Bicriterion a priori route choice in stochastic time-dependent networks.

In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path, but rather to a time-adaptive strategy. In some applications, however, it makes good sense to require that the routing policy corresponds to a loopless path in the network, that is, the time-adaptive aspect disappears and a priori route choice is considered. In this paper we consider bicriterion a priori route choice in STD networks, i.e. the problem of finding the set of efficient paths. Both expectation and min-max criteria are considered and a solution method based on the two-phase approach is devised. Experimental results reveal that the full set of efficient solutions can be determined on rather large test instances, which is in contrast to previously reported results for the time-adaptive caseStochastic time-dependent networks; Bicriterion shortest path; A priori route choice; Two-phase method

A multistage linear array assignment problem

The implementation of certain algorithms on parallel processing computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomially-bounded algorithms are developed for the case of two stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NP-complete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented with one of the exact problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice

Finding the K shortest hyperpaths using reoptimization

The shortest hyperpath problem is an extension of the classical shortest path problem and has applications in many different areas. Recently, algorithms for finding the K shortest hyperpaths in a directed hypergraph have been developed by Andersen, Nielsen and Pretolani. In this paper we improve the worst-case computational complexity of an algorithm for finding the K shortest hyperpaths in an acyclic hypergraph. This result is obtained by applying new reoptimization techniques for shortest hyperpaths. The algorithm turns out to be quite effective in practice and has already been successfully applied in the context of stochastic time-dependent networks, for finding the K best strategies and for solving bicriterion problems.Network programming; Directed hypergraphs; K shortest hyperpaths; K shortest paths

Bicriterion scheduling with equal processing times on a batch processing machine

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard

State-of-the-art posted-price mechanisms for submodular bidders with $m$ items achieve approximation guarantees of $O((\log \log m)^3)$ [Assadi and Singla, 2019]. Their truthfulness, however, requires bidders to compute an NP-hard demand-query. Some computational complexity of this form is unavoidable, as it is NP-hard for truthful mechanisms to guarantee even an $m^{1/2-\varepsilon}$-approximation for any $\varepsilon > 0$ [Dobzinski and Vondr\'ak, 2016]. Together, these establish a stark distinction between computationally-efficient and communication-efficient truthful mechanisms. We show that this distinction disappears with a mild relaxation of truthfulness, which we term implementation in advised strategies, and that has been previously studied in relation to "Implementation in Undominated Strategies" [Babaioff et al, 2009]. Specifically, advice maps a tentative strategy either to that same strategy itself, or one that dominates it. We say that a player follows advice as long as they never play actions which are dominated by advice. A poly-time mechanism guarantees an $\alpha$-approximation in implementation in advised strategies if there exists poly-time advice for each player such that an $\alpha$-approximation is achieved whenever all players follow advice. Using an appropriate bicriterion notion of approximate demand queries (which can be computed in poly-time), we establish that (a slight modification of) the [Assadi and Singla, 2019] mechanism achieves the same $O((\log \log m)^3)$-approximation in implementation in advised strategies

K shortest paths in stochastic time-dependent networks

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. In some particular cases, the shortest origin-destination path must nevertheless be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is NP-hard, while the best time-adaptive strategy can be found in polynomial time. In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily adapted to the ranking of the first K shortest paths. Moreover, we present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effectiveShortest paths; K shortest paths; stochastic time-dependent networks; routing; directed hypergraphs

VIVA: An Online Algorithm for Piecewise Curve Estimation Using ℓ\u3csup\u3e0\u3c/sup\u3e Norm Regularization

Many processes deal with piecewise input functions, which occur naturally as a result of digital commands, user interfaces requiring a confirmation action, or discrete-time sampling. Examples include the assembly of protein polymers and hourly adjustments to the infusion rate of IV fluids during treatment of burn victims. Estimation of the input is straightforward regression when the observer has access to the timing information. More work is needed if the input can change at unknown times. Successful recovery of the change timing is largely dependent on the choice of cost function minimized during parameter estimation. Optimal estimation of a piecewise input will often proceed by minimization of a cost function which includes an estimation error term (most commonly mean square error) and the number (cardinality) of input changes (number of commands). Because the cardinality (ℓ0 norm) is not convex, the ℓ2 norm (quadratic smoothing) and ℓ1 norm (total variation minimization) are often substituted because they permit the use of convex optimization algorithms. However, these penalize the magnitude of input changes and therefore bias the piecewise estimates. Another disadvantage is that global optimization methods must be run after the end of data collection. One approach to unbiasing the piecewise parameter fits would include application of total variation minimization to recover timing, followed by piecewise parameter fitting. Another method is presented herein: a dynamic programming approach which iteratively develops populations of candidate estimates of increasing length, pruning those proven to be dominated. Because the usage of input data is entirely causal, the algorithm recovers timing and parameter values online. A functional definition of the algorithm, which is an extension of Viterbi decoding and integrates the pruning concept from branch-and-bound, is presented. Modifications are introduced to improve handling of non-uniform sampling, non-uniform confidence, and burst errors. Performance tests using synthesized data sets as well as volume data from a research system recording fluid infusions show five-fold (piecewise-constant data) and 20-fold (piecewise-linear data) reduction in error compared to total variation minimization, along with improved sparsity and reduced sensitivity to the regularization parameter. Algorithmic complexity and delay are also considered

Dynamic programming and minimum risk paths

This paper addresses the problem of computing minimum risk paths by taking as objective the expected accident cost. The computation is based on a dynamic programming formulation which can be considered an extension of usual dynamic programming models: path costs are recursively computed via functions which are assumed to be monotonic. A large part of the paper is devoted to analyze in detail this formulation and provide some new results. Based on the dynamic programming model a linear programming model is also presented to compute minimum risk paths. This formulation turns out to be useful in solving a biobjective version of the problem, in which also expected travel length is taken into consideration. This leads to define nondominated mixed strategies. Finally it is shown how to extend the basic updating device of dynamic programming in order to enumerate all nondominated paths