Vehicle Routing Problems that Minimize the Completion Time: Heuristics, Worst-Case Analyses, and Computational Results

In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles to deliver the demands of all customers such that the total distance traveled by the fleet is minimized. In this dissertation, we study variants of the VRP that minimize the completion time, i.e., we minimize the distance of the longest route. We call it the min-max objective function. In applications such as disaster relief efforts and military operations, the objective is often to finish the delivery or the task as soon as possible, not to plan routes with the minimum total distance. Even in commercial package delivery nowadays, companies are investing in new technologies to speed up delivery instead of focusing merely on the min-sum objective. In this dissertation, we compare the min-max and the standard (min-sum) objective functions in a worst-case analysis to show that the optimal solution with respect to one objective function can be very poor with respect to the other. The results motivate the design of algorithms specifically for the min-max objective. We study variants of min-max VRPs including one problem from the literature (the min-max Multi-Depot VRP) and two new problems (the min-max Split Delivery Multi-Depot VRP with Minimum Service Requirement and the min-max Close-Enough VRP). We develop heuristics to solve these three problems. We compare the results produced by our heuristics to the best-known solutions in the literature and find that our algorithms are effective. In the case where benchmark instances are not available, we generate instances whose near-optimal solutions can be estimated based on geometry. We formulate the Vehicle Routing Problem with Drones and carry out a theoretical analysis to show the maximum benefit from using drones in addition to trucks to reduce delivery time. The speed-up ratio depends on the number of drones loaded onto one truck and the speed of the drone relative to the speed of the truck.

Design Optimization and Security For Communication Networks

In this work we introduce a new mathematical tool for optimization of routes, topology design, and energy efficiency in wireless sensor networks. We introduce a vector field formulation that models communication in the network, and routing is performed in the direction of this vector field at every location of the network. The magnitude of the vector field at every location represents the density of amount of data that is being transited through that location. We define the total communication cost in the network as the integral of a quadratic form of the vector field over the network area. With the above formulation, we introduce a mathematical machinery based on partial differential equations very similar to the Maxwell's equations in electrostatic theory. We show that in order to minimize the cost, the routes should be found based on the solution of these partial differential equations. In our formulation, the sensors are sources of information, and they are similar to the positive charges in electrostatics, the destinations are sinks of information and they are similar to negative charges, and the network is similar to a non-homogeneous dielectric media with variable dielectric constant (or permittivity coefficient). In one of the applications of our mathematical model based on the vector fields, we offer a scheme for energy efficient routing. Our routing scheme is based on changing the permittivity coefficient to a higher value in the places of the network where nodes have high residual energy, and setting it to a low value in the places of the network where the nodes do not have much energy left. Our simulations show that our method gives a significant increase in the network life compared to the shortest path and weighted shortest path schemes. Our initial focus is on the case where there is only one destination in the network, and later we extend our approach to the case where there are multiple destinations in the network. In the case of having multiple destinations, we need to partition the network into several areas known as regions of attraction of the destinations. Each destination is responsible for collecting all messages being generated in its region of attraction. The complexity of the optimization problem in this case is how to define regions of attraction for the destinations and how much communication load to assign to each destination to optimize the performance of the network. We use our vector field model to solve the optimization problem for this case. We define a vector field, which is conservative, and hence it can be written as the gradient of a scalar field (also known as a potential field). Then we show that in the optimal assignment of the communication load of the network to the destinations, the value of that potential field should be equal at the locations of all the destinations. Another application of our vector field model is to find the optimal locations of the destinations in the network. We show that the vector field gives the gradient of the cost function with respect to the locations of the destinations. Based on this fact, we suggest an algorithm to be applied during the design phase of a network to relocate the destinations for reducing the communication cost function. The performance of our proposed schemes is confirmed by several examples and simulation experiments. In another part of this work we focus on the notions of responsiveness and conformance of TCP traffic in communication networks. We introduce the notion of responsiveness for TCP aggregates and define it as the degree to which a TCP aggregate reduces its sending rate to the network as a response to packet drops. We define metrics that describe the responsiveness of TCP aggregates, and suggest two methods for determining the values of these quantities. The first method is based on a test in which we drop a few packets from the aggregate intentionally and measure the resulting rate decrease of that aggregate. This kind of test is not robust to multiple simultaneous tests performed at different routers. We make the test robust to multiple simultaneous tests by using ideas from the CDMA approach to multiple access channels in communication theory. Based on this approach, we introduce tests of responsiveness for aggregates, and call it CDMA based Aggregate Perturbation Method (CAPM). We use CAPM to perform congestion control. A distinguishing feature of our congestion control scheme is that it maintains a degree of fairness among different aggregates. In the next step we modify CAPM to offer methods for estimating the proportion of an aggregate of TCP traffic that does not conform to protocol specifications, and hence may belong to a DDoS attack. Our methods work by intentionally perturbing the aggregate by dropping a very small number of packets from it and observing the response of the aggregate. We offer two methods for conformance testing. In the first method, we apply the perturbation tests to SYN packets being sent at the start of the TCP 3-way handshake, and we use the fact that the rate of ACK packets being exchanged in the handshake should follow the rate of perturbations. In the second method, we apply the perturbation tests to the TCP data packets and use the fact that the rate of retransmitted data packets should follow the rate of perturbations. In both methods, we use signature based perturbations, which means packet drops are performed with a rate given by a function of time. We use analogy of our problem with multiple access communication to find signatures. Specifically, we assign orthogonal CDMA based signatures to different routers in a distributed implementation of our methods. As a result of orthogonality, the performance does not degrade because of cross interference made by simultaneously testing routers. We have shown efficacy of our methods through mathematical analysis and extensive simulation experiments.

