Quadratic Assignment Research Articles

Use of proximity loggers to Estimate Affiliative and Agonistic Relationships among Group-housed Holstein calves.

We used proximity loggers to map the social network of 15 group-housed suckling Holstein calves over a 70-day period divided into five trial periods. Tag ID, encountered tag ID, and encounter start time and length were collected from the proximity loggers. Use of 3D matrices and trendlines distinguished three encounter types: "rapid decline" (up to ~ 120 s), "moderate decline" (~120 to ~ 600 s), and "exponential decline" (longer than ~ 600 s). We hypothesized that a random encounter between two calves with an agonistic relationship would terminate quickly, whereas affiliative encounters would linger. Quadratic assignment with 5000 random permutations revealed a significant negative correlation between short encounters ("agonistic") and long encounters ("affiliative") matrices in periods 1 and 5 (r = -0.490 and -0.767, respectively), tendency toward negative correlation in period 3 (r = -0.141, p = 0.104), and no significant correlations in periods 2 and 4. These results were in accordance with the social network analyses revealing agonistic (short encounters) relationships in those periods. We suggest using this method in further studies on the effects of various factors on social network dynamics and its effect on health, intake, growth, and efficiency.

Evolutionary Algorithm-Based Iterated Local Search Hyper-Heuristic for Combinatorial Optimization Problems

Hyper-heuristics are widely used for solving numerous complex computational search problems because of their intrinsic capability to generalize across problem domains. The fair-share iterated local search is one of the most successful hyper-heuristics for cross-domain search with outstanding performances on six problem domains. However, it has recorded low performances on three supplementary problems, namely knapsack, quadratic assignment, and maximum-cut problems, which undermines its credibility across problem domains. The purpose of this study was to design an evolutionary algorithm-based iterated local search (EA-ILS) hyper-heuristic that applies a novel mutation operator to control the selection of perturbative low-level heuristics in searching for optimal sequences for performance improvement. The algorithm was compared to existing ones in the hyper-heuristics flexible (HyFlex) framework to demonstrate its performance across the problem domains of knapsack, quadratic assignment, and maximum cut. The comparative results have shown that the EA-ILS hyper-heuristic can obtain the best median objective function values on 22 out of 30 instances in the HyFlex framework. Moreover, it has achieved superiority in its generalization capability when compared to the reported top-performing hyper-heuristic algorithms.

Discriminating and Clustering Ordered Permutations Using Artificial Neural Networks: A Potential Application in ANN-Guided Genetic Algorithms

Traveling salesman, linear ordering, quadratic assignment, and flow shop scheduling are typical examples of permutation-based combinatorial optimization problems with real-life applications. These problems naturally represent solutions as an ordered permutation of objects. However, as the number of objects increases, finding optimal permutations is extremely difficult when using exact optimization methods. In those circumstances, approximate algorithms such as metaheuristics are a plausible way of finding acceptable solutions within a reasonable computational time. In this paper, we present a technique for clustering and discriminating ordered permutations with potential applications in developing neural network-guided metaheuristics to solve this class of problems. In this endeavor, we developed two different techniques to convert ordered permutations to binary-vectors and considered Adaptive Resonate Theory (ART) neural networks for clustering the resulting binary vectors. The proposed binary conversion techniques and two neural networks (ART-1 and Improved ART-1) are examined under various performance indicators. Numerical examples show that one of the binary conversion methods provides better results than the other, and Improved ART-1 is superior to ART-1. Additionally, we apply the proposed clustering and discriminating technique to develop a neural-network-guided Genetic Algorithm (GA) to solve a flow-shop scheduling problem. The investigation shows that the neural network-guided GA outperforms pure GA.

Digital Annealer for quadratic unconstrained binary optimization: A comparative performance analysis

Digital Annealer (DA) is a computer architecture designed for tackling combinatorial optimization problems formulated as quadratic unconstrained binary optimization (QUBO) models. In this paper, we present the results of an extensive computational study to evaluate the performance of DA in a systematic way in comparison to multiple state-of-the-art solvers for different problem classes. We examine pure QUBO models, as well as QUBO reformulations of three constrained problems, namely quadratic assignment, quadratic cycle partition, and selective graph coloring, with the last two being new applications for DA. For the selective graph coloring problem, we also present a size reduction heuristic that significantly increases the number of eligible instances for DA. Our experimental results show that despite being in its development stage, DA can provide good-quality solutions quickly and in that regard rivals the state of the art particularly for large instances. Moreover, as opposed to established solvers, within its limit on the number of decision variables, DA’s solution times are not affected by the increase in instance size. These findings illustrate that DA has the potential to become a successful technology in tackling combinatorial optimization problems.

