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Operations Research (OR) analytics play a crucial role in optimizing decision-making processes for real-world problems. The assignment problem, with applications in supply chains, healthcare logistics, and production scheduling, represents a prominent optimization challenge. This paper focuses on addressing the Generalized Quadratic Assignment Problem (GQAP), a well-known NP-hard combinatorial optimization problem. To tackle the GQAP, we propose an OR analytical approach that incorporates efficient relaxations, reformulations, heuristics, and a metaheuristic algorithm. Initially, we employ the Reformulation Linearization Technique (RLT) to generate various linear relaxation models, carefully selecting the most efficient ones. Building upon this foundation, we introduce a robust reformulation based on Benders Decomposition (BD), which serves as the basis for an iterative optimization algorithm applied to the GQAP. Furthermore, we develop a constructive heuristic algorithm to identify near-optimal solutions, followed by an enhancement utilizing an Adaptive Large Neighborhood Search (ALNS) metaheuristic algorithm. This ALNS algorithm is enhanced through the integration of a tabu list derived from Tabu Search (TS) and a decision rule inspired by Simulated Annealing (SA). To validate our approach and evaluate its performance, we conduct a comparative analysis against state-of-the-art algorithms documented in the literature. This comparison confirms the significant improvements achieved in terms of solution quality and computational efficiency through our proposed methodology. These advancements contribute to the state of the art in solving the GQAP and hold the potential to enhance decision-making processes in a wide range of domains. Our methodology demonstrates remarkable improvements in solution quality and computational efficiency when compared to existing approaches, as evidenced by the comparative results with state-of-the-art algorithms. The potential implications of our research extend to optimizing decision-making processes in diverse fields, rendering it highly relevant and impactful. • Analyzing different reformulation linearization inequalities for the GQA. • Introducing a novel Benders decomposition reformulation method for the GQAP. • Developing a new constructive heuristic algorithm for the initial solution of the GQAP. • Proposing different removal–insertion​ heuristics and a local search using a tabu list. • Introducing an efficient adaptive large neighborhood search algorithm for solving the GQAP. [ABSTRACT FROM AUTHOR]

Connection patterns among Local Optima Networks (LONs) can inform heuristic design for optimisation. LONresearch has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON sampling algorithms are therefore important. In this article, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Usingmachine learning,we use estimated LON features to predict search performance for competitive heuristics used in the QAP domain. The results show that by using random forest regression, LONconstruction algorithms produce fitness landscape features which can explain almost all search variance.We find that LON samples better relate to search than enumerated LONs do. The importance of fitness levels of sampled LONs in search predictions is crystallised. Features from LONs produced by different algorithms are combined in predictions for the first time, with promising results for this "super-sampling": a model to predict tabu search success explained 99% of variance. Arguments are made for the use-case of each LON algorithm and for combining the exploitative process of one with the exploratory optimisation of the other. [ABSTRACT FROM AUTHOR]

The noisy intermediate-scale quantum (NISQ) devices that have just emerged in recent years provide an opportunity for the physical realization of quantum circuits. As the first step of mapping quantum circuits to these devices, qubit allocation imposes a great impact on the number of additional quantum operations required throughout the mapping. The global optimization of qubit allocation is NP-hard, but since many current NISQ devices have very few qubits, it is possible to solve this problem exactly. In this paper, we propose an exact approach for qubit allocation, which takes advantage of the branch and bound algorithm as the basic framework. In order to further prune the considerably huge state space, three techniques have been proposed and integrated into the exact approach, including an optimized lower bound for quadratic assignment problem, prioritization of logical qubits, and branch pruning by structural symmetry of physical qubits. Moreover, based on the multiple optimal solutions obtained by the exact approach, we give an error-aware qubit allocation method. For problems that are too large to be solved by the exact approach, we also give a heuristic qubit allocation approach with polynomial time complexity. Experimental evaluations show that the exact approach proposed in this paper is feasible for the qubit allocation of current NISQ architectures. For all benchmarks considered, this exact approach can find multiple optimal solutions to the qubit allocation problem on IBM Melbourne, a 16-qubit NISQ architecture, in no more than 20 min. It can serve as a evaluation baseline of any heuristic approach. Experimental evaluations also show that the proposed heuristic approach is near-optimal in terms of routing cost. Both the exact approach and the heuristic approach can be integrated into existing quantum circuit mapping approaches. [ABSTRACT FROM AUTHOR]

