We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binaryquadratic problems subject to assignment constraints that has been proposed by...
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We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binaryquadratic problems subject to assignment constraints that has been proposed by Liberti (4OR 5(3):231-245, 2007, The new conditions resolve inconsistencies that can occur when the original method is used. We also present a mixed-integer linear program to compute a minimally sized linearization. When all the assignment constraints have non-overlapping variable support, this program is shown to have a totally unimodular constraint matrix. Finally, we give a polynomial-time combinatorial algorithm that is exact in this case and can be used as a heuristic otherwise.
The efficiency of top-k recommendation is vital to large-scale recommender systems. Hashing is not only an efficient alternative but also complementary to distributed computing, and also a practical and effective opti...
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ISBN:
(纸本)9781450355520
The efficiency of top-k recommendation is vital to large-scale recommender systems. Hashing is not only an efficient alternative but also complementary to distributed computing, and also a practical and effective option in a computing environment with limited resources. Hashing techniques improve the efficiency of online recommendation by representing users and items by binary codes. However, objective functions of existing methods are not consistent with ultimate goals of recommender systems, and are often optimized via discrete coordinate descent, easily getting stuck in a local optimum. To this end, we propose a Discrete Ranking-based Matrix Factorization (DRMF) algorithm based on each user's pairwise preferences, and formulate it into binary quadratic programming problems to learn binary codes. Due to non-convexity and binary constraints, we further propose self-paced learning for improving the optimization, to include pairwise preferences gradually from easy to complex. We finally evaluate the proposed algorithm on three public real-world datasets, and show that the proposed algorithm outperforms the state-of-the-art hashing-based recommendation algorithms, and even achieves comparable performance to matrix factorization methods.
A way of minimizing the opportunity of cheating in exams is to assign different tests to students. The likelihood of cheating then depends on the proximity of the students' desks, and the similarity of the tests. ...
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ISBN:
(纸本)9781509060177
A way of minimizing the opportunity of cheating in exams is to assign different tests to students. The likelihood of cheating then depends on the proximity of the students' desks, and the similarity of the tests. The test-assignment problem is to find an assignment of tests to desks that minimizes that total likelihood of cheating. The problem is a variant of a graph coloring problem and is NP-hard. We propose a new heuristic solution for this problem. Our approach differs from the usual way of designing heuristics in two ways. First, we reduce test-assignment to the more general unconstrained binary quadratic programming. Second, we search for a good heuristic using an automatic algorithm configuration tool that evolves heuristics in a space of algorithms built from known components for binary quadratic programming. The best hybrid heuristics found repeatedly recombine elements of a population of elite solutions and improve them by a tabu search. Computational tests suggest that the resulting algorithms are competitive with existing heuristics that have been designed manually.
A new algorithm based on global equilibrium search (GES) is developed to solve an unconstrained binary quadratic programming (UBQP) problem. It is compared with the best methods of solving this problem. The GES algori...
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A new algorithm based on global equilibrium search (GES) is developed to solve an unconstrained binary quadratic programming (UBQP) problem. It is compared with the best methods of solving this problem. The GES algorithm is shown to be better both in speed and solution quality.
Mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indee...
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ISBN:
(纸本)9783319600451;9783319600444
Mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indeed, they combine productions and they make a better use of biodiversity. These agroforestry systems are based on a complex set of interactions modifying the utilization of light, water and nutrients. Thus, designing such a system must optimize the use of these resources: by maximizing positive interactions (facilitation) and minimizing negative ones (competition). To attain these objectives, the system's design has to include the spatial and temporal dimensions, taking into account the evolution of above-and belowground interactions over a time horizon. For that, we define the Mixed Fruit-Vegetable Crop Allocation Problem (MFVCAP) using a discrete representation of the land and the interactions between vegetable crops and fruit trees. First, we give a direct formulation as a binaryquadratic program (BQP). Then we reformulate the problem using a Benders decomposition approach. The master problem has 0/1 binary variables and deals with tree positioning. The subproblem deals with crop quantities. The BQP objective function becomes linear in the continuous subproblem by exploiting the fact that it depends only on the quantity of crops assigned to land units having shade, root, or nothing. This problem decomposition allows us to reformulate the MFVCAP into a Mixed Integer linear Program (MIP). The detailed spatial-temporal crop allocation plan is easy to obtain after solving the MIP. Experimental results show the efficiency of our approach compared to a direct solving of the original BQP formulation.
