Multi-dimension Multi-choice Knapsack Problem Research Articles

Cooperative Edge Caching With Location-Based and Popular Contents for Vehicular Networks

In this article, we propose a cooperative edge caching scheme, which allows vehicles to fetch one content from multiple caching servers cooperatively. In specific, we consider two types of vehicular content requests, i.e., location-based and popular contents, with different delay requirements. Both types of contents are encoded according to fountain code and cooperatively cached at multiple servers. The proposed scheme can be optimized by finding an optimal cooperative content placement that determines the placing locations and proportions for all contents. To this end, we first analyze the upper bound proportion of content caching at a single server, which is determined by both the downloading rate and the association duration when the vehicle drives through the server's coverage. For both types of contents, the respective theoretical analysis of transmission delay and service cost (including content caching and transmission cost) are provided. We then formulate an optimization problem of cooperative content placement to minimize the overall transmission delay and service cost. As the problem is a multi-objective multi-dimensional multi-choice knapsack problem, which is proved to be NP-hard, we devise an ant colony optimization-based algorithm to solve the problem and achieve a near-optimal solution. Simulation results are provided to validate the performance of the proposed algorithm, including its convergence and optimality of caching, while guaranteeing low transmission delay and service cost.

Smart Contract-Based Long-Term Auction for Mobile Blockchain Computation Offloading

In a mobile blockchain network, many mobile devices have insufficient computational capacity to execute computation-intensive tasks locally. To tackle this problem, blockchain tasks can be offloaded to edge servers with the aid of auction. However, most auction mechanisms on mobile blockchain ignore the automatic parallel execution and long-term performance. This paper aims to solve the problem of computation offloading in a mobile blockchain network. We transform this problem into a multi-choice multi-dimensional knapsack problem which is NP-hard. To improve the total utility of auction participants, this paper proposes a smart-contract-based double auction mechanism, named long-term auction for mobile blockchain (LAMB). The subtasks can be offloaded from one mobile device to heterogeneous edge servers. Also, LAMB satisfies the economic properties of an auction mechanism. Experimental results demonstrate that, the utility and utilization ratio can be achieved by 130.55% higher and 138.64% higher, respectively, in comparison to the existing auction algorithm WBD. Furthermore, the proposed LAMB can guarantee long-term performance for task offloading, and it can achieve automatic execution in an autonomous and secure environment.

QoS-Aware Web Service Selection with Internal Complementarity

Service composition is a key enabling technology in service-oriented computing for developing versatile applications by integrating various existing interoperable services. Although actively studied, most existing works on service composition neglect the existence of complementarity among candidate services within a service class, so-called internal complementarity. In fact, complementary candidate services within a service class can be composed to form a composite candidate service which may yield better service utility than that provided by any existing candidate service within that service class. This work focuses on web service composition where internal complementarity is more likely to happen. Specifically, we aim at addressing the problem of QoS-aware web service selection with internal complementarity (WSS-IC). We first transform this problem into a multi-choice multi-dimensional knapsack problem (MMKP) and prove such a transformation per se has non-polynomial time complexity in the worse case.Then, we perform complexity analysis to demonstrate that existing approaches to MMKPs are not computationally feasible to resolve QoS-aware WSS-IC. This fact motivates us to propose an iteratively improving framework for deriving the solution iteration by iteration while taking into account both solution structure and QoS constraints. At each iteration, the current solution gets improved by solving a disjunctively constrained knapsack problem. To verify the effectiveness of the proposed framework, two heuristic approaches are implemented under this framework. Experimental results demonstrate that our approaches outperform the compared methods in terms of both solution quality and computation time.

