Multiple Multidimensional Knapsack Problem Research Articles

Improving access to housing and supportive services for runaway and homeless youth: Reducing vulnerability to human trafficking in New York City

Recent estimates indicate that there are over a million runaway and homeless youth and young adults (RHY) in the United States (US). Exposure to trauma, violence, and substance abuse, coupled with a lack of community support services, puts homeless youth at high risk of being exploited and trafficked. Although access to safe housing and supportive services such as physical and mental healthcare is an effective response to the vulnerability of RHY towards being trafficked, the number of youth experiencing homelessness exceeds the capacity of available housing resources in most US communities. We undertake a RHY-informed, systematic, and data-driven approach to project the collective capacity required by service providers to adequately meet the needs of RHY in New York City, including those most at risk of being trafficked. Our approach involves an integer linear programming model that extends the multiple multidimensional knapsack problem and is informed by partnerships with key stakeholders. The mathematical model allows for time-dependent allocation and capacity expansion, while incorporating stochastic youth arrivals and length of stays, services provided in a periodic fashion, and service delivery time windows. Our RHY and service provider-centered approach is an important step toward meeting the actual, rather than presumed, survival needs of vulnerable youth.

Cost, energy, and response delay awareness-solution for cloud resources management: proposition of a predictive dynamic algorithm for VMs allocation over a distributed cloud infrastructure

Virtual resources allocation and placement problem in a distributed Cloud infrastructure presents a compromising question. The geographic position of data centers; their available free resources; the correspondent delay and energy consumption constraints are factors that involve determining the best allocation and placement decision. Allocation and placement cost will be relatively determined according to that choice. In fact, data centers, installed in cold regions, offer lower costs because they need few cooling maintenances, consequently, energy consumptions are minimized. However, data centers, installed closer to population areas, could impose higher costs because of their limited resources or high need for cooling maintenance, so energy consumptions have to be higher. On the other hand, and within acceptable network conditions, allocating powerful resources placed in closer data centers may guarantee shorter global response delay. This could be helpful to support delay-sensitive applications such as Massively Multi-players Online Gaming (MMOG) and enhance their relative Quality of Experience (QoE). However, it may engender high costs and vice versa. In this view, the present paper highlights the critical relationship between the three basics metrics affecting the QoE of the MMOG service, namely the cost, the energy consumption, and the global response delay. We propose a Predictive Dynamic Virtual Machines (VMs) Allocation and Placement algorithm based on the Seasonal Autoregressive Integrated Moving Average (SARIMA) prediction model that captures the intrinsic trade-off of these metrics and outcomes the best mapping of necessary allocated resources. Our contribution is formulated as a Multiple Multidimensional Knapsack Problem (MMKP). Results show the effectiveness of our contribution in maintaining the balance between low-cost objective, low energy consumption by minimizing the inter-migrations of VMs over data centers, and acceptable delay maintained under a predefined threshold.

A Container Based Edge Offloading Framework for Autonomous Driving

Autonomous driving is one of the most innovative applications nowadays. However, autonomous driving is still suffering from heavy calculation, high energy consumption and strict real-time execution constraints. Different from cloud computing, edge computing deploys calculation, storage and service on the edge of network. It is a better platform to serve efficiency and privacy oriented autonomous driving service offloading. To this end, we proposed a container-based edge offloading framework for autonomous driving. This framework builds an Offloading Decision Module, an Offloading Scheduler Module and an Edge Offloading Middleware on top of the lightweight virtualization. It provides the abstraction and management of the execution environment in the granularity of containers on edge. Therefore, it enables the privacy preserve and resource isolation for autonomous driving execution constraints. Its utility preferable offloading schedule strategy formalized the multi-application multi-edge nodes mapping problem into a multiple multidimensional knapsack problem (MMKP) and gave a utility oriented greedy algorithm (GA) for real-time solving. The experimental results show that the proposed framework has high feasibility and isolation meanwhile can guarantee millisecond-level autonomous driving offloading on edge.

A Hierarchical Vehicular-Based Architecture for Vehicular Networks: A Case Study on Computation Offloading

In order to realize an intelligent transportation system (ITS) which will provide smooth urban traffic, autonomous driving, accurate route navigation, etc., enormous computations need to be migrated from cloud centers to edge nodes, especially for the services requiring stringent latency. In addition to base stations and road side units (RSUs), vehicles can be alteratively considered as a kind of computation resources. In this article, a hierarchical vehicular-based architecture which consists of cloud centers and vehicles is investigated. Computation offloading performance in the hierarchical architecture is also studied. In specific, the main components in vehicular networks and their characteristics on communication and computations are presented firstly. Several communication techniques that are essential in enabling computation offloading among these components are then discussed. Secondly, a hierarchical vehicular-based architecture, which integrates the main components, is constructed. Thirdly, a case study on computation offloading in the proposed architecture is conducted. In the concerned scenario, the computation offloading problem is modelled as a multi-dimensional multiple knapsack problem (MMKP). Two algorithms are investigated, among which, the first algorithm is a greedy heuristic method providing a sub-optimal solution with a low computational complexity. The second algorithm is a modified branch and bound (B&B) method, which can obtain the best solution with a high computational complexity. Numerical results are also presented to verify the performance of the two algorithms. It can be demonstrated that the proposed architecture can migrate more computations from cloud centers to vehicular nodes, when the computations require more communication resources.

The Multiple Multidimensional Knapsack with Family-Split Penalties

The Multiple Multidimensional Knapsack Problem with Family-Split Penalties (MMdKFSP) is introduced as a new variant of both the more classical Multi-Knapsack and Multidimensional Knapsack Problems. It reckons with items categorized into families and where if an individual item is selected to maximize the profit, all the items of the same family must be selected as well. Items belonging to the same family can be assigned to different knapsacks; however, in this case, split penalties are incurred. This problem arises in resource management of distributed computing contexts and Service Oriented Architecture environments. An exact algorithm based on the exploitation of a specific combinatorial Benders’ cuts approach is proposed. Computational experiments on different sets of benchmark test problems show the effectiveness of the proposed algorithm. The comparison against a state-of-the-art commercial solver confirms the validity of the proposed approach considering also the scalability issue.

Model and algorithms for multi-period sea cargo mix problem

In this paper, we consider the sea cargo mix problem in international ocean container shipping industry. We describe the characteristics of the cargo mix problem for the carrier in a multi-period planning horizon, and formulate it as a multi-dimensional multiple knapsack problem (MDMKP). In particular, the MDMKP is an optimization model that maximizes the total profit generated by all freight bookings accepted in a multi-period planning horizon subject to the limited shipping capacities. We propose two heuristic algorithms that can solve large scale problems with tens of thousands of decision variables in a short time. Finally, numerical experiments on a wide range of randomly generated problem instances are conducted to demonstrate the efficiency of the algorithms.