Metaheuristics gained world-wide popularity and researchers have been studying them vigorously in the last two decades. A relatively less explored approach in the improvement of metaheuristics is to design new neighbor generation mechanisms. Neighbor generation mechanisms are very important in the success of any single solution-based heuristic since they directly guide the search. In this study, a neighbor generation mechanism called cantor-set based (CB) method for single solution-based heuristics which use permutation solution representation is described. The inspiration for CB method stems from the recursive algorithm that constructs a cantor set which is a fractal set. Three variations of CB method are discussed (CB-1, CB-2, CB-3) considering the presented design possibilities. The computational experiments are conducted by embedding the mechanisms into the classical local search and simulated annealing algorithms, separately, to test their efficiency and effectiveness by comparing them to classical swap and insertion mechanisms. The traveling salesman problem (TSP) and quadratic assignment problem (QAP) which are very different problems that have incompatible characteristics have been chosen to test the mechanisms and sets of benchmark instances with varying sizes are chosen for the comparisons. The computational tests show that CB-2 gives very favorable results for TSP and CB-1 gives favorable results for QAP which means that CB-2 is suitable for problems that have steep landscapes and CB-1 is suitable for the problems that have flat landscapes. It is observed that CB-3 is a more generalized mechanism because it gives consistently good results for both TSP and QAP instances. The best mechanism for a given instance of the both problem types outperforms the classical neighbor generation of swap and insertion in terms of effectiveness. [ABSTRACT FROM AUTHOR]

Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graphs. However, graph matching that incorporates pairwise constraints can be formulated as a quadratic assignment problem (QAP), which is NP-complete and results in intrinsic computational difficulties. This paper presents a functional representation for graph matching (FRGM) that aims to provide more geometric insights on the problem and reduce the space and time complexities. To achieve these goals, we represent each graph by a linear function space equipped with a functional such as inner product or metric, that has an explicit geometric meaning. Consequently, the correspondence matrix between graphs can be represented as a linear representation map. Furthermore, this map can be reformulated as a new parameterization for matching graphs in Euclidean space such that it is consistent with graphs under rigid or nonrigid deformations. This allows us to estimate the correspondence matrix and geometric deformations simultaneously. We use the representation of edge-attributes rather than the affinity matrix to reduce the space complexity and propose an efficient optimization strategy to reduce the time complexity. The experimental results on both synthetic and real-world datasets show that the FRGM can achieve state-of-the-art performance. [ABSTRACT FROM AUTHOR]

This study investigated the network agenda setting (NAS) model with data gathered from Taiwan's 2012 presidential election. Networks of important objects and candidate attributes in the news were compared with the counterparts generated from public opinion. The overall correlation between the media and public network agendas was positive and significant, thus supporting the NAS model in a non-Western context. In addition, this study found that the NAS model offered more predictive power at the attribute than the object level. The effects of selective exposure in a partisan media system were also incorporated into the investigation. Results showed that partisan selective exposure did not lead to consistent findings about the accentuated association between like-minded media consumption and candidate evaluation. [ABSTRACT FROM AUTHOR]

The bilinear assignment problem (BAP) is a generalization of the well-known quadratic assignment problem. In this paper, we study the problem from the computational analysis point of view. Several classes of neighborhood structures are introduced for the problem along with some theoretical analysis. These neighborhoods are then explored within a local search and variable neighborhood search frameworks with multistart to generate robust heuristic algorithms. In addition, we present several very fast construction heuristics. Our systematic experimental analysis disclosed some interesting properties of the BAP, different from those of comparable models. We have also introduced benchmark test instances that can be used for future experiments on exact and heuristic algorithms for the problem. [ABSTRACT FROM AUTHOR]

We provide the first meaningful documentation and analysis of the 'Idiot' crash implemented by Forrest in Clp that aims to obtain an approximate solution to linear programming (LP) problems for warm-starting the primal simplex method. The underlying algorithm is a penalty method with naive approximate minimization in each iteration. During initial iterations an approach similar to augmented Lagrangian is used. Later the technique corresponds closely to a classical quadratic penalty method. We discuss the extent to which it can be used to obtain fast approximate solutions of LP problems, in particular when applied to linearizations of quadratic assignment problems. [ABSTRACT FROM AUTHOR]