This article presents BiqCrunch, an exact solver for binaryquadratic optimization problems. BiqCrunch is a branch-and-bound method that uses an original, efficient semidefinite-optimization-based bounding procedure. ...
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This article presents BiqCrunch, an exact solver for binaryquadratic optimization problems. BiqCrunch is a branch-and-bound method that uses an original, efficient semidefinite-optimization-based bounding procedure. It has been successfully tested on a variety of well-known combinatorial optimization problems, such as Max-Cut, Max-k-Cluster, and Max-Independent-Set. The code is publicly available online;a web interface and many conversion tools are also provided.
We present two recent integer programming models in molecular biology and study practical reformulations to compute solutions to some of these problems. In extension of previously tested linearization techniques, we f...
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We present two recent integer programming models in molecular biology and study practical reformulations to compute solutions to some of these problems. In extension of previously tested linearization techniques, we formulate corresponding semidefinite relaxations and discuss practical rounding strategies to find good feasible approximate solutions. Our computational results highlight the possible advantages and remaining challenges of this approach especially on large-scale problems.
Given a set N, a pairwise distance function d and an integer number m, the Dispersion Problems (DPs) require to extract from N a subset M of cardinality m, so as to optimize a suitable function of the distances betwee...
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Given a set N, a pairwise distance function d and an integer number m, the Dispersion Problems (DPs) require to extract from N a subset M of cardinality m, so as to optimize a suitable function of the distances between the elements in M. Different functions give rise to a whole family of combinatorial optimization problems. In particular, the max-sum DP and the max-min DP have received strong attention in the literature. Other problems (e.g., the max-minsum DP and the min-diffsum DP) have been recently proposed with the aim to model the optimization of equity requirements, as opposed to that of more classical efficiency requirements. Building on the main ideas which underly some state-of-the-art methods for the max-sum DP and the max-min DP, this work proposes some constructive procedures and a Tabu Search algorithm for the new problems. In particular, we investigate the extension to the new context of key features such as initialization, tenure management and diversification mechanisms. The computational experiments show that the algorithms applying these ideas perform effectively on the publicly available benchmarks, but also that there are some interesting differences with respect to the DPs more studied in the literature. As a result of this investigation, we also provide optimal results and bounds as a useful reference for further studies. (C) 2014 Elsevier B.V. All rights reserved.
Near-duplicate retrieval (NDR) in merchandize images is of great importance to a lot of online applications on e-Commerce websites. In those applications where the requirement of response time is critical, however, th...
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Near-duplicate retrieval (NDR) in merchandize images is of great importance to a lot of online applications on e-Commerce websites. In those applications where the requirement of response time is critical, however, the conventional techniques developed for a general purpose NDR are limited, because expensive post-processing like spatial verification or hashing is usually employed to compromise the quantization errors among the visual words used for the images. In this paper, we argue that most of the errors are introduced because of the quantization process where the visual words are considered individually, which has ignored the contextual relations among words. We propose a "spelling or phrase correction" like process for NDR, which extends the concept of collocations to visual domain for modeling the contextual relations. binary quadratic programming is used to enforce the contextual consistency of words selected for an image, so that the errors (typos) are eliminated and the quality of the quantization process is improved. The experimental results show that the proposed method can improve the efficiency of NDR by reducing vocabulary size by 1000% times, and under the scenario of merchandize image NDR, the expensive local interest point feature used in conventional approaches can be replaced by color-moment feature, which reduces the time cost by 9202% while maintaining comparable performance to the state-of-the-art methods.
The standard linearization of a binaryquadratic program yields an equivalent reformulation as an integer linear program, but the resulting LP-bounds are very weak in general. We concentrate on applications where the ...
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The standard linearization of a binaryquadratic program yields an equivalent reformulation as an integer linear program, but the resulting LP-bounds are very weak in general. We concentrate on applications where the underlying linear problem is tractable and exploit the fact that, in this case, the optimization problem is still tractable in the presence of a single quadratic term in the objective function. We propose to strengthen the standard linearization by the use of cutting planes that are derived from jointly considering each single quadratic term with the underlying combinatorial structure. We apply this idea to the quadratic minimum spanning tree and spanning forest problems and present complete polyhedral descriptions of the corresponding problems with one quadratic term, as well as efficient separation algorithms for the resulting polytopes. Computationally, we observe that the new inequalities significantly improve dual bounds with respect to the standard linearization, particularly for sparse graphs. (C) 2014 Elsevier B.V. All rights reserved.
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