Interior-point methods for P∗(κ)-linear complementarity problem based on generalized trigonometric barrier function

Recently, M.~Bouafoa, et al. investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for $P_{*}(\kappa)$ Linear Complementarity Problems (LCPs). It is shown that the iteration bound for primal-dual large-update and small-update interior-point methods based on this function is as good as the currently best known iteration bounds for these type methods. The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.publishedVersio

New predictor-corrector interior-point algorithm for symmetric cone horizontal linear complementarity problems

In this paper we propose a new predictor-corrector interior-point algorithm for solving P_* (κ) horizontal linear complementarity problems defined on a Cartesian product of symmetric cones, which is not based on a usual barrier function. We generalize the predictor-corrector algorithm introduced in [13] to P_* (κ)-linear horizontal complementarity problems on a Cartesian product of symmetric cones. We apply the algebraic equivalent transformation technique proposed by Darvay [9] and we use the function φ(t)=t-√t in order to determine the new search directions. In each iteration the proposed algorithm performs one predictor and one corrector step. We prove that the predictor-corrector interior-point algorithm has the same complexity bound as the best known interior-point algorithms for solving these types of problems. Furthermore, we provide a condition related to the proximity and update parameters for which the introduced predictor-corrector algorithm is well defined

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

Bandit algorithms for searching large spaces

Bandit games consist of single-state environments in which an agent must sequentially choose actions to take, for which rewards are given. The objective being to maximise the cumulated reward, the agent naturally seeks to build a model of the relationship between actions and rewards. The agent must both choose uncertain actions in order to improve its model (exploration), and actions that are believed to yield high rewards according to the model (exploitation). The choice of an action to take is called a play of an arm of the bandit, and the total number of plays may or may not be known in advance. Algorithms designed to handle the exploration-exploitation dilemma were initially motivated by problems with rather small numbers of actions. But the ideas they were based on have been extended to cases where the number of actions to choose from is much larger than the maximum possible number of plays. Several problems fall into this setting, such as information retrieval with relevance feedback, where the system must learn what a user is looking for while serving relevant documents often enough, but also global optimisation, where the search for an optimum is done by selecting where to acquire potentially expensive samples of a target function. All have in common the search of large spaces. In this thesis, we focus on an algorithm based on the Gaussian Processes probabilistic model, often used in Bayesian optimisation, and the Upper Confidence Bound action-selection heuristic that is popular in bandit algorithms. In addition to demonstrating the advantages of the GP-UCB algorithm on an image retrieval problem, we show how it can be adapted in order to search tree-structured spaces. We provide an efficient implementation, theoretical guarantees on the algorithm's performance, and empirical evidence that it handles large branching factors better than previous bandit-based algorithms, on synthetic trees

Annual Review of Progress in Applied Computational Electromagnetics

Approved for public release; distribution is unlimited