Multiple-choice Knapsack Problem Research Articles

Optimal local rejection for classifiers

We analyse optimal rejection strategies for classifiers with input space partitioning, e.g. prototype-based classifiers, support vector machines or decision trees using certainty measures such as the distance to the closest decision border. We provide new theoretical results: we link this problem to the multiple choice knapsack problem and devise an exact polynomial-time dynamic programming (DP) scheme to determine optimal local thresholds on given data. Further, we propose a linear time, memory efficient approximation thereof. We show in experiments that the approximation has a competitive performance compared to the full DP. Further, we evaluate the performance of classification with rejection in various benchmarks: we conclude that local rejection is beneficial in particular for simple classifiers, while the improvement is less pronounced for advanced classifiers. An evaluation on speech prosody and biomedical data highlights the benefit of local thresholds.

Multimode Image Compression Algorithm Employing Multiple-Choice Knapsack Problem-Based Encoding Mode Selection

In this paper, we first formulate the encoding mode selection of a multimode image compression algorithm, which adaptively determines the encoding mode to encode a patch of a given image as a multiple-choice knapsack problem (MCKP). Then, we present a multimode image compression algorithm that takes advantage of the MCKP-formulated mode selection problem and a memory-efficient implementation of the MCKP-based mode selection algorithm. To emphasize the effect of the MCKP-based mode selection, the proposed multimode image compression algorithm adopts encoding modes from conventional multimode image compression algorithms. In experiments using the Kodak test image set, the proposed algorithm outperformed benchmark algorithms by 2.6–7.8 dB in the average peak signal-to-noise ratio when the target compression ratio is 1/6.

On Optimal Scheduling Algorithms for Well-Structured Workflows in the Cloud with Budget and Deadline Constraints

In this paper, we consider optimal scheduling algorithms for scientific workows with two typical structures, fork&join and tree, on a set of provisioned (virtual) machines under budget and deadline constraints in cloud computing. First, given a total budget B, by leveraging a bi-step dynamic programming technique, we propose optimal algorithms in pseudo-polynomial time for both workows with minimum scheduling length as a goal. Our algorithms are efficient if the total budget B is polynomially bounded by the number of jobs in respective workows, which is usually the common case in practice. Second, we consider the dual of this optimization problem to minimize the cost when the deadline of the computation D is fixed. We change this problem into the standard multiple-choice knapsack problem via a parallel transformation.

Allocating metrology capacity to multiple heterogeneous machines

The measurement of lots to check process quality is crucial but also a non-added value operation in manufacturing systems. This paper is motivated by semiconductor manufacturing, where metrology tools are expensive, thus limiting metrology capacity which must be optimally used. In a context where multiple heterogeneous machines are sharing a common metrology workshop, the problem of minimising risk while considering metrology capacity arises. An integer linear programming (ILP) model is presented, which corresponds to a multiple-choice knapsack problem. Simple rounding heuristics are proposed, whose results on randomly generated instances are compared with the optimal solutions obtained using a standard solver on the ILP. Additionally, numerical experiments on industrial data are presented and discussed.

An empirical study of population-based metaheuristics for the multiple-choice multidimensional knapsack problem

An empirical study of population-based metaheuristics for the multiple-choice multidimensional knapsack problem

네트워크 코딩을 쓰는 언더레이 인지 무선 네트워크에서의 주파수 할당과 경로 선택 기법

In this paper, we propose frequency allocation and path selection scheme in underlay cognitive radio (CR) networks using network coding. In the proposed scheme, we choose the path with consideration of network coding and interference temperature in underlay CR networks and propose an optimization problem to maximize the system throughput of secondary users (SUs). Then, we represent the proposed optimization problem as the multi-dimensional multiple-choice knapsack problem and give the theoretical upper bound for the system throughput of SUs by using linear programming. Finally, we compute the system throughput of SUs by using brute-force search (BFS) and link quality first (LQF) scheme in underlay CR networks. Simulation results show that the system throughput of SUs with BFS is higher than that with LQF in underlay CR networks with and without application of network coding, respectively.

