arXiv subjects

Joost Berkhout

Publications and source records attributed to Joost Berkhout.

8 recordsLinked to original sources

arXiv2026

Using Less for More: When Warm-Starting Accelerates Branch-and-Cut for Stochastic Programs

Two-stage stochastic programs quickly become intractable