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23-30
High-dimensional high-frequency time series prediction with a mixed integer optimisation method
(2023)
23-07
One of the fundamental problems in neurobiological research is to understand how neural circuits generate behaviors in response to sensory stimuli. Elucidating such neural circuits requires anatomical and functional information about the neurons that are active during the processing of the sensory information and generation of the respective response, as well as an identification of the connections between these neurons. With modern imaging techniques, both morphological properties of individual neurons as well as functional information related to sensory processing, information integration and behavior can be obtained. Given the resulting information, neurobiologists are faced with the task of identifying the anatomical structures down to individual neurons that are linked to the studied behavior and the processing of the respective sensory stimuli. Here, we present a novel interactive tool that assists neurobiologists in the aforementioned task by allowing them to extract hypothetical neural circuits constrained by anatomical and functional data. Our approach is based on two types of structural data: brain regions that are anatomically or functionally defined, and morphologies of individual neurons.
Both types of structural data are interlinked and augmented with additional information. The presented tool allows the expert user to identify neurons using Boolean queries. The interactive formulation of these queries is supported by linked views, using, among other things, two novel 2D abstractions of neural circuits.
The approach was validated in two case studies investigating the neural basis of vision-based behavioral responses in zebrafish larvae. Despite this particular application, we believe that the presented tool will be of general interest for exploring hypotheses about neural circuits in other species, genera and taxa.
23-28
A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems there is either incomplete information describing variable relations, or the relations between variables are highly complex. To overcome both these hurdles, machine learning (ML) models are often used and embedded in the MIP as surrogate models to represent these relations. Due to the large amount of available ML frameworks, formulating ML models into MIPs is highly non-trivial. In this paper we propose a tool for the automatic MIP formulation of trained ML models, allowing easy integration of ML constraints into MIPs. In addition, we introduce a library of MIP instances with embedded ML constraints. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.
23-17
Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017.
23-21
The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set.
23-15
It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.
23-06
Classic models to derive a timetable for public transport often face a chicken-and-egg situation: A good timetable should offer passengers routes with small travel times, but the route choice of passengers depends on the timetable. While models that fix passenger routes were frequently considered in the literature, integrated models that simultaneously optimize timetables and passenger routes have seen increasing attention lately. This creates a growing need for a set of instances that allows to test and compare new algorithmic developments for the integrated problem. Our paper addresses this requirement by presenting TimPassLib, a new benchmark library of instances for integrated periodic timetabling and passenger routing.
23-04
We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for two instances derived from real world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions.
23-20
Construction of a Test Library for the Rolling Stock Rotation Problem with Predictive Maintenance
(2023)
We describe the development of a test library for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). Our approach involves the utilization of genuine timetables from a private German railroad company. The generated instances incorporate probability distribution functions for modeling the health states of the vehicles and the considered trips possess varying degradation functions. RSRP-PdM involves assigning trips to a fleet of vehicles and scheduling their maintenance based on their individual health states. The goal is to minimize the total costs consisting of operational costs and the expected costs associated with vehicle failures. The failure probability is dependent on the health states of the vehicles, which are assumed to be random variables distributed by a family of probability distributions. Each distribution is represented by the parameters characterizing it and during the operation of the trips, these parameters get altered. Our approach incorporates non-linear degradation functions to describe the inference of the parameters but also linear ones could be applied. The resulting instances consist of the timetables of the individual lines that use the same vehicle type. Overall, we employ these assumptions and utilize open-source data to create a library of instances with varying difficulty. Our approach is vital for evaluating and comparing algorithms designed to solve the RSRP-PdM.
23-29
We present a heuristic solution approach for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). The task of this problem is to assign a sequence of trips to each of the vehicles
and to schedule their maintenance such that all trips can be operated. Here, the health states of the vehicles are considered to be random variables distributed by a family of probability distribution functions, and the maintenance services should be scheduled based on the failure probability of the vehicles. The proposed algorithm first generates a solution by solving an integer linear program and then heuristically improves this solution by applying a local search procedure. For this purpose, the trips assigned to the vehicles are split up and recombined, whereby additional deadhead trips can be inserted between the partial assignments. Subse-
quently, the maintenance is scheduled by solving a shortest path problem in a state-expanded version of a space-time graph restricted to the trips of the individual vehicles. The solution approach is tested and evaluated on a set of test instances based on real-world timetables.