Single Commodity Stochastic Network Design Under Probabilistic Constraint with Discrete Random Variables

Single commodity networks are considered, where demands at the nodes are random. The problem is to find minimum cost optimal built in capacities at the nodes and arcs subject to the constraint that all demands should be met on a prescribed probability level (reliability constraint) and some deterministic constraints should be satisfied. The reliability constraint is formulated in terms of the Gale–Hoffman feasibility inequalities, but their number is reduced by elimination technique. The concept of a p-efficient point is used in a smart way to convert and then relax the problem into an LP. The p-efficient points are simultaneously generated with the solution of the LP. The joint distribution of the demands is used to obtain the p-efficient points for all stochastic inequalities that were not eliminated and the solution of a multiple choice knapsack problem is used to generate p-efficient points. The model can be applied to planning in interconnected power systems, flood control networks, design of shelter and road capacities in evacuation, parking lot capacities, financial networks, cloud computing system design, etc. Numerical examples are presented.

A set partitioning reformulation for the multiple-choice multidimensional knapsack problem

The Multiple-choice Multidimensional Knapsack Problem (MMKP) is a well-known -hard combinatorial optimization problem that has received a lot of attention from the research community as it can be easily translated to several real-world problems arising in areas such as allocating resources, reliability engineering, cognitive radio networks, cloud computing, etc. In this regard, an exact model that is able to provide high-quality feasible solutions for solving it or being partially included in algorithmic schemes is desirable. The MMKP basically consists of finding a subset of objects that maximizes the total profit while observing some capacity restrictions. In this article a reformulation of the MMKP as a set partitioning problem is proposed to allow for new insights into modelling the MMKP. The computational experimentation provides new insights into the problem itself and shows that the new model is able to improve on the best of the known results for some of the most common benchmark instances.

An exact algorithm for the reliability redundancy allocation problem

Abstract The redundancy allocation problem is the problem of finding an optimal allocation of redundant components subject to a set of resource constraints. The problem studied in this paper refers to a series-parallel system configuration and allows for component mixing. We propose a new modeling/solution approach, in which the problem is transformed into a multiple choice knapsack problem and solved to optimality via a branch and cut algorithm. The algorithm is tested on well-known sets of benchmark instances. All instances have been solved to optimality in milliseconds or very few seconds on a normal workstation.

Teacher training enhances the teaching-learning-based optimisation metaheuristic when used to solve multiple-choice multidimensional knapsack problems

A new metaheuristic, the teaching-learning-based optimisation TLBO metaheuristic, based on the relationship between teachers and learners has recently been proposed by Rao, Savsani and Vakharia 2011 for solving continuous nonlinear optimisation problems. It is of particular interest because it is a population-based metaheuristic that can be easily adapted to solve combinatorial optimisation problems and requires no parameter fine-tuning other than determining the size of the population and convergence criteria. In this paper, we enhance the performance of the TLBO method by introducing 'teacher training' before the teaching phase of TLBO. That is, before the teaching phase of TLBO, we perform a local neighbourhood search on the best solution the teacher in the current population. The effectiveness of teacher training TT in terms of both solution quality and convergence rate will be demonstrated by using this approach TT-TLBO to solve a large 393 number of problem instances from the literature for the important NP-Hard multiple-choice multidimensional knapsack problem MMKP. Furthermore, we will demonstrate that TLBO outperforms the best published solution approaches for the MMKP.

Finding a risk-constrained shortest path for an unmanned combat vehicle

We consider a problem of finding a reconnaissance route of an unmanned combat vehicle (UCV) in a terrain, which is modeled as a grid. It is assumed that the traverse time to pass through each cell in the grid and risk level associated with each cell are given and that the cells where the reconnaissance points to be visited by the UCV are located and the visiting sequence of such cells are given in advance as in real situation of military operation. We focus on the problem with the objective of minimizing the total travel time of the UCV for a given limit on the sum of risk level values associated with the cells on the path of the UCV. We develop an optimal solution algorithm based on a dynamic programming algorithm for multiple-choice knapsack problems. We also present a heuristic algorithm, which can be used for large-size problems. For evaluation of the performance of the proposed algorithms, computational experiments are performed on a number of problem instances, and results show that the proposed algorithms give optimal or good solutions within an acceptable time for real military operations.

Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem

This article addresses a Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem, an NP-hard combinatorial optimization problem. The problem is solved by using a cooperative approach that uses a local search for exploring a series of neighbourhoods induced from the Lagrangian relaxation. Each neighbourhood is submitted to an optimization process using two alternative strategies: reducing and moving strategies. The reducing strategy serves to reduce the current search space whereas the moving strategy explores the new search space. The performance of the proposed approach is evaluated on benchmark instances taken from the literature. Its obtained results are compared with those reached by some recent methods available in the literature. New solutions have been obtained for almost 80% of the instances tested.

Web services composition: Complexity and models

A web service is a modular and self-described application callable with standard web technologies. A workflow describes how to combine the functionalities of different web services in order to create a new value added functionality resulting in composite web service. QoS-aware web service composition means to select a composite web service that maximizes a QoS objective function while satisfying several QoS constraints (e.g. price or duration). The workflow-based QoS-aware web service composition problem has received a lot of interest, mainly in web service community. This general problem is NP-hard since it is equivalent to the multidimensional multiple choice knapsack problem (MMKP). In this article, the theoretical complexity is analysed more precisely in regard to the property of the workflow structuring the composition. For some classes of workflows and some QoS models, the composition problem can be solved in polynomial time (since the workflow is a series–parallel directed graph). Otherwise, when there exist one or several QoS constraints to verify, the composition problem becomes NP-hard. In this case, we propose a new mixed integer linear program to represent the problem with a polynomial number of variables and constraints. Then, using CPLEX, we present some experimental results showing that our proposed model is able to solve big size instances.

Implicit cover inequalities

In this paper we consider combinatorial optimization problems whose feasible sets are simultaneously restricted by a binary knapsack constraint and a cardinality constraint imposing the exact number of selected variables. In particular, such sets arise when the feasible set corresponds to the bases of a matroid with a side knapsack constraint, for instance the weighted spanning tree problem and the multiple choice knapsack problem. We introduce the family of implicit cover inequalities which generalize the well-known cover inequalities for such feasible sets and discuss the lifting of the implicit cover inequalities. A computational study for the weighted spanning tree problem is reported.

Budget-Driven Scheduling Algorithms for Batches of MapReduce Jobs in Heterogeneous Clouds

In this paper, we consider task-level scheduling algorithms with respect to budget and deadline constraints for a batch of MapReduce jobs on a set of provisioned heterogeneous (virtual) machines in cloud platforms. The heterogeneity is manifested in the popular “pay-as-you-go” charging model where the service machines with different performance would have different service rates. We organize the batch of jobs as a k-stage workflow and study two related optimization problems, depending on whether the constraints are on monetary budget or on scheduling length of the workflow. First, given a total monetary budget B, by combining an in-stage local greedy algorithm (whose optimality is also proven) and dynamic programming (DP) techniques, we propose a global optimal scheduling algorithm to achieve minimum scheduling length of the workflow within O(kB <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). Although the optimal algorithm is efficient when B is polynomially bounded by the number of tasks in the MapReduce jobs, the quadratic time complexity is still high. To improve the efficiency, we further develop two greedy algorithms, called Global Greedy Budget (GGB) and Gradual Refinement (GR), each adopting different greedy strategies. In GGB we extend the idea of the local greedy algorithm to the efficient global distribution of the budget with minimum scheduling length as a goal whilst in GR we iteratively apply the DP algorithm to the distribution of exponentially reduced budget so that the solutions are gradually refined. Second, we consider the optimization problem of minimizing cost when the (time) deadline of the computation D is fixed. We convert this problem into the standard Multiple-Choice Knapsack Problem via a parallel transformation. Our empirical studies verify the proposed optimal algorithms and show the efficiencies of the greedy algorithms in cost-effectiveness to distribute the budget for performance optimizations of the MapReduce workflows.

Target Tracking via Crowdsourcing: A Mechanism Design Approach

In this paper, we propose a crowdsourcing based framework for myopic target tracking by designing an incentive-compatible mechanism based optimal auction in a wireless sensor network (WSN) containing sensors that are selfish and profit-motivated. For typical WSNs which have limited bandwidth, the fusion center (FC) has to distribute the total number of bits that can be transmitted from the sensors to the FC among the sensors. To accomplish the task, the FC conducts an auction by soliciting bids from the selfish sensors, which reflect how much they value their energy cost. Furthermore, the rationality and truthfulness of the sensors are guaranteed in our model. The final problem is formulated as a multiple-choice knapsack problem (MCKP), which is solved by the dynamic programming method in pseudo-polynomial time. Simulation results show the effectiveness of our proposed approach in terms of both the tracking performance and lifetime of the sensor network.