Coordinated road-network search route planning by a team of UAVs

This paper presents a road-network search route planning algorithm by which multiple autonomous vehicles are able to efficiently visit every road identified in the map in the context of the Chinese postman problem. Since the typical Chinese postman algorithm can be applied solely to a connected road-network in which ground vehicles are involved, it is modified to be used for a general type of road map including unconnected roads as well as the operational and physical constraints of unmanned aerial vehicles (UAVs). For this, a multi-choice multi-dimensional knapsack problem is formulated to find an optimal solution minimising flight time and then solved via mixed integer linear programming. To deal with the dynamic constraints of the UAVs, the Dubins theory is used for path generation. In particular, a circular–circular–circular type of the Dubins path is exploited based on a differential geometry to guarantee that the vehicles follow the road precisely in a densely distributed road environment. Moreover, to overcome the computational burden of the multi-choice multi-dimensional knapsack algorithm, a nearest insertion and auction-based approximation algorithm is newly introduced. The properties and performance of the proposed algorithm are evaluated via numerical simulations operating on a real village map and randomly generated maps with different parameters.

Study on Highway Investment Decision under Uncertainty with Shackle Model

Shackle model is used to study highway investment decision under uncertainty. In Shackle model, the uncertainty associated with possible outcomes for project benefit analysis is measured by degree of surprise, and a priority index for performance evaluation of each possible outcome and degree of surprise pair is proposed, thus, the standardized focus gain value and focus loss value from the expected outcome can be established. The standardized focus gain-over-loss ratios corresponding to multiple performance measures are synthesized into an overall ratio as the overall benefits, and then the proposed problem can be built as a multi-choice multi-dimensional knapsack problem which could be solved.

Fast multidimension multichoice knapsack heuristic for MP-SoC runtime management

Since the application complexity is growing and applications can be dynamically activated, the major challenge for heterogeneous multiprocessor platforms is to select at runtime an energy-efficient mapping of these applications. Taking into account that many different possible implementations per application can be available, and that the selection must meet the application deadlines under the available platform resources, this runtime optimization problem can be modeled as a Multidimension Multichoice Knapsack Problem (MMKP), which is known to be NP-hard. Not only algorithms for an optimal solution, but also state-of-the-art heuristics for real-time systems are still too slow for runtime management of multiprocessor platforms. This article provides a new fast and lightweight heuristic for finding near-optimal solutions for MMKP problems. The main contribution of this heuristic is: (i) the Pareto filtering of each initial MMKP set to reduce the search space, (ii) the sorting of all Pareto points together in a single two-dimension search space, where (iii) a very fast greedy algorithm solves the MMKP. Experiments show that our heuristic finds solutions close (within 0% to 0.4%) to the ones obtained by the fastest state-of-the-art heuristics, in just a fraction of the execution time (more than 97.5% gain on a StrongARM processor) and can run in less than 1ms for multiprocessor problem sizes. This is required for realistic OS reaction times in video and wireless application sets.

A Heuristic Algorithm for Resource Allocation/Reallocation Problem

This paper presents a 1-opt heuristic approach to solve resource allocation/reallocation problem which is known as 0/1 multichoice multidimensional knapsack problem (MMKP). The intercept matrix of the constraints is employed to find optimal or near‐optimal solution of the MMKP. This heuristic approach is tested for 33 benchmark problems taken from OR library of sizes upto 7000, and the results have been compared with optimum solutions. Computational complexity is proved to be O(klmn2) of solving heuristically MMKP using this approach. The performance of our heuristic is compared with the best state‐of‐art heuristic algorithms with respect to the quality of the solutions found. The encouraging results especially for relatively large‐size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP‐hard problems.

Stochastic Optimization Model and O(N2) Solution Algorithm for Highway Investment Decision Making under Budget Uncertainty

One of the key tasks in highway investment decision making is to conduct project selection. The existing optimization models for project selection concerning an entire highway system do not address the issue of budget uncertainty, limiting their ability to produce truly optimal results. This paper presents a stochastic optimization model that explicitly addresses budget uncertainty in highway investment decision making. The model is formulated as the stochastic multichoice multidimensional Knapsack problem with Ω -stage budget recourses that facilitates the selection of a subset of candidate highway projects, proposed to address the needs of a highway system across a multiyear project selection and programming period, in the most cost-effective manner. An efficient solution algorithm with the computational complexity of O ( N2 ) is developed for the proposed model. A computational study is performed to compare the investment decision outcomes by applying the proposed model with and without budget uncertai...