The firefly algorithm (FA) is a swarm intelligence optimization algorithm based on the glow behavior of fireflies in nature. The classic firefly algorithm has the problem that it is easy to fall into the local optimum and the search accuracy is not high in the later stage. An improved firefly algorithm based on chaos mapping strategy was proposed to solve the quadratic assignment problem (QAP). The egocentricity of chaos just avoids the firefly algorithm from falling into the local optimum, enhances its search ability and solves the convergence prematurely phenomenon of the firefly algorithm. The improved algorithm is compared with genetic algorithm (GA), particle swarm optimization (PSO) algorithm and the classic firefly algorithm to solve the same quadratic assignment problems. The simulation experiments results verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we suggest a new rule for parent selection in genetic algorithms inspired by natural evolutionary processes. The new rule is simple to implement in any genetic or hybrid genetic algorithm. We also review some biological principles that inspire genetic algorithms and their extensions. The new rule is tested on the planar p-median problem, also termed the location–allocation problem or the multi-source Weber problem, and the quadratic assignment problem. The genetic algorithm incorporating the new rule provided better results without increasing the computing time including five new best known solutions to well researched problem instances. [ABSTRACT FROM AUTHOR]

We propose a hybrid application of Population Based Ant Colony Optimization that uses a data mining procedure to wisely initialize the pheromone entries. Hybridization of metaheuristics with data mining techniques has been studied by several researchers in recent years. In this line of research, frequent patterns in a number of initial high-quality solutions are extracted to guide the subsequent iterations of an algorithm, which results in an improvement in solution quality and computational time. Our proposal possesses certain differences from and contributions to existing literature. Instead of one single run that incorporates both the main metaheuristic and the data mining module inside, we propose to carry out independent runs and collect elite sets over these trials. Another contribution is the way we use the knowledge gained from the application of the data mining module. The extracted knowledge is used to initialize the memory model in the algorithm rather than to construct new initial solutions. One additional contribution is the use of a path mining algorithm (a specific sequence mining algorithm) rather than Apriori-like association mining algorithms. Computational experiments, conducted both on symmetric Travelling Salesman Problem and symmetric/asymmetric Quadratic Assignment Problem instances, showed that our proposal produces significantly better results, and is more robust than pure applications of population-based ant colony optimization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The transportation and storage of dangerous goods are gradually increasing with the rapid development of China's economy. To ensure safety and increase the operational efficiency of warehouses, we propose a four-door dangerous goods warehouse and a kind of route planning method for forklifts in the newly proposed warehouse. The main innovation of this study is to revolutionize the warehouse design through elevating the routing optimization problem of two forklifts operating in the four-door warehouse considered as a quadratic assignment problem (QAP). Theoretically, the classic particle swarm algorithm (PSO) is used to develop a unique genetic-discrete particle swarm algorithm (DPSO) to solve the proposed QAP. For the simulation, this study utilizes the database from real dangerous goods warehouse using the proposed genetic DPSO algorithm, after which it compares the results with the classic DPSO algorithm and other mathematical calculations. In conclusion, the four-door dangerous goods warehouse concept can improve the efficiency of warehouse management and reduce the cost of management under the condition of maintaining the original safety level, which provides a train of thought for the reform of the dangerous goods warehouse. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper we discuss the problem of locating items within carousel bins in order to minimize the average carousel rotational distance per retrieval. We consider two cases: (1) a single two-dimensional carousel and (2) a group of two one-dimensional carousels. The corresponding problems are formulated as mixed-integer programs. In the second problem we apply concepts from Markovian performance evaluation methods to write the objective functions in a simple linear form. We also define a set of uniqueness constraints that significantly reduces the size of the solution feasibility space. We then apply Benders decomposition algorithm to solve both problems. We develop a closed form solution for the dual subprobem and present numerical results to show the efficiency of the proposed solution methodology. [ABSTRACT FROM AUTHOR]

Two modifications of the repeated iterated tabu algorithm for solving the quadratic assignment problem (with and without kernel allocation technology) are proposed. These modifications are analyzed and compared with the best modern algorithms for solving this problem. The efficiency of the developed algorithms is shown, in particular, for large-scale problems for which new records were found with their help. [ABSTRACT FROM AUTHOR]

We derive an explicit formula, as well as an efficient procedure, for constructing a generalized Jacobian for the projector of a given square matrix onto the Birkhoff polytope, i.e., the set of doubly stochastic matrices. To guarantee the high efficiency of our procedure, a semismooth Newton method for solving the dual of the projection problem is proposed and efficiently implemented. Extensive numerical experiments are presented to demonstrate the merits and effectiveness of our method by comparing its performance against other powerful solvers such as the commercial software Gurobi and the academic code PPROJ (Hager and Zhang in SIAM J Optim 26:1773–1798, 2016). In particular, our algorithm is able to solve the projection problem with over one billion variables and nonnegative constraints to a very high accuracy in less than 15 min on a modest desktop computer. More importantly, based on our efficient computation of the projections and their generalized Jacobians, we can design a highly efficient augmented Lagrangian method (ALM) for solving a class of convex quadratic programming (QP) problems constrained by the Birkhoff polytope. The resulted ALM is demonstrated to be much more efficient than Gurobi in solving a collection of QP problems arising from the relaxation of quadratic assignment problems. [ABSTRACT FROM AUTHOR]