Intersectoral collaboration at a decentralized level: information flows in child welfare and healthcare networks

BackgroundAs needs of families with social and behavioral health problems often exceed the expertise and possibilities of a single professional, service or organization, cross-service collaboration is indispensable to adequately meeting those needs. Despite the progressive focus on organizing integrated care, service fragmentation and service duplication remain persistent problems in child welfare and healthcare service delivery systems. A crucial factor to overcome these problems is information exchange between organizations. This study explores and compares the development over time of structures of information exchange in networks, concerning both material and knowledge-based information.MethodsA comparative case study and social network analysis of three inter-organizational networks of child welfare and healthcare services in different-sized municipalities in the Netherlands. The research population consisted of organizations from various sectors participating in the networks. Data were collected at two moments in time with a mixed method: semi-structured interviews with network managers and an online questionnaire for all network members. Density and degree centralization were used to examine the information exchange structures. Ucinet was used to analyze the data, with use of the statistical tests: Compare Density Procedure and Quadratic Assignment Procedure.ResultsThis study shows that different structures of information exchange can be distinguished, concerning both material and knowledge-based information. The overall connectedness of the studied structures of the networks are quite similar, but the way in which the involvement is structured turns out to be different between the networks. Over time, the overall connectedness of those structures appears to be stable, but the internal dynamics reveals a major change in relationships between organizations in the networks.ConclusionsOur study yields empirical evidence for the existence of and the differences between structures and dynamics of both material and knowledge-based information exchange relationships. With a loss of more than a half of the relations in a year, the relationships between the organizations in the network are not very stable over time. The contrast between major internal dynamics and the stable overall connectedness is an important point of concern for network managers and public officials, since this impermanence of relations means that long-term integrated care cannot be guaranteed.

Multi- and many-objective path-relinking: A taxonomy and decomposition approach

This paper proposes a decomposition-based path-relinking method for multi- and many-objective combinatorial optimization problems. The proposed approach, referred to as MOPR/D, considers the localization of solutions in the objective space and can handle this information to make choices regarding intermediate solutions in the path-relinking trajectory. Because it does not require aggregation functions, it does not suffer from a tendency to introduce search bias to specific regions of the Pareto front. The proposed approach was compared with seven path-relinking techniques from the literature on three differently structured combinatorial optimization problems: 0/1 multidimensional knapsack, quadratic assignment, and spanning tree. Experiments were conducted on sets of benchmark instances with up to five objectives. This study also reviewed multi-objective path generation strategies, investigated their behaviors, and a taxonomy is proposed for standardizing and classifying them.

Partial neighborhood local searches

AbstractIn this work, we study partial neighborhood local search (PNLS) techniques, which consist of adaptive walks where moves are chosen in a random subset of the current solution neighborhood. PNLSs balance between intensification and diversification is mainly determined by its single parameter λ designing the subset size. We analyze and discuss three PNLSs variants, using the abstraction of several combinatorial optimization problems into fitness landscapes: NK landscapes, Unconstrained Binary Quadratic Programming, Flow‐shop scheduling, and Quadratic Assignment. Our empirical study first analyses the structure of these landscapes through indicators. Then, we perform a parameter study of PNLSs for two computational budgets to study the impact of the sample size on the balance between intensification and diversification on different landscapes. Moreover, these experiments allow us to set an appropriate parameter value to compare the ability of PNLSs to reach good‐quality solutions accurately. Finally, we compare PNLS variants with two classical metaheuristics, identifying links between landscape characteristics and algorithms behavior.

