Shieu-Hong Lin

A linear-time algorithm for finding optimal vehicle refueling policies

We explore a fixed-route vehicle refueling problem as a special case of the inventory-capacitated lot-sizing problem, and present a linear-time greedy algorithm for finding optimal refueling policies.

Finding Optimal Refueling Policies in Transportation Networks

We study the combinatorial properties of optimal refueling policies, which specify the transportation paths and the refueling operations along the paths to minimize the total transportation costs between vertices. The insight into the structure of optimal refueling policies leads to an elegant reduction of the problem of finding optimal refueling policies into the classical shortest path problem, which ends in simple and more efficient algorithms for finding optimal refueling policies.

LOCALIZED TEMPORAL REASONING USING SUBGOALS AND ABSTRACT EVENTS

We are concerned with temporal reasoning problems where there is uncertainty about the order in which events occur. The task of temporal reasoning is to derive an event sequence consistent with a given set of ordering constraints to achieve a goal. Previous research shows that the associated decision problems are hard even for very restricted cases. In this article, we investigate locality in event ordering and causal dependencies. We present a localized temporal reasoning algorithm that uses subgoals and abstract events to exploit locality. The computational efficiency of our algorithm for a problem instance is quantified by the inherent locality in the instance. We theoretically demonstrate the substantial improvement in performance gained by exploiting locality. This work provides solid evidence of the usefulness of localized reasoning in exploiting locality.

Coordinating time-constrained multi-agent resource sharing with fault detection

Sharing common resources in a distributed multi-agent environment requires coordination to avoid faulty system states. The statuses of resources such as personnel, equipments, and environmental factors at a point in time determine the system state at that time. When an agent takes an action at any time point within a scheduled time interval, it becomes a state-transition event occurring at that time. For each event, the underlying state transition relation can be compactly encoded as causal rules, which describe how statuses of resources and environmental factors may change in different ways based on preconditions before the event occurs. The central coordinator needs to check in advance whether any of the possible event sequences consistent with a proposed schedule may end in faulty system states. This fault detection task is NP-complete even for a polynomial-size state space in general. In this paper, we investigate the computational complexity of the fault detection task when agents fairly constrain the maximal length of time intervals. We develop a decomposition algorithm to divide the fault detection task over all events into subtasks involving subsets of the events with overlapping time intervals. For each subtask, only a subspace with reduced dimensionality is involved instead of the whole original state space. When the maximal length of time intervals is constrained below a fair threshold, we prove that with probability approaching one as the size of the problem instance grows the algorithm can accomplish the fault detection task in polynomial time even if the original underlying state space is exponential in size.

Data mapping of linear programming on fixed-size hypercubes

Abstract Although many solution methods are available for the linear programming problem, the simplex method is undoubtedly the most widely used one for its simplicity. In this paper, we propose an implementation of the simplex method on fixed-size hypercubes. A partitioning technique and a mapping technique are presented to fit large-size problem instances into relatively small-size hypercubes. Two cases, pipelined broadcasting allowed and pipelined broadcasting not allowed, are considered. We show that the proposed implementation achieves the linear speedup asymptotically for both cases. Also, under the given mapping method, we discuss how to partition data so as to minimize the total run time and the communication time. We derive sufficient conditions for optimal partitionings. These sufficient conditions are helpful to obtain better partitionings. The optimal partitioning is obtained for a special case.

Multi-objective constrained vehicle refueling planning: Complexity and polynomial-time approximation schemes

For point-to-point direct delivery over the transportation network, timely delivery of commodity and reduction of total fuel cost are both important objectives to consider. Since fuel prices can vary significantly over a broad region, often there is a tradeoff between fuel cost and travel time. A short path may not be economical in terms of fuel cost while routing through regions with lower fuel prices may take more time. In this paper, we consider multi-objective constrained vehicle refueling planning in two settings: (i) minimizing the fuel cost given an upper bound on travel time or (ii) minimizing travel time given an upper bound on the fuel cost. We prove that the computational task is NP-Complete even when the fuel price is fixed or when the amount of fuel consumption and the travel time are linearly dependent. We then show fully polynomial-time approximation schemes for refueling planning in these two situations.

Multi-objective vehicle refueling planning using mixed integer programming

For point-to-point direct delivery over the transportation network, timely delivery of commodity and reduction of total fuel cost are both important objectives to consider. Since fuel prices can vary significantly over a broad region, often there is a tradeoff between fuel cost and travel time. A short path may not be economical in terms of fuel cost while routing through areas with lower fuel prices may take more time. In this paper, we address multi-objective refueling optimization problems in the context of two priority models regarding fuel cost and travel time. Unlike the shortest path problem, optimal refueling paths may not be simple paths, which complicates the setup of mixed integer programs. We first start with arbitrage-free vehicle refueling planning that restricts refueling paths to simple paths in the network only. We then show how we can augment the mixed integer formulation for vehicle refueling planning without the arbitrage-free assumption.

Checking multi-agent schedules with temporal and causal information

Time management in a distributed multi-agent environment requires agents to progressively collaborate and negotiate before reaching a final feasible schedule of future events. In this process, it is important for individual agents to check whether a prototype schedule can meet their requirements and are free from undesirable effects in all possible event sequences. We present a modelling framework for encoding events with causal and temporal information. We show that the schedule validation task under this framework is NP-complete when the uncertainty in event ordering is very high. We develop a search algorithm for reasoning about possible consequences over a given set of events and show that the algorithm can effectively improve the computation efficiency by exploiting event-chain structure embedded in the time-interval information, which ends in tractable polynomial-time performance for events with moderate uncertainty in event ordering.

Managing routing information for optimal vehicle refueling in transportation networks

Managing routing information is an important aspect of point-to-point delivery by motor carriers. In this paper, we describe the data structures and algorithms needed for implementing a system that can effectively maintain the routing and refueling information dynamically to minimize the fuel cost of point-to-point delivery by motor vehicles. Given a transportation network of n vertices, the system can maintain and update the critical routing information using quadratic space of n and cubic time of n. Given any starting point and an initial fuel level, the system can then on the fly determine an optimal refueling plan in quadratic time of n based on the established routing information.

Data mining for managing stock keeping units

Stock keeping units (SKUs) are compact identifiers representing billable products in the inventory for sale. Merchants often assign SKUs by transforming the text descriptions of the products following various implicit SKU encoding schemes. In the transformation process, the text description of a product is divided into character blocks, some blocks are skipped, and the remaining are abbreviated and aligned into the SKU in a new order. In this paper, we describe an instance-based data mining approach for automatically (i) extracting likely underlying SKU encoding schemes as explicit formal encoding and alignment patterns, (ii) inferring a list of likely SKUs given the text description of a new product, and (iii) inferring a list of likely text descriptions given the SKU of a product with missing text description. We have built a prototype system for testing on real-world datasets, and the empirical results confirm the effectiveness of the approach.