This paper discusses efficient parallel algorithms for obtaining strong lower bounds and exact solutions for large instances of the quadratic assignment problem (QAP). Our parallel architecture is comprised of both multicore processors and compute unified device architecture–enabled NVIDIA graphics processing units (GPUs) on the Blue Waters Supercomputing Facility at the University of Illinois at Urbana–Champaign. We propose novel parallelization of the Lagrangian dual ascent algorithm on the GPUs, which is used for solving a QAP formulation based on the level-2 reformulation linearization technique. The linear assignment subproblems in this procedure are solved using our accelerated Hungarian algorithm [Date K, Rakesh N (2016) GPU-accelerated Hungarian algorithms for the linear assignment problem. Parallel Computing 57:52–72.]. We embed this accelerated dual-ascent algorithm in a parallel branch-and-bound scheme and conduct extensive computational experiments on single and multiple GPUs, using problem instances with up to 42 facilities from the quadratic assignment problem library (QAPLIB). The experiments suggest that our GPU-based approach is scalable, and it can be used to obtain tight lower bounds on large QAP instances. Our accelerated branch-and-bound scheme is able to comfortably solve Nugent and Taillard instances (up to 30 facilities) from the QAPLIB, using a modest number of GPUs. [ABSTRACT FROM AUTHOR]

We propose a new method for computing accurate point‐to‐point mappings between a pair of triangle meshes given imperfect initial correspondences. Unlike the majority of existing techniques, we optimize for a map while leveraging information from the inverse map, yielding results which are highly consistent with respect to composition of mappings. Remarkably, our method considers only a linear number of candidate points on the target shape, allowing us to work directly with high resolution meshes, and to avoid a delicate and possibly error‐prone up‐sampling procedure. Key to this dimensionality reduction is a novel candidate selection process, where the mapped points drift over the target shape, finalizing their location based on intrinsic distortion measures. Overall, we arrive at an iterative scheme where at each step we optimize for the map and its inverse by solving two relaxed Quadratic Assignment Problems using off‐the‐shelf optimization tools. We provide quantitative and qualitative comparison of our method with several existing techniques, and show that it provides a powerful matching tool when accurate and consistent correspondences are required. [ABSTRACT FROM AUTHOR]

The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box, and complementarity (BBC) constraints. Given a POP in the class and a relaxation order, BBCPOP constructs a simple conic optimization problem (COP), which serves as a doubly nonnegative relaxation of the POP, and then solves the COP by applying the bisection and projection method. The COP is expressed with a linear objective function and constraints described as a single hyperplane and two cones, which are the Cartesian product of positive semidefinite cones and a polyhedral cone induced from the BBC constraints. BBCPOP aims to compute a tight lower bound for the optimal value of a large-scale POP in the class that is beyond the comfort zone of existing software packages. The robustness, reliability, and efficiency of BBCPOP are demonstrated in comparison to the state-of-the-art software SDP package SDPNAL+ on randomly generated sparse POPs of degree 2 and 3 with up to a few thousands variables, and ones of degree from 5 to 8 with up to a few hundred variables. Numerical results on BBC-constrained POPs that arise from quadratic assignment problems are also reported. The software package BBCPOP is available at https://sites.google.com/site/bbcpop1/. [ABSTRACT FROM AUTHOR]

In the last decade, many works in combinatorial optimisation have shown that, due to the advances in multi-objective optimisation, the algorithms from this field could be used for solving single-objective problems as well. In this sense, a number of papers have proposed multi-objectivising single-objective problems in order to use multi-objective algorithms in their optimisation. In this article, we follow up this idea by presenting a methodology for multi-objectivising combinatorial optimisation problems based on elementary landscape decompositions of their objective function. Under this framework, each of the elementary landscapes obtained from the decomposition is considered as an independent objective function to optimise. In order to illustrate this general methodology, we consider four problems from different domains: the quadratic assignment problem and the linear ordering problem (permutation domain), the 0-1 unconstrained quadratic optimisation problem (binary domain), and the frequency assignment problem (integer domain). We implemented two widely known multi-objective algorithms, NSGA-II and SPEA2, and compared their performance with that of a single-objective GA. The experiments conducted on a large benchmark of instances of the four problems show that the multi-objective algorithms clearly outperform the single-objective approaches. Furthermore, a discussion on the results suggests that the multi-objective space generated by this decomposition enhances the exploration ability, thus permitting NSGA-II and SPEA2 to obtain better results in the majority of the tested instances. [ABSTRACT FROM AUTHOR]