Hybrid slime mould algorithm with adaptive guided differential evolution algorithm for combinatorial and global optimization problems

The Slime Mould Algorithm (SMA) is a recent metaheuristic inspired by the oscillation of slime mould. Similar to other original metaheuristic algorithms (MAs), SMA may suffer from drawbacks, such as being trapped in minimum local regions and improper balance between exploitation and exploration phases. To overcome these weaknesses, this paper proposes a hybrid algorithm: SMA combined to Adaptive Guided Differential Evolution Algorithm (AGDE) (SMA-AGDE). The AGDE mutation method is employed to enhance the swarm agents’ local search, increase the population’s diversity, and help avoid premature convergence. The SMA-AGDE’s performance is evaluated on the CEC’17 test suite, three engineering design problems – tension/compression spring, pressure vessel, and rolling element bearing – and two combinatorial optimization problems – bin packing and quadratic assignment. The SMA-AGDE is compared with three categories of optimization methods: (1) The well-studied MAs, i.e., Biogeography-Based Optimizer (BBO), Gravitational Search Algorithm (GSA), and Teaching Learning-Based Optimization (TLBO), (2) Recently developed MAs, i.e., Harris Hawks Optimization (HHO), Manta Ray Foraging optimization (MRFO), and the original SMA, and (3) High-performance MAs, i.e., Evolution Strategy with Covariance Matrix Adaptation (CMA-ES), and AGDE. The overall simulation results reveal that the SMA-AGDE ranked first among the compared algorithms, and so, over different function landscapes. Thus, the proposed SMA-AGDE is a promising optimization tool for global and combinatorial optimization problems and engineering design problems.

Scalable Semidefinite Programming

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs. Numerical evidence shows that the method is effective for a range of applications, including relaxations of MaxCut, abstract phase retrieval, and quadratic assignment. Running on a laptop equivalent, the algorithm can handle SDP instances where the matrix variable has over $10^{14}$ entries.

Managing randomization in the multi-block alternating direction method of multipliers for quadratic optimization

The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical computational efficiency of the method, because one big matrix factorization is needed at least once even for linear and convex quadratic programming. This drawback may be overcome by enforcing a multi-block structure of the decision variables in the original optimization problem. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. On the other hand, two positive developments have been made: first, if in each cyclic loop one randomly permutes the updating order of the multiple blocks, then the method converges in expectation for solving any system of linear equations with any number of blocks. Secondly, such a randomly permuted ADMM also works for equality-constrained convex quadratic programming even when the objective function is not separable. The goal of this paper is twofold. First, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Secondly, using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM, with a variable-grouping strategy, could significantly improve the computation efficiency on solving most quadratic optimization problems.

Applying the big bang-big crunch metaheuristic to large-sized operational problems

In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature.

An exact completely positive programming formulation for the discrete ordered median problem: an extended version

This paper presents a first continuous, linear, conic formulation for the discrete ordered median problem (DOMP). Starting from a binary, quadratic formulation in the original space of location and allocation variables that are common in location analysis (L.A.), we prove that there exists a transformation of that formulation, using the same space of variables, that allows us to cast DOMP as a continuous, linear programming problem in the space of completely positive matrices. This is the first positive result that states equivalence between the family of continuous, convex problems and some hard combinatorial problems in L.A. The result is of theoretical interest because it allows us to share the tools from continuous optimization to shed new light into the difficult combinatorial structure of the class of ordered median problems that combines elements of the p-median, quadratic assignment and permutation polytopes.

Uncertain random quadratic bottleneck assignment problem

Uncertain random expected value simulation is one of the most important techniques to solve uncertain random optimization problems where random variables coexist with uncertain variables. A general simulation algorithm is designed to estimate the uncertain random expected value. Furthermore, an uncertain random quadratic bottleneck assignment problem is proposed and an uncertain random expected value model is presented. An algorithm is designed to find a lower bound of the uncertain random quadratic bottleneck assignment problem.

A Multi-Agent Based Optimization Method for Combinatorial Optimization Problems

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.

