A combinatorial congestion estimation approach with generalized detours

AbstractCongestion estimation plays an important role in the physical layout of VLSI design. This paper presents a new probabilistic estimation model that improves the previous estimators by relaxing the constraint on detours in a route. The model is more general and realistic for it gives the flexibility for the wires to have wider usage area to bypass the congestion regions and blockages. Given a routing grid and a set of nets to be routed, the model predicts the routing density on each edge of the grid. The routing density provides direct congestion estimation. We compare our estimation results to the actual routing results. Experimental results show the effectiveness of our estimator

Operational research and simulation methods for autonomous ride-sourcing

Ride-sourcing platforms provide on-demand shared transport services by solving decision problems related to ride-matching and pricing. The anticipated commercialisation of autonomous vehicles could transform these platforms to fleet operators and broaden their decision-making by introducing problems such as fleet sizing and empty vehicle redistribution. These problems have been frequently represented in research using aggregated mathematical programs, and alternative practises such as agent-based models. In this context, this study is set at the intersection between operational research and simulation methods to solve the multitude of autonomous ride-sourcing problems. The study begins by providing a framework for building bespoke agent-based models for ride-sourcing fleets, derived from the principles of agent-based modelling theory, which is used to tackle the non-linear problem of minimum fleet size. The minimum fleet size problem is tackled by investigating the relationship of system parameters based on queuing theory principles and by deriving and validating a novel model for pickup wait times. Simulating the fleet function in different urban areas shows that ride-sourcing fleets operate queues with zero assignment times above the critical fleet size. The results also highlight that pickup wait times have a pivotal role in estimating the minimum fleet size in ride-sourcing operations, with agent-based modelling being a more reliable estimation method. The focus is then shifted to empty vehicle redistribution, where the omission of market structure and underlying customer acumen, compromises the effectiveness of existing models. As a solution, the vehicle redistribution problem is formulated as a non-linear convex minimum cost flow problem that accounts for the relationship of supply and demand of rides by assuming a customer discrete choice model and a market structure. An edge splitting algorithm is then introduced to solve a transformed convex minimum cost flow problem for vehicle redistribution. Results of simulated tests show that the redistribution algorithm can significantly decrease wait times and increase profits with a moderate increase in vehicle mileage. The study is concluded by considering the operational time-horizon decision problems of ride-matching and pricing at periods of peak travel demand. Combinatorial double auctions have been identified as a suitable alternative to surge pricing in research, as they maximise social welfare by relying on stated customer and driver valuations. However, a shortcoming of current models is the exclusion of trip detour effects in pricing estimates. The study formulates a shared-ride assignment and pricing algorithm using combinatorial double auctions to resolve the above problem. The model is reduced to the maximum weighted independent set problem, which is APX-hard. Therefore, a fast local search heuristic is proposed, producing solutions within 10\% of the exact approach for practical implementations.Open Acces

Timing-Driven Macro Placement

Placement is an important step in the process of finding physical layouts for electronic computer chips. The basic task during placement is to arrange the building blocks of the chip, the circuits, disjointly within a given chip area. Furthermore, such positions should result in short circuit interconnections which can be routed easily and which ensure all signals arrive in time. This dissertation mostly focuses on macros, the largest circuits on a chip. In order to optimize timing characteristics during macro placement, we propose a new optimistic timing model based on geometric distance constraints. This model can be computed and evaluated efficiently in order to predict timing traits accurately in practice. Packing rectangles disjointly remains strongly NP-hard under slack maximization in our timing model. Despite of this we develop an exact, linear time algorithm for special cases. The proposed timing model is incorporated into BonnMacro, the macro placement component of the BonnTools physical design optimization suite developed at the Research Institute for Discrete Mathematics. Using efficient formulations as mixed-integer programs we can legalize macros locally while optimizing timing. This results in the first timing-aware macro placement tool. In addition, we provide multiple enhancements for the partitioning-based standard circuit placement algorithm BonnPlace. We find a model of partitioning as minimum-cost flow problem that is provably as small as possible using which we can avoid running time intensive instances. Moreover we propose the new global placement flow Self-Stabilizing BonnPlace. This approach combines BonnPlace with a force-directed placement framework. It provides the flexibility to optimize the two involved objectives, routability and timing, directly during placement. The performance of our placement tools is confirmed on a large variety of academic benchmarks as well as real-world designs provided by our industrial partner IBM. We reduce running time of partitioning significantly and demonstrate that Self-Stabilizing BonnPlace finds easily routable placements for challenging designs – even when simultaneously optimizing timing objectives. BonnMacro and Self-Stabilizing BonnPlace can be combined to the first timing-driven mixed-size placement flow. This combination often finds placements with competitive timing traits and even outperforms solutions that have been determined manually by experienced designers