Downlink Resource Allocation for Autonomous Infrastructure-based Multihop Cellular Networks

Considering a multihop cellular system with one relay per sector, an effective modeling for the joint base-station/relay assignment, rate allocation, and routing scheme is proposed and formulated under a single problem for the downlink. This problem is then formulated as a multidimensional multichoice knapsack problem (MMKP) to maximize the total achieved throughput in the network. The well-known MMKP algorithm based on Lagrange multipliers is modified, which results in a near-optimal solution with a linear complexity. The notion of the infeasibility factor is also introduced to adjust the transmit power of base stations and relays adaptively. To reduce the complexity, and in order to analyze the underlying key factors in the system, the framework is restricted to a two-base-station two-relay system. In fact, the output of the proposed algorithm is the joint optimization of the routing path, and base-station selection to achieve the maximum total throughput in the system, which in conjunction with the proposed adaptive scheme leads to the implementation of the cell breathing via allocating the proper transmit power to the base-stations and relays.

Application of Shackle’s Model and System Optimization for Highway Investment Decision Making under Uncertainty

This paper introduces a new methodology for highway investment decision making under uncertainty that uses Shackle's model for uncertainty-based project benefit analysis and system optimization for project selection. Shackle's model overcomes limitations of the risk-based life-cycle cost analysis approach by using degree of surprise as a measure of uncertainty associated with possible outcomes of performance measures utilized for project benefit analysis instead of probability distribution. It also employs a priority index that jointly evaluates each possible outcome and degree of surprise pair for a performance measure to establish the standardized focus gain value and focus loss value from the expected outcome. The standardized focus gain-over-loss ratios corresponding to multiple performance measures are synthesized into an overall ratio that is regarded as the overall benefits of a highway project under uncertainty. This ratio is used as the basis of project selection. An optimization model is formulated as the multichoice multidimensional knapsack problem for project selection. A case study reveals significant differences in project selection results between the use of the proposed methodology and the existing risk-based approach.

Resource allocation on computational grids using a utility model and the knapsack problem

This work introduces a utility model (UM) for resource allocation on computational grids and formulates the allocation problem as a variant of the 0–1 multichoice multidimensional knapsack problem. The notion of task-option utility is introduced, and it is used to effect allocation policies. We present a variety of allocation policies, which are expressed as functions of metrics that are both intrinsic and external to the task and resources. An external user-defined credit-value metric is shown to allow users to intervene in the allocation of urgent or low priority tasks. The strategies are evaluated in simulation against random workloads as well as those drawn from real systems. We measure the sensitivity of the UM-derived schedules to variations in the allocation policies and their corresponding utility functions. The UM allocation strategy is shown to optimally allocate resources congruent with the chosen policies.

A New Heuristic for Solving the Multichoice Multidimensional Knapsack Problem

A new heuristic for solving the multichoice multidimensional knapsack problem (MMKP) is presented in this paper. The MMKP is first reduced to a multidimensional knapsack problem (MKP). A linear programming relaxation of the resulting MKP is solved, and a series of new values for the variables is computed. These values, pseudo-utility values, and resource value coefficients computed as well, are used in order to obtain a feasible solution for the original MMKP. Finally, the quality of the feasible solution is improved using the pseudo-utility values and the coefficient values of the objective function. Numerical results show that the performance of this approach is superior to that of previous techniques.

Self assessment and cognitive performance tests during EEG recording with a database-controlled interactive assessment tool (DIAT)

This work introduces a utility model (UM) for resource allocation on computational grids and formulates the allocation problem as a variant of the 0–1 multichoice multidimensional knapsack problem. The notion of task-option utility is introduced, and it is used to effect allocation policies. We present a variety of allocation policies, which are expressed as functions of metrics that are both intrinsic and external to the task and resources. An external user-defined credit-value metric is shown to allow users to intervene in the allocation of urgent or low priority tasks. The strategies are evaluated in simulation against random workloads as well as those drawn from real systems. We measure the sensitivity of the UM-derived schedules to variations in the allocation policies and their corresponding utility functions. The UM allocation strategy is shown to optimally allocate resources congruent with the chosen policies.