Abstract With the rapid growth of the Chinese economy, environmental pollution from traditional resource endowments and extensive economic development is becoming an increasingly prominent problem. Research into the present pollution control situation is thus relevant to adjusting pollution control methods and improving pollution control effects. However, pollution control has the externality characteristics of a public good, creating a problem of spatial association. This paper used the social network analysis method to analyse this problem. First, a spatial association network of provincial pollution control in China was established based on a gravitation model, and the structural characteristics of this spatial association network were analysed. Then, the quadratic assignment procedure (QAP) analysis method was employed to explore the main influencing factors impacting the association intensity of this spatial association network. These results contribute by illustrating the current situation of Chinese pollution control and provide a theoretical foundation for the government when it formulates future development directions and policies. [ABSTRACT FROM AUTHOR]

Abstract Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first given a partial alignment that we are tasked with completing. In this article, we modify the state-of-the-art approximate graph matching algorithm "FAQ" of Vogelstein et al. (2015) to make it a fast approximate seeded graph matching algorithm, adapt its applicability to include graphs with differently sized vertex sets, and extend the algorithm so as to provide, for each individual vertex, a nomination list of likely matches. We demonstrate the effectiveness of our algorithm via simulation and real data experiments; indeed, knowledge of even a few seeds can be extremely effective when our seeded graph matching algorithm is used to recover a naturally existing alignment that is only partially observed. [ABSTRACT FROM AUTHOR]

We consider the assignment problem with a special structure with a general form value function and constraints prohibiting certain matchings. In this case, the matching cost may be undefined until some permutation is found. We formulate the problem in terms of graph theory and reduce it to finding a minimal cost path in a graph with nonlocal edge weights. The proposed method for solving the problem is a modification of the Dijkstra's shortest path algorithm in a weighted directed graph. This research is motivated by well drilling applications. We also show the analysis of our numerical experiments. [ABSTRACT FROM AUTHOR]

We mimic alpha male social structure, which is common in many species of animals, for designing genetic algorithms. The population of solutions is partitioned into a number of social groups. One member of each is assigned alpha male status and the rest are reproductive females. A generation is defined as females producing one offspring each. Once all the females produce one offspring each, new groups are formed and one member of each is selected as the alpha male for the next generation. The procedure was extensively tested on instances of the quadratic assignment problem. We obtained better solutions using the same computer run time and found two new best known solutions, confirming the effectiveness of the alpha male approach. [ABSTRACT FROM AUTHOR]

Music listening is an inherently cultural behavior, which may be shaped by users’ backgrounds and contextual characteristics. Due to geographical, socio-economic, linguistic, and cultural factors as well as friendship networks, users in different countries may have different music preferences. Investigating cultural-socio-economic factors that might be associated with between-country differences in music preferences can facilitate music information retrieval, contribute to the prediction of users’ music preferences, and improve music recommendation in cross-country contexts. However, previous literature provides limited empirical evidence of the relationships between possible cross-country differences on a wide range of socio-economic aspects and those in music preferences. To bridge this research gap, and drawing on a large-scale dataset, LFM-1b, this study examines the possible relationship between cross-country differences in artist, album, and genre listening frequencies as well as the cross-country distance in geographical, socio-economic, linguistic, cultural, and friendship connections using the Quadratic Assignment Procedure. Results indicate: (1) there is no significant relationship between geographical and economic distance on album, artist, and genre preferences’ distance at the country-level; (2) the cross-country distance of three cultural dimensions (masculinity, long-term orientation, and indulgence) is positively associated with both the album and artist preferences distances; (3) the between-country distance in main languages has a positive relationship with the album, artist, and genre preferences distances across countries; (4) the density of friendship connections among countries negatively correlates to the cross-country preference distances in terms of artist and genre. Findings from this study not only expand knowledge of factors related to music preferences at the country level, but also can be integrated into real-world music recommendation systems that consider country-level music preferences. [ABSTRACT FROM AUTHOR]

We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding smoothness restriction is pervasive in first order methods, and recently was circumvented for convex composite optimization by Bauschke, Bolte, and Teboulle, through a simple framework which captures, all at once, the geometry of the function and of the feasible set. Building on this work, we tackle genuine nonconvex problems. We first complement and extend their approach to derive an extended descent lemma by introducing the notion of smooth adaptable functions. We then consider a Bregman-based proximal gradient method for the nonconvex composite model with smooth adaptable functions, which is proven to globally converge to a critical point under natural assumptions on the problem's data, and in particular for semialgebraic problems. To illustrate the potential of our general framework and results, we consider a broad class of quadratic inverse problems with sparsity constraints which arises in many fundamental applications, and we apply our approach to derive new globally convergent schemes for this class. [ABSTRACT FROM AUTHOR]