Architectural-Physical Co-Design of 3D CPUs with Micro-Fluidic Cooling

The performance, energy efficiency and cost improvements due to traditional technology scaling have begun to slow down and present diminishing returns. Underlying reasons for this trend include fundamental physical limits of transistor scaling, the growing significance of quantum effects as transistors shrink, and a growing mismatch between transistors and interconnects regarding size, speed and power. Continued Moore's Law scaling will not come from technology scaling alone, and must involve improvements to design tools and development of new disruptive technologies such as 3D integration. 3D integration presents potential improvements to interconnect power and delay by translating the routing problem into a third dimension, and facilitates transistor density scaling independent of technology node. Furthermore, 3D IC technology opens up a new architectural design space of heterogeneously-integrated high-bandwidth CPUs. Vertical integration promises to provide the CPU architectures of the future by integrating high performance processors with on-chip high-bandwidth memory systems and highly connected network-on-chip structures. Such techniques can overcome the well-known CPU performance bottlenecks referred to as memory and communication wall. However the promising improvements to performance and energy efficiency offered by 3D CPUs does not come without cost, both in the financial investments to develop the technology, and the increased complexity of design. Two main limitations to 3D IC technology have been heat removal and TSV reliability. Transistor stacking creates increases in power density, current density and thermal resistance in air cooled packages. Furthermore the technology introduces vertical through silicon vias (TSVs) that create new points of failure in the chip and require development of new BEOL technologies. Although these issues can be controlled to some extent using thermal-reliability aware physical and architectural 3D design techniques, high performance embedded cooling schemes, such as micro-fluidic (MF) cooling, are fundamentally necessary to unlock the true potential of 3D ICs. A new paradigm is being put forth which integrates the computational, electrical, physical, thermal and reliability views of a system. The unification of these diverse aspects of integrated circuits is called Co-Design. Independent design and optimization of each aspect leads to sub-optimal designs due to a lack of understanding of cross-domain interactions and their impacts on the feasibility region of the architectural design space. Co-Design enables optimization across layers with a multi-domain view and thus unlocks new high-performance and energy efficient configurations. Although the co-design paradigm is becoming increasingly necessary in all fields of IC design, it is even more critical in 3D ICs where, as we show, the inter-layer coupling and higher degree of connectivity between components exacerbates the interdependence between architectural parameters, physical design parameters and the multitude of metrics of interest to the designer (i.e. power, performance, temperature and reliability). In this dissertation we present a framework for multi-domain co-simulation and co-optimization of 3D CPU architectures with both air and MF cooling solutions. Finally we propose an approach for design space exploration and modeling within the new Co-Design paradigm, and discuss the possible avenues for improvement of this work in the future.

Energy Cooperation in Energy Harvesting Communication Systems

In energy harvesting communications, users transmit messages using energy harvested from nature. In such systems, transmission policies of the users need to be carefully designed according to the energy arrival profiles. When the energy management policies are optimized, the resulting performance of the system depends only on the energy arrival profiles. In this dissertation, we introduce and analyze the notion of energy cooperation in energy harvesting communications where users can share a portion of their harvested energy with the other users via wireless energy transfer. This energy cooperation enables us to control and optimize the energy arrivals at users to the extent possible. In the classical setting of cooperation, users help each other in the transmission of their data by exploiting the broadcast nature of wireless communications and the resulting overheard information. In contrast to the usual notion of cooperation, which is at the signal level, energy cooperation we introduce here is at the battery energy level. In a multi-user setting, energy may be abundant in one user in which case the loss incurred by transferring it to another user may be less than the gain it yields for the other user. It is this cooperation that we explore in this dissertation for several multi-user scenarios, where energy can be transferred from one user to another through a separate wireless energy transfer unit. We first consider the offline optimal energy management problem for several basic multi-user network structures with energy harvesting transmitters and one-way wireless energy transfer. In energy harvesting transmitters, energy arrivals in time impose energy causality constraints on the transmission policies of the users. In the presence of wireless energy transfer, energy causality constraints take a new form: energy can flow in time from the past to the future for each user, and from one user to the other at each time. This requires a careful joint management of energy flow in two separate dimensions, and different management policies are required depending on how users share the common wireless medium and interact over it. In this context, we analyze several basic multi-user energy harvesting network structures with wireless energy transfer. To capture the main trade-offs and insights that arise due to wireless energy transfer, we focus our attention on simple two- and three-user communication systems, such as the relay channel, multiple access channel and the two-way channel. Next, we focus on the delay minimization problem for networks. We consider a general network topology of energy harvesting and energy cooperating nodes. Each node harvests energy from nature and all nodes may share a portion of their harvested energies with neighboring nodes through energy cooperation. We consider the joint data routing and capacity assignment problem for this setting under fixed data and energy routing topologies. We determine the joint routing of energy and data in a general multi-user scenario with data and energy transfer. Next, we consider the cooperative energy harvesting diamond channel, where the source and two relays harvest energy from nature and the physical layer is modeled as a concatenation of a broadcast and a multiple access channel. Since the broadcast channel is degraded, one of the relays has the message of the other relay. Therefore, the multiple access channel is an extended multiple access channel with common data. We determine the optimum power and rate allocation policies of the users in order to maximize the end-to-end throughput of this system. Finally, we consider the two-user cooperative multiple access channel with energy harvesting users. The users cooperate at the physical layer (data cooperation) by establishing common messages through overheard signals and then cooperatively sending them. For this channel model, we investigate the effect of intermittent data arrivals to the users. We find the optimal offline transmit power and rate allocation policy that maximize the departure region. When the users can further cooperate at the battery level (energy cooperation), we find the jointly optimal offline transmit power and rate allocation policy together with the energy transfer policy that maximize the departure region.