arXiv subjects

Nicholas G. Hall

Publications and source records attributed to Nicholas G. Hall.

3 recordsLinked to original sources

arXiv2026

Vehicle Platooning

Vehicle platooning offers significant benefits, including reduced energy consumption, lower emissions, improved road utilization, enhanced safety, and reduced driver fatigue. As intelligent driving technologies continue to advance, platoon sizes are expected to increase substantially, making the efficient sequencing and resequencing of vehicles increasingly important. We study the vehicle platoon sequencing and resequencing problem on road networks with varying segment lengths under two fundamental objectives: minimizing total energy consumption and minimizing the maximum energy consumption of any vehicle. For the typically encountered combinations of vehicle and road characteristics, we provide a complete computational complexity classification, either developing polynomial-time algorithms or proving computational intractability. For several intractable cases, we design fully polynomial-time approximation schemes and polynomial-time heuristics with provable performance guarantees. A computational study demonstrates that the proposed heuristics achieve average solutions within 1\% of optimal. We also consider settings in which only limited information about position-dependent energy savings is available and develop a heuristic with bounded worst-case performance. In addition, we present an efficient algorithm for on-road vehicle resequencing when only limited position changes are permitted. Together, these results provide a comprehensive algorithmic framework for energy-efficient vehicle platoon sequencing and resequencing.

math.OC↗

arXiv2026

Symmetric Numerical Three-Dimensional Matching: Intractability and Inapproximability

Symmetric Numerical Three-Dimensional Matching (SN3DM) asks whether three disjoint labeled classes with identical weight multisets can be partitioned into class-transversal triples of one common target sum. Its theme is role recovery under marginal symmetry: identical numerical catalogues force the asymmetric source roles to be reconstructed from incidence structure alone. This tutorial develops three complementary hardness results for that symmetry restriction. Part I gives a unary-polynomial reduction from N3DM. Source roles become ports in one common occurrence set, a uniquely forced filler system reserves one main incidence per port, bipartite edge coloring restores the output-class labels, and a no-carry mixed-radix encoding packs four coordinates into positive integers. Hence SN3DM is strongly NP-complete. Part II studies Max-SN3DM, for which strong NP-hardness alone does not exclude a PTAS. Two numerical compilers lift Petrank's perfect-completeness gap for bounded 3DM to unary Max-N3DM, and a defect-stability lemma shows that a symmetric matching of size 13n - d yields a source matching of size at least n - 21d, where n is the multiset cardinality, and d is a symmetric defect. Hence, for some epsilon > 0, it is NP-hard to separate perfect instances from those of optimum at most (1- epsilon) times perfect, so no PTAS exists unless P = NP. Every maximal legal triple matching is a 3-approximation, placing the problem in APX. Part III supplies the approximation-preserving reduction Part II does not claim. An exact pair compiler and a one-live-port separation map degree-three Maximum 3DM to unary Max-SN3DM with OPT(Max-SN3DM) = Gamma + OPT(Max-3DM) for a fixed offset Gamma and one-for-one optimum-error transfer. The L-reduction has constants alpha = 764 and beta = 1, so Max-SN3DM is APX-complete. The two are incomparable; worked yes / no instances audit each construction.

cs.CC↗

arXiv2025

Collective Wisdom: Policy Averaging with an Application to the Newsvendor Problem

We propose a Policy Averaging Approach (PAA) that synthesizes the strengths of existing approaches to create more reliable, flexible and justifiable policies for stochastic optimization problems. An important component of the PAA is risk diversification to reduce the randomness of policies. A second component emulates model averaging from statistics. A third component involves using cross-validation to diversify and optimize weights among candidate policies. We demonstrate the use of the PAA for the newsvendor problem. For that problem, model-based approaches typically use specific and potentially unreliable assumptions of either independently and identically distributed (i.i.d.) demand or feature-dependent demand with covariates or autoregressive functions. Data-driven approaches, including sample averaging and the use of functions of covariates to set order quantities, typically suffer from overfitting and provide limited insights to justify recommended policies. By integrating concepts from statistics and finance, the PAA avoids these problems. We show using theoretical analysis, a simulation study, and an empirical study, that the PAA outperforms all those earlier approaches. The demonstrated benefits of the PAA include reduced expected cost, more stable performance, and improved insights to justify recommendations. Extensions to consider tail risk and the use of stratified sampling are discussed. Beyond the newsvendor problem, the PAA is applicable to a wide variety of decision-making problems under uncertainty.

stat.AP↗