The use of smartphones and handheld devices in our daily activities has sharply increased. The added features of wireless technology and related applications on these devices make it possible to write emails, notes, and long text. Even though the most commonly used electronic input device is a keyboard, very little work has been dedicated for finding an optimal layout for this device. In this research, the aim is to propose a better layout for the single-finger keyboard in terms of rapid typing. The keyboard layout problem can be formulated as a quadratic assignment problem, which is one of the hardest combinatorial optimization problems. Some well-known literary works in English are chosen for estimating the keying-in-time. A variant of genetic algorithm, namely, the estimation of distribution algorithms is used to find a better layout. The new layout is found to be efficient compared with some of the existing prominent keyboard layouts. [ABSTRACT FROM AUTHOR]

This paper introduces a Multi-Agent based Optimization Method for Combinatorial Optimization Problems named MAOM-COP. In this method, a set of agents are cooperatively interacting to select the appropriate operators of metaheuristics using learning techniques. MAOM-COP is a flexible architecture, whose objective is to produce more generally applicable search methodologies. In this paper, the MAOM-COP explores genetic algorithm and local search metaheuristics. Using these metaheuristics, the decision-maker agent, the intensification agents and the diversification agents are seeking to improve the search. The diversification agents can be divided into the perturbation agent and the crossover agents. The decision-maker agent decides dynamically which agent to activate between intensification agents and crossover agents within reinforcement learning. If the intensification agents are activated, they apply local search algorithms. During their searches, they can exchange information, as they can trigger the perturbation agent. If the crossover agents are activated, they perform recombination operations. We applied the MAOM-COP to the following problems: quadratic assignment, graph coloring, winner determination and multidimensional knapsack. MAOMCOP shows competitive performances compared with the approaches of the literature. [ABSTRACT FROM AUTHOR]

Crossover operators play a very important role by creation of genetic algorithms (GAs) which are applied in various areas of computer science, including combinatorial optimization. In this paper, fifteen genetic crossover procedures are designed and implemented using a modern C# programming language. The computational experiments have been conducted with these operators by solving the famous combinatorial optimization problem - the quadratic assignment problem (QAP). The results of the conducted experiments on the characteristic benchmark instances from the QAP instances library QAPLIB illustrate the relative performance of the examined crossover operations. All crossover procedures are publicly available with the intention that the GA researchers will choose a procedure which suits the individual demand at the highest degree. [ABSTRACT FROM AUTHOR]

Registration of vascular networks is an indispensable element of prognostic and diagnostic studies that require structural analysis and comparison over time, among different samples, and to a gold standard. However, vascular networks manifest low spatial texture and sparse structural content so that even small variations in their location can make the intensity-based registration inefficient and prone to errors. Motivated by geometrical graph-based models developed in our prior work, we use the shape information in the graph topology sense to enhance the registration performance. An efficient feature-based registration is presented that seeks correspondence of the bifurcations and branches in a graph matching scheme. Since the graph matching is originally posed a NP-hard quadratic assignment problem (QAP) in the literature, we have designed a node signature that incorporates edge correspondences indirectly. This allows removing the quadratic term in the QAP to recast the problem as a linear assignment problem (LAP) to relieve the computational burden. The LAP is efficiently solvable and is scalable to data with graph representation of larger size. The performance is tested and validated using clinical 3-D angiography images of the human cerebrovasculature as well as synthetic datasets. This method proves to be robust in the face of different structural and algorithm’s parameters. Quality of inter-subject and multimodal matching of clinical data has also been confirmed. [ABSTRACT FROM AUTHOR]

Quadratic assignment problem (QAP) is one of the most difficult combinatorial optimization problems in the NP-hard class. Due to the difficulty of the problem, many researchers have been studying this type of assignment problem. In this work, simulated annealing method is parallelized on MATLAB platform and is used to solve 36 problems from QAPLIB which is a well-known QAP library. The performance of different parallelization methods is compared for the problems used. As a result, when compared with the serial simulated annealing method, it is seen that the parallel methods give faster results when the appropriate parameters are used. [ABSTRACT FROM AUTHOR]

Network on Chip (NoC) has been suggested as an appropriate solution for the communication demands in Systems on Chip (SoCs). Due to the limitation of the resources in NoC, suitable load distribution over limited resources which is known as mapping problem is a challenging issue. This paper proposes a linearized model of quadratic assignment problem (QAP) to map the tasks to the cores not only to minimize the power consumption but also to improve the performance in NoCs. In addition to the proposed linearized model, two meta-heuristic algorithms such as genetic algorithm and simulated annealing are suggested to solve the considered mapping problem as QAP. The extensive computational study over the well-known benchmarks of the literature of NoCs proves that the proposed linearized formulation performs better than the meta-heuristic approaches in terms of power dissipation and performance of the NoCs. [ABSTRACT FROM AUTHOR]