Exact Recovery with Symmetries for the Doubly Stochastic Relaxation

Graph matching, or quadratic assignment, is the problem of labeling the vertices of two graphs so that they are as similar as possible. A common method for approximately solving the NP-hard graph matching problem is relaxing it to a convex optimization problem over the set of doubly stochastic (DS) matrices. Recent analysis has shown that for almost all pairs of isomorphic and asymmetric graphs, the DS relaxation succeeds in correctly retrieving the isomorphism between the graphs. Our goal in this paper is to analyze the case of symmetric isomorphic graphs. This goal is motivated by shape matching applications where the graphs of interest usually have reflective symmetry. For symmetric problems the graph matching problem has multiple isomorphisms, and so convex relaxations admit all convex combinations of these isomorphisms as viable solutions. If the convex relaxation does not admit any additional superfluous solution, we say that it is convex exact. We show that convex exactness depends strongly on the symmetry group of the graphs; for a fixed symmetry group $G$, the DS relaxation either will be convex exact for almost all pairs of isomorphic graphs with symmetry group $G$, or will fail for all such pairs. We show that for reflective groups with at least one full orbit, convex exactness holds almost everywhere. The importance of this result stems from the fact that such groups are the most common symmetry groups in shape matching applications. Finally, we provide some simple examples of nonreflective symmetry groups for which convex exactness always fails. These examples also show that the property of having generic convex exactness is not invariant under group isomorphisms. When convex exactness holds, the isomorphisms of the graphs are the extreme points of the convex solution set and the task of finding an isomorphism in polynomial time is tractable. We discuss several common algorithms capable of retrieving an isomorphism in this case. We also show that interior point algorithms will not return an isomorphism in this case but will return the centroid of the set of isomorphisms, which gives a “fuzzy encoding” of the symmetries of the shape. In fact, for any symmetry group $G$, the centroid solution can be recovered efficiently for almost all pairs of isomorphic graphs with symmetry group $G$.

Chemical reaction optimization for solving shortest common supersequence problem

Shortest common supersequence (SCS) is a classical NP-hard problem, where a string to be constructed that is the supersequence of a given string set. The SCS problem has an enormous application of data compression, query optimization in the database and different bioinformatics activities. Due to NP-hardness, the exact algorithms fail to compute SCS for larger instances. Many heuristics and meta-heuristics approaches were proposed to solve this problem. In this paper, we propose a meta-heuristics approach based on chemical reaction optimization, CRO_SCS that is designed inspired by the nature of the chemical reactions. For different optimization problems like 0-1 knapsack, quadratic assignment, global numeric optimization problems CRO algorithm shows very good performance. We have redesigned the reaction operators and a new reform function to solve the SCS problem. The outcomes of the proposed CRO_SCS algorithm are compared with those of the enhanced beam search (IBS_SCS), deposition and reduction (DR), ant colony optimization (ACO) and artificial bee colony (ABC) algorithms. The length of supersequence, execution time and standard deviation of all related algorithms show that CRO_SCS gives better results on the average than all other algorithms.

A multi-step method for partial quadratic pole assignment problem with time delay

In this paper, the partial quadratic pole assignment problem with time delay is considered. We propose a multi-step method for solving this problem in which the unwanted eigenvalues are moved to desired values and all other eigenpairs remain unchanged. Our method is easy to realize and need not use the receptance matrix or solve the Sylvester equation. Numerical examples show that the proposed method is effective.

A Special Role of Boolean Quadratic Polytopes among Other Combinatorial Polytopes

We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family

Evaluating the quality of image matrices in blockmodeling

One approach for analyzing large networks is to partition its nodes into classes where the nodes in a class have similar characteristics with respect to their connections in the network. A class is represented as a blockmodel (or image matrix). In this context, a specific question is to test whether a presumed blockmodel is well reflected in the network or to select from a choice of possible blockmodels the one fitting best. In this paper, we formulate these problems as combinatorial optimization problems. We show that the evaluation of a blockmodel’s quality is a generalization of well-known optimization problems such as quadratic assignment, minimum $$k$$ -cut, traveling salesman, and minimum edge cover. A quadratic integer programming formulation is derived and linearized by making use of properties of these special cases. With a branch-and-cut approach, the resulting formulation is solved up to 10,000 times faster than a comparable formulation from the literature.

RLT insights into lift-and-project closures

This paper examines relationships between the two methods for constructing polyhedral outer-approximations of mixed 0-1 linear programs known in the literature as the level-1 Reformulation–Linearization-Technique (RLT) and the elementary closure of lift-and-project (L&P) cuts based on the level-1 L&P. The latter can be obtained, via a transformation of variables, as a relaxed version of the former through the removal of constraints. Whereas both approaches derive formulations in lifted spaces by scaling problem constraints with suitable multipliers, a key difference is that the multipliers used by the RLT are defined in terms of the binary variables of the given problem. As a consequence, these multipliers, in contrast to those used in the L&P, portend important advantages, including the ability to handle nonlinear expressions, to recognize redundant inequalities, and to exploit special structures. This paper compares the two methods, and uses RLT constructs to provide insights into the L&P approach. Some particular insights are illustrated on the quadratic assignment and MAX-2SAT problems, with level-2 RLT and level-2 L&P comparisons also given for the latter problem.