The Multidimensional Knapsack Problem: Structure and Algorithms

Puchinger, Jakob; Raidl, Günther R.; Pferschy, Ulrich

doi:10.1287/ijoc.1090.0344

Cited by 153 publications

(86 citation statements)

References 32 publications

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“…In particular, the multidimensional 0-1 knapsack problem has received greater attention, possibly because of its increased solution complexity under higher correlations among problem data. This research spans several years, as the following citations show: Gavish and Pirkul (1985), Freville and Plateau (1994), Chu andBeasley (1998), Freville (2004), Freville and Hanafi (2005), Vasquez and Vimont (2005), and Puchinger et al (2010). Martello et al (1999) present a combination of two new algorithms, which is shown to outperform all previous methods, for solving a single-constraint 0-1 knapsack problem exactly.…”

Section: Nonlinear Separable Discrete-optimization Modelmentioning

confidence: 99%

“…Once these core variables are identified, then determining their solution was the key to solving the entire problem. The core concept was recently generalized to the multiconstraint case by Puchinger et al (2010) and used as a basis for both optimal and heuristic solution techniques. In a similar vein, Vasquez and Vimont (2005) used variable fixing to obtain "good" families of solutions in their heuristic.…”

Section: Nonlinear Separable Discrete-optimization Modelmentioning

confidence: 99%

“…To generalize the problem from a single-constraint problem to a multidimensional problem, Puchinger et al (2010) proposed using surrogate multipliers to combine the constraints to calculate the efficiency measures required for determining the core variables. Our entropy-based approach too relies on a similar mechanism where the constraints of the problem are combined into a single surrogate constraint as a first step.…”

Section: Nonlinear Separable Discrete-optimization Modelmentioning

confidence: 99%

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Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models

et al. 2014

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T his paper develops a new way to help solve difficult linear and nonlinear discrete-optimization decision models more efficiently by introducing a problem-difficulty metric that uses the concept of entropy from information theory. Our entropy metric is employed to devise rules for problem partitioning within an implicit enumeration method, where branching is accomplished based on the subproblem complexity. The only requirement for applying our metric is the availability of (upper) bounds on branching subproblems, which are often computed within most implicit enumeration methods such as branch-and-bound (or cutting-plane-based) methods. Focusing on problems with a relatively small number of constraints, but with a large number of variables, we develop a hybrid partitioning and enumeration solution scheme by combining the entropic approach with the recently developed improved surrogate constraint (ISC) method to produce the new method we call ISCENT. Our computational results indicate that ISCENT can be an order of magnitude more efficient than commercial solvers, such as CPLEX, for convex instances with no more than eight constraints. Furthermore, for nonconvex instances, ISCENT is shown to be significantly more efficient than other standard global solvers.

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Section: Nonlinear Separable Discrete-optimization Modelmentioning

confidence: 99%

Section: Nonlinear Separable Discrete-optimization Modelmentioning

confidence: 99%

Section: Nonlinear Separable Discrete-optimization Modelmentioning

confidence: 99%

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Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models

et al. 2014

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“…It can be observed that the alternative formulation (i.e., F2) is a multidimensional knapsack problem [24], which is NP-complete [13] in general. Many approaches have been proposed to solve it, such as LP-relaxation [25], the primaldual method [6] and dynamic programming [26].…”

Section: Problem Formulationmentioning

confidence: 99%

Peer-assisted texture streaming in metaverses

Liang

Zimmermann

Ooi

2011

Proceedings of the 19th ACM International Conference on Multimedia

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User-extensible metaverses need an effective way to disseminate massive and dynamic 3D contents (i.e., meshes, textures, animations, etc.) to end users, and at the same time maintain a low consumption of server bandwidth. Peer-topeer (or peer-assisted) technologies have been widely considered as a desirable complementary solution to efficaciously offload servers in large-scale media streaming applications. However, due to both the bandwidth constraints of heterogeneous users and unpredictable access patterns of latencysensitive 3D contents, it is very challenging to cut the server bandwidth cost in metaverses. In this paper, we propose a peer-assisted texture streaming architecture to minimize the server bandwidth consumption without degrading the end-user satisfaction. We propose a game-theoretic peer selection strategy which achieves a good trade-off between performance and complexity. Our algorithm is light-weight, and can efficiently utilize the bandwidth of users in a fully decentralized manner by enabling each peer (i.e., user) to quickly select its content providers which can satisfy the requests of the peer within the latency constraint of the content. We evaluate our algorithm through an extensive comparison study based on simulations using realistic data (i.e., avatar mobility traces and textures) collected from Second Life. The simulation results show that the proposed algorithm can effectively reduce the server bandwidth consumption without degrading the user experience.

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“…More recently, the 0-1 knapsack problem has also been used and discussed. [11][12][13][14][15][16] No discussion however seems to exist on the possibility of obtaining inferior solutions from the classical (0-1) knapsack problem formulation (1)-(2) compared to the competing cost-benefit approach for optimal allocation of resources. Despite the very large volume of existing research related to the (0-1) knapsack dynamic programming approach, this important point has been overlooked.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Optimal allocation of limitted resources among discrete risk-reduction options

Todinov

2014

AIR

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This study exposes a critical weakness of the (0-1) knapsack dynamic programming approach, widely used for optimal allocation of resources. The (0-1) knapsack dynamic programming approach could waste resources on insignificant improvements and prevent the more efficient use of the resources to achieve maximum benefit. Despite the numerous extensive studies, this critical shortcoming of the classical formulation has been overlooked. The main reason is that the standard (0-1) knapsack dynamic programming approach has been devised to maximise the benefit derived from items filling a space with no intrinsic value. While this is an appropriate formulation for packing and cargo loading problems, in applications involving capital budgeting, this formulation is deeply flawed. The reason is that budgets do have intrinsic value and their efficient utilisation is just as important as the maximisation of the benefit derived from the budget allocation.Accordingly, a new formulation of the (0-1) knapsack resource allocation model is proposed where the weighted sum of the benefit and the remaining budget is maximised instead of the total benefit. The proposed optimisation model produces solutions superior to both -the standard (0-1) dynamic programming approach and the cost-benefit approach.On the basis of common parallel-series systems, the paper also demonstrates that because of synergistic effects, sets including the same number of identical options could remove different amount of total risk. The existence of synergistic effects does not permit the application of the (0-1) dynamic programming approach. In this case, specific methods for optimal resource allocation should be applied. Accordingly, the paper formulates and proves a theorem stating that the maximum amount of removed total risk from operations and systems with parallel-series logical arrangement is achieved by using preferentially the available budget on improving the reliability of operations/components belonging to the same parallel branch. Improving the reliability of randomly selected operations/components not forming a parallel branch leads to a sub-optimal risk reduction. The theorem is a solid basis for achieving a significant risk reduction for systems and processes with parallel-series logical arrangement.

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The Multidimensional Knapsack Problem: Structure and Algorithms

Cited by 153 publications

References 32 publications

Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models

Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models

Peer-assisted texture streaming in metaverses

Optimal allocation of limitted resources among discrete risk-reduction options

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