This paper presents a new local search approach, called randomized decomposition (RD), for solving nonlinear, nonconvex mathematical programs. Starting from a feasible solution, RD partitions the problem's decision variables into a randomly ordered list of randomly generated subsets. RD then optimizes over the variables in each subset, keeping all other variables fixed. Unlike most other decomposition methods, no knowledge of the problem structure is required. RD has been combined with a metaheuristic RDPerturb, for escaping local optima, to create a generic framework for solving mathematical programs, especially hard combinatorial nonconvex problems. The framework has been implemented as an optimization platform we call RDSolver and successfully applied to over 400 instances of the quadratic assignment problem (QAP). The results obtained by RDSolver are competitive with the solutions obtained by heuristics specially tailored for those problems, even though RDSolver is a general purpose mathematical programming solver. In addition to a strong performance on previously solved problems, RDSolver has found two new best known solutions and provided solutions to 68 large QAP problems for which no solutions have been previously reported. [ABSTRACT FROM AUTHOR]

In this paper, we consider a binary quadratic program (BQP) with random objective coefficients. Given only information on the marginal distributions of the objective coefficients, we propose a tight bound on the expected optimal value of the random BQP. We show that the complexity of computing this bound does not increase substantially with respect to the complexity of solving the corresponding deterministic BQP. For the quadratic unconstrained binary optimization (QUBO) problem with nonnegative off-diagonal random entries, the bound is shown to be computable in polynomial time. We generalize the asymptotic bound for the random quadratic assignment problem from independent random variables to dependent random variables and propose a new closed-form bound on the expected optimal value of the quadratic k-cluster problem. We also provide polynomial time computable upper bounds on the expected optimal value for the NP-hard instances using the linear and semidefinite programming relaxation of the deterministic BQP. The semidefinite programming bound of the expected optimal value of the random MAX-CUT problem inherits the approximation ratio of 0:878 from the semidefinite relaxation of the deterministic MAX-CUT problem. Computational experiments on random QUBO problems and random quadratic knapsack problems provide evidence of the quality of the bounds. Overall, our results indicate that the new bound on the ex- pected optimal value of the random BQP is attractive since it exploits many of the nice results and formulations of the deterministic BQP and is valid under limited distributional information. [ABSTRACT FROM AUTHOR]

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with $$q\ge 1$$ , the objective function sums the costs for travelling from one city to each of the next q cities in the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic assignment problem. We analyze the computational complexity of the q-stripe TSP for various classes of specially structured distance matrices. We derive NP-hardness results as well as polynomially solvable cases. One of our main results generalizes a well-known theorem of Kalmanson from the classical TSP to the q-stripe TSP. [ABSTRACT FROM AUTHOR]

The concept of discrete higher-order sliding mode has received increased attention in the recent literature. This paper presents an optimal discrete higher-order sliding mode control for an uncertain discrete LTI system using partial state information, which has been missing in literature. A new technique is proposed to design an optimal time-varying higher-order sliding surface and control input through the minimization of a quadratic performance index. Moreover, disturbance estimation technique is utilized to modify the control algorithm to reduce the width of the discrete higher-order sliding mode band. The proposed algorithm is experimentally validated on a rectilinear plant. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper provides a comprehensive treatment of full-block multipliers within the integral quadratic constraints framework for stability analysis of feedback systems containing repeated, slope-restricted scalar nonlinearities. We develop a novel stability result that offers more flexibility in its application because it allows for the inclusion of general Popov and Yakubovich criteria in combination with the well-established Circle and Zames-Falb stability tests within integral quadratic constraint theory. A particular focus lies on the formulation of stability criteria in terms of full-block multipliers, some of which are new, and thus typically involve less conservatism than current methods. Furthermore, a new asymptotically exact parametrization of full-block Zames-Falb multipliers is given that allows to exploit the complete potential of this stability test. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The quadratic assignment problem (QAP) is one of the most studied combinatorial optimization problems with various practical applications. In This paper, we present an Elite Opposition-Flower Pollination Algorithm (EOFPA) for solving Quadratic Assignment Problems. The performance of the proposed algorithm is tested against a set of benchmarks of QAP from the public QAPLIB Library. we compare the algorithm against the best proposals from the related literatures and we determine that the proposed algorithm is superior to some other algorithms. [ABSTRACT FROM AUTHOR]