CAD-MAC: A Channel-Aggregation Diversity Based MAC Protocol for Spectrum and Energy Efficient Cognitive Ad Hoc Networks

In cognitive Ad Hoc networks (CAHN), because the contentions and mutual interferences among secondary nodes are inevitable as well as secondary nodes usually have limited power budget, spectrum efficiency and energy efficiency are critically important to the CAHN, especially for the medium access control (MAC) protocol design. Aiming at improving both spectrum and energy efficiencies, we in this paper propose a diversity technology called Channel-Aggregation Diversity (CAD), through which each node can utilize multiple channels simultaneously and efficiently allocate the upper-bounded power resource with only one data radio. Based on the proposed CAD technology, we further develop a CAD-based MAC (CAD-MAC) protocol, which enables the secondary nodes to sufficiently use available channel resources under the upper-bounded power and transmit multiple data packets in one transmission process subject to the transmission-time fairness constraint. In order to improve the performance of CAHNs, we propose two joint power-channel allocation schemes. In the first scheme, we aim at maximizing the data transmission rate. By converting the joint power-channel allocation to the Multiple-Choice Knapsack Problem, we derive the optimal allocation policy through dynamic programming. In the second scheme, our objective is to optimize the energy efficiency and we obtain the corresponding allocation policy through fractional programming. Simulation results show that our proposed CAD-MAC protocol can efficiently increase the spectrum and energy efficiencies as well as the throughput of the CAHN compared with existing protocols. Moreover, the energy efficiency of the CAHN can be further improved by adopting the energy efficiency optimization based resource allocation scheme.

Parallel Machine Selection and Job Scheduling to Minimize Sum of Machine Holding Cost, Total Machine Time Costs, and Total Tardiness Costs

This paper is concerned with scheduling of a set of single-operation tasks on a set of parallel machines where subcontracting is allowed. The objective is to choose a subset of machines/subcontractors from a set of available machines/subcontractors to perform all jobs to minimize sum of several costs. Processing time of jobs is assumed to be equal. Lower and upper bound for number of jobs assigned to a machine/subcontractor is considered. We first present a comprehensive survey of applications and models. We show special case of the problem when lower bound for number of jobs assigned to each machine/subcontractor is equal to zero is equivalent to single-sink fixed-charge transportation problem (SSFCT). This proves NP-hardness of the problem. Efficient dynamic programming algorithm for this special case is presented. Complicating issues regarding the general case with nonzero lower bounds for number of jobs assigned to machines/subcontractors is discussed. We transfer the general problem to multiple choice knapsack problem (MCKP) that can be solved efficiently using available algorithms. Several new problems are introduced. Complexity of each problem is resolved. Transformation to MCKP is provided that allows available algorithms to solve the problems. The main contribution of this paper is to establish theoretical results regarding the solution of these difficult problems.

Randomization inference for the trimmed mean of effects attributable to treatment

Randomization is described by Fisher (1935) as the reasoned basis for about the effectiveness of treatments. Fisher advocated both using in design- ing experiments and using randomization inference to analyze experiments that have been randomized. Randomization is that assumes only the physical act of for its validity. It provides exact, distrib ution free inferences in randomized experiments. In this paper, we expand the scope of by developing for the trimmed mean of effects attributable to treatment. Trimmed means of the effects attributable to treatment are interpre table summaries of the treatment effect that are robust to outliers. We connect the problem for trimmed means of effects attributable to treatment to a multiple choice knap sack problem, and use an efficient combinatorial optimization algorithm.

Adaptive perturbed neighbourhood search for the expanding capacity multiple-choice knapsack problem

In this paper, we develop a perturbed reactive-based neighbourhood search algorithm for the expanding constraint multiple-choice knapsack problem. It combines reactive tabu search with some specific neighbourhood search strategies to approximately solve the problem. The tests were conducted on randomly generated instances and executed in comparable benchmark scenarios to those of the literature. The results outperform those of the Cplex solver and demonstrate the high quality of the two approach versions.