Optimization and Control (math.OC)
Fri, 12 May 2023
1.Projected solution for Generalized Nash Games with Non-ordered Preferences
Authors:Asrifa Sultana, Shivani Valecha
Abstract: Any individual's preference represents his choice in the set of available options. It is said to be complete if the person can compare any pair of available options. We aim to initiate the notion of projected solutions for the generalized Nash equilibrium problem with non-ordered (not necessarily complete and transitive) preferences and non-self constraint map. We provide the necessary and sufficient conditions under which projected solutions of a quasi-variational inequality and the considered GNEP coincide. Based on this variational reformulation, we derive the occurrence of projected solutions for the considered GNEP. Alternatively, by using a fixed point result, we ensure the existence of projected solutions for the considered GNEP without requiring the compactness of choice sets.
2.An Ant Colony System for the Team Orienteering Problem with Time Windows
Authors:Roberto Montemanni, Luca Maria Gambardella
Abstract: This paper discusses a heuristic approach for Team Orienteering Problems with Time Windows. The method we propose takes advantage of a solution model based on a hierarchic generalization of the original problem, which is combined with an Ant Colony System algorithm. Computational results on benchmark instances previously adopted in the literature suggest that the algorithm we propose is effective in practice.
3.A shape optimization pipeline for marine propellers by means of reduced order modeling techniques
Authors:Anna Ivagnes, Nicola Demo, Gianluigi Rozza
Abstract: In this paper, we propose a shape optimization pipeline for propeller blades, applied to naval applications. The geometrical features of a blade are exploited to parametrize it, allowing to obtain deformed blades by perturbating their parameters. The optimization is performed using a genetic algorithm that exploits the computational speed-up of reduced order models to maximize the efficiency of a given propeller. A standard offline-online procedure is exploited to construct the reduced-order model. In an expensive offline phase, the full order model, which reproduces an open water test, is set up in the open-source software OpenFOAM and the same full order setting is used to run the CFD simulations for all the deformed propellers. The collected high-fidelity snapshots and the deformed parameters are used in the online stage to build the non-intrusive reduced-order model. This paper provides a proof of concept of the pipeline proposed, where the optimized propeller improves the efficiency of the original propeller.
4.Efficient Dynamic Allocation Policy for Robust Ranking and Selection under Stochastic Control Framework
Authors:Hui Xiao, Zhihong Wei
Abstract: This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured by its worst-case performance. We formulate the dynamic simulation budget allocation decision problem as a stochastic control problem under a Bayesian framework. Following the approximate dynamic programming theory, we derive a one-step-ahead dynamic optimal budget allocation policy and prove that this policy achieves consistency and asymptotic optimality. Numerical experiments demonstrate that the proposed procedure can significantly improve performance.
5.Jointly optimization of passenger-route assignment and transfer incentivization scheme for a customized modular bus system
Authors:Jianbiao Wang, Tomio Miwa, Takayuki Morikawa
Abstract: As an emerging travel mode, the modular vehicle system (MVS) is receiving increasing attention. In particular, the operators could connect multiple modular vehicles as an assembled bus in response to the temporary demand varies. Therefore, in this study, the MVS is adopted in the context of customized bus design to satisfy passengers reserved travel demand. In addition, to increase the potential of the customized modular bus system, the transfer among buses can be considered to group the passengers with the same or close destinations. However, the passengers will not actively transfer as it is viewed as a disutility. Thus, the appropriate incentivization should be provided. To this end, we jointly optimize the passenger-route assignment and the transfer incentivization scheme, in which the transfer demand is considered elastically under different incentivization. Then, the linearization approaches are adopted to transform the original nonlinear model into a mixed integer linear programming model, which can be solved by state-of-the-art solvers. The experiment on the small network reveals that the performance of the bus system with an incentivization scheme is better than that without an incentivization scheme, and the extent of such superiority depends on the total demand level in the system.
6.On the Partial Convexification for Low-Rank Spectral Optimization: Rank Bounds and Algorithms
Authors:Yongchun Li, Weijun Xie
Abstract: A Low-rank Spectral Optimization Problem (LSOP) minimizes a linear objective subject to multiple two-sided linear matrix inequalities intersected with a low-rank and spectral constrained domain set. Although solving LSOP is, in general, NP-hard, its partial convexification (i.e., replacing the domain set by its convex hull) termed "LSOP-R," is often tractable and yields a high-quality solution. This motivates us to study the strength of LSOP-R. Specifically, we derive rank bounds for any extreme point of the feasible set of LSOP-R and prove their tightness for the domain sets with different matrix spaces. The proposed rank bounds recover two well-known results in the literature from a fresh angle and also allow us to derive sufficient conditions under which the relaxation LSOP-R is equivalent to the original LSOP. To effectively solve LSOP-R, we develop a column generation algorithm with a vector-based convex pricing oracle, coupled with a rank-reduction algorithm, which ensures the output solution satisfies the theoretical rank bound. Finally, we numerically verify the strength of the LSOP-R and the efficacy of the proposed algorithms.