Online Learning of Energy Consumption for Navigation of Electric Vehicles

Energy efficient navigation constitutes an important challenge in electric vehicles, due to their limited battery capacity. We employ a Bayesian approach to model the energy consumption at road segments for efficient navigation. In order to learn the model parameters, we develop an online learning framework and investigate several exploration strategies such as Thompson Sampling and Upper Confidence Bound. We then extend our online learning framework to the multi-agent setting, where multiple vehicles adaptively navigate and learn the parameters of the energy model. We analyze Thompson Sampling and establish rigorous regret bounds on its performance in the single-agent and multi-agent settings, through an analysis of the algorithm under batched feedback. Finally, we demonstrate the performance of our methods via experiments on several real-world city road networks

Online Learning of Energy Consumption for Navigation of Electric Vehicles

Energy efficient navigation constitutes an important challenge in electric vehicles, due to their limited battery capacity. We employ a Bayesian approach to model the energy consumption at road segments for efficient navigation. In order to learn the model parameters, we develop an online learning framework and investigate several exploration strategies such as Thompson Sampling and Upper Confidence Bound. We then extend our online learning framework to the multi-agent setting, where multiple vehicles adaptively navigate and learn the parameters of the energy model. We analyze Thompson Sampling and establish rigorous regret bounds on its performance in the single-agent and multi-agent settings, through an analysis of the algorithm under batched feedback. Finally, we demonstrate the performance of our methods via experiments on several real-world city road networks.Comment: Extension of arXiv:2003.0141

Timing-Constrained Global Routing with RC-Aware Steiner Trees and Routing Based Optimization

In this thesis we consider the global routing problem, which arises as one of the major subproblems in the physical design step in VLSI design. In global routing, we are given a three-dimensional grid graph G with edge capacities representing available routing space, and we have to connect a set of nets in G without overusing any edge capacities. Here, each net consists of a set of pins corresponding to vertices of G, where one pin is the sender of signals, while all other pins are receivers. Traditionally, next to obeying all edge capacity constraints, the objective has been to minimize wire length and possibly via (edges in z-direction) count, and timing constraints on the chip were only modeled indirectly. We present a new approach, where timing constraints are modeled directly during global routing: In joint work with Stephan Held, Dirk Mueller, Daniel Rotter, Vera Traub and Jens Vygen, we extend the modeling of global routing as a Min-Max Resource Sharing Problem to also incorporate timing constraints. For measuring signal delays we use the well-established Elmore delay model. One of the key subproblems here is the computation of Steiner trees minimizing a weighted sum of routing space usages and signal delays. For k pins, this problem is NP-hard to approximate within o(log k), and even the special case k = 2 is NP-hard, as was shown by Haehnle and Rotter. We present a fast approximation algorithm with strong approximation bounds for the case k = 2. For k > 2 we use a multi-stage approach based on modifying the topology of a short Steiner tree and using our algorithm for the two-pin case for computing new connections. Moreover, we present a layer assignment algorithm that assigns z-coordinates to the edges of a given two-dimensional tree. We also discuss the topic of routing based optimization. Here, the starting point is a complete routing, and timing optimization tools make changes that require incremental adaptations of the underlying routing. We investigate several aspects of this problem and derive a new routing flow that includes our timing-aware global router and routing based optimization steps. We evaluate our results from this thesis in practice on industrial 14nm microprocessor designs from IBM. Our theoretical results are validated in practice by a strong performance of our timing-aware global routing framework and our new routing flow, yielding significant improvements over the traditional global routing method and the previously used routing flow. Therefore, we conclude that our approaches and results from this thesis are not only theoretically sound but also give compelling results in practice

Integrated Special Event Traffic Management Strategies in Urban Transportation Network

How to effectively optimize and control spreading traffic in urban network during the special event has emerged as one of the critical issues faced by many transportation professionals in the past several decades due to the surging demand and the often limited network capacity. The contribution of this dissertation is to develop a set of integrated mathematical programming models for unconventional traffic management of special events in urban transportation network. Traffic management strategies such as lane reorganization and reversal, turning restriction, lane-based signal timing, ramp closure, and uninterrupted flow intersection will be coordinated and concurrently optimized for best overall system performance. Considering the complexity of the proposed formulations and the concerns of computing efficiency, this study has also developed efficient solution heuristics that can yield sufficiently reliable solutions for real-world application. Case studies and extensive numerical analyses results validate the effectiveness and applicability of the proposed models