In this article, we will examine whether the Problem Aware Local Search, an efficient method initially proposed for the DNA Fragment Assembly Problem, can also be used in other application domains and with other optimization problems. The main idea is to maintain the key features of PALS and apply it to different permutation-based combinatorial problems. In order to carry out a comprehensive analysis, we use a wide benchmark of well-known problems with different kinds of variation operators and fitness functions, such as the Quadratic Assignment Problem, the Flow Shop Scheduling Problem, and the Multiple Knapsack Problem. We also discuss the main design alternatives for building an efficient and accurate version of PALS for these problems in a competitive manner. In general, the results show that PALS can achieve high-quality solutions for these problems and do it efficiently. [ABSTRACT FROM AUTHOR]

This paper presents an application of the ant algorithm and bees algorithm in optimization of QAP problem as an example of NPhard optimization problem. The experiments with two types of algorithms: the bees algorithm and the ant algorithm were performed for the test instances of the quadratic assignment problem from QAPLIB, designed by Burkard, Karisch and Rendl. On the basis of the experiments results, an influence of particular elements of algorithms, including neighbourhood size and neighbourhood search method, will be determined. [ABSTRACT FROM AUTHOR]

With this study, we propose a novel parallel robust tabu-search algorithm (Parallel-Tabu-QAP) for the NP-Hard Quadratic Assignment Problem (QAP)of whose instances having large number of location and facilites have not been reported to be solved exactly so far. Parallel- Tabu-QAP algorithm that has two phases optimizes the parameters of tabu-search algorithm in its first phase by using genetic algorithms through generations. The individuals that have parameters of the tabu-search are optimized in a population that is located on a master processor. In the second phase, slave processors optimize the solution of the problem by restarting their search process in case of stagnations. With its stagnation prevention and parallel optimization talents, parallel-tabu-QAP algorithm is observed to obtain better results than its sequential and statically parameter-tuned counterparts. The algorithm has 0.05% deviation for the benchmark tests performed on more than 100 problem instances. These experimental results show that the parallel-tabu-QAP algoritm is one the best performing techniques in its heuristics algorithms class when compared with state-of-the-art QAP algorithms. [ABSTRACT FROM AUTHOR]

In this study, we propose a novel hybrid multiobjective evolutionary algorithm for solving multiobjective quadratic assignment problems. During the last decade, the researchers gave increasing attention to the multiobjective structure of quadratic assignment problems and developed and/or used several multi objective metaheuristics. The nondominated sorting genetic algorithm (NSGA-II) has been shown to solve various multiobjective problems much better than other recently-proposed constraint handling approaches. Besides, the effectiveness of conic scalarization method was also proven for solution of multiobjective problems, that have non-linear structure. Here, a hybrid multiobjective evolutionary algorithm (cNSGA-II) featured with NSGA-II and conic scalarization's Pareto solutions is developed to obtain as much Pareto points, as possible. To test the performance of the algorithm we have selected the test problems from the literature and compared the performances by well-known diameter metric. It has been shown that cNSGA-II is effective in solving multiobjective quadratic assignment problems. [ABSTRACT FROM AUTHOR]

In fact, the architectures and applications of networks are dynamic, heterogeneous, and complex, in which machine learning tasks are faced with a variety of multiple parties, such as Internet of Things (IoT), mobile telecom networks, cognitive networks, wired/wireless heterogeneous backbone networks, and so on. A dynamic reputation evaluation method based on supervision feedback of user information behavior is helpful to promote social network self-discipline and achieve good community autonomy. With the rapid development of data science, machine learning has been widely applied to many important fields such as computer vision, healthcare systems, and financial predictions, to support the design of constructs of Artificial Intelligence. [Extracted from the article]

The Quadratic Assignment Problem (QAP) and its corollary Quadratic Bottleneck Assignment Problem (QBAP) are reputed for being non-deterministic polynomial-time hard (NP-hard) problems. In aviation, they have been used to assign aircraft to gates. This paper, based on the case of SeattlelTacoma International airport, proposes to illustrate how the QAP and QBAP models can be used to help measure the impact of runway reassignment decisions in terms of tarmac times. This study identifies the global optimal solution for the QAP as a Mixed Integer Linear Programming and the local optimal solution for the QBAP as a Mixed Integer Non-Linear Programming. [ABSTRACT FROM AUTHOR]

A new repeated iterated tabu search for the quadratic assignment problem is developed. A comparative study of this algorithm and the best existing algorithms for solving this problem has shown its competitiveness with respect to both its performance and quality of solutions. [ABSTRACT FROM AUTHOR]