtained were extremely competitive both in terms of solution quality and CPU time, such that all best known solutions were found in a matter of seconds. Moreover, we developed and solved benchmark instances for Portuguese, which currently has more than 230 million speakers, as a first or second language, and also uses the Latin alphabet. We have also proposed and solved bilingual instances, combining English, one of the top spoken languages in the world, with each of the remaining four ones. In addition, we quantify the potential practical benefits of adopting alternative and smartphone-oriented optimized single-finger keyboards, when compared to well-known layouts, namely QWERTY and AZERTY, for the five languages and bilingual variants considered. Finally, we show the efficiency of the proposed algorithm when generating layouts based on other existing arrangements, namely Metropolis and FITALY.

International audience; The graph edit distance (GED) is a widely used distance measure for attributed graphs. It has recently been shown that the problem of computing GED, which is a NP-hard optimization problem, can be formulated as a quadratic assignment problem (QAP). This formulation is useful, since it allows to derive well performing approximative heuristics for GED from existing techniques for QAP. In this paper, we focus on the case where the edit costs that underlie GED are quasimetric. This is the case in many applications of GED. We show that, for quasimetric edit costs, it is possible to reduce the size of the corresponding QAP formulation. An empirical evaluation shows that this reduction significantly speeds up the QAP-based approximative heuristics for GED.

Algorithms for data visualizations are essential tools for transforming data into useful narratives. Unfortunately, very few visualization algorithms can handle the large datasets of many real-world scenarios. In this study, we address the visualization of these datasets as a Multi-Objective Optimization Problem. We propose mQAPViz, a divide-and-conquer multi-objective optimization algorithm to compute large-scale data visualizations. Our method employs the Multi-Objective Quadratic Assignment Problem (mQAP) as the mathematical foundation to solve the visualization task at hand. The algorithm applies advanced sampling techniques originating from the field of machine learning and efficient data structures to scale to millions of data objects. The algorithm allocates objects onto a 2D grid layout. Experimental results on real-world and large datasets demonstrate that mQAPViz is a competitive alternative to existing techniques., Proceeding GECCO 18 Proceedings of the Genetic and Evolutionary Computation Conference. Pages 737-744 Kyoto, Japan - July 15 - 19, 2018

Optimal flight gate assignment is a highly relevant optimization problem from airport management. Among others, an important goal is the minimization of the total transit time of the passengers. The corresponding objective function is quadratic in the binary decision variables encoding the flight-to-gate assignment. Hence, it is a quadratic assignment problem being hard to solve in general. In this work we investigate the solvability of this problem with a D-Wave quantum annealer. These machines are optimizers for quadratic unconstrained optimization problems (QUBO). Therefore the flight gate assignment problem seems to be well suited for these machines. We use real world data from a mid-sized German airport as well as simulation based data to extract typical instances small enough to be amenable to the D-Wave machine. In order to mitigate precision problems, we employ bin packing on the passenger numbers to reduce the precision requirements of the extracted instances. We find that, for the instances we investigated, the bin packing has little effect on the solution quality. Hence, we were able to solve small problem instances extracted from real data with the D-Wave 2000Q quantum annealer., Comment: Updated figure 2

Semidefinite optimization is a strong tool in the study of NP-hard combinatorial optimization problems. On the one hand, semidefinite optimization problems are in principle solvable in polynomial time (with fixed precision), on the other hand, their modeling power allows to naturally handle quadratic constraints. Contrary to linear optimization with the efficiency of the Simplex method, the algorithmic treatment of semidefinite problems is much more subtle and also practically quite expensive. This survey-type article is meant as an introduction for a non-expert to this exciting area. The basic concepts are explained on a mostly intuitive level, and pointers to advanced topics are given. We provide a variety of semidefinite optimization models on a selection of graph optimization problems and give a flavour of their practical impact.

The problem of finding the state of minimum potential energy through the rearrangement of water parcels with a nonlinear equation of state is discussed in the context of a combinatorial optimization problem. It is found that the problem is identical to a classical optimization problem called the linear assignment problem. This problem belongs to a problem class known as P, a class of problems that have known efficient solutions. This is very fortunate since this study’s problem has been suggested to be an asymmetric traveling salesman problem. A problem that belongs to a class called NP-hard, for which no efficient solutions are known. The difference between the linear assignment problem and the traveling salesman problem is discussed and made clear by looking at the different constraints used for the two problems. It is also shown how the rearrangement of water parcels that minimizes the potential energy can be found in polynomial time using the so-called Hungarian algorithm. The Hungarian algorithm is then applied to a simplified ocean stratification, and the result is compared to a few different approximate solutions to the minimization problem. It is found that the improved accuracy over the approximate methods comes at a high computational cost. Last, the algorithm is applied to a realistic ocean stratification using a technique that splits the minimization problem into smaller bits.

Teaching–Learning-Based Optimization (TLBO) is a novel swarm intelligence metaheuristic that is reported as an efficient solution method for many optimization problems. It consists of two phases where all individuals are trained by a teacher in the first phase and interact with classmates to improve their knowledge level in the second phase. In this study, we propose a set of TLBO-based hybrid algorithms to solve the challenging combinatorial optimization problem, Quadratic Assignment. Individuals are trained with recombination operators and later a Robust Tabu Search engine processes them. The performances of sequential and parallel TLBO-based hybrid algorithms are compared with those of state-of-the-art metaheuristics in terms of the best solution and computational effort. It is shown experimentally that the performance of the proposed algorithms are competitive with the best reported algorithms for the solution of the Quadratic Assignment Problem with which many real life problems can be modeled.

Display Omitted A major optimization problem in synthesis of sequential circuits is State Assignment (SA).Cuckoo search optimization (CSO) algorithm is employed for solving the SA problem.CSO targets area minimization of synthesized sequential circuits.CSO results outperform deterministic and non-deterministic heuristic optimization methods. A major optimization problem in the synthesis of sequential circuits is State Assignment or State Encoding in Finite State Machines (FSMs). The state assignment of an FSM determines the complexity of its combinational circuit and thus area, delay, testability and power dissipation. Since optimal state assignment is an NP-hard problem and existing deterministic algorithms produce solutions far from best known solutions, we resort to the use of non-deterministic iterative optimization heuristics. This paper proposes the use of cuckoo search optimization (CSO) algorithm for solving the state assignment problem (SAP) of FSMs with the aim of minimizing area of the resulting sequential circuit. Results obtained from the CSO algorithm are compared with those obtained from binary particle swarm optimization (BPSO) algorithm, genetic algorithm (GA), and the well-known deterministic methods of NOVA and JEDI. The results indicate that CSO outperforms deterministic methods as well as other non-deterministic heuristic optimization methods.

This paper deals with the problem of optimizing a factory floor layout in a Slovenian furniture factory. First, the current state of the manufacturing system is analyzed by constructing a discrete event simulation (DES) model that reflects the manufacturing processes. The company produces over 10,000 different products, and their manufacturing processes include approximately 30,000 subprocesses. Therefore, manually constructing a model to include every subprocess is not feasible. To overcome this problem, a method for automated model construction was developed to construct a DES model based on a selection of manufacturing orders and relevant subprocesses. The obtained simulation model provided insight into the manufacturing processes and enable easy modification of model parameters for optimizing the manufacturing processes. Finally, the optimization problem was solved: the total distance the products had to traverse between machines was minimized by devising an optimal machine layout. With the introduction of certain simplifications, the problem was best described as a quadratic assignment problem. A novel heuristic method based on force-directed graph drawing algorithms was developed. Optimizing the floor layout resulted in a significant reduction of total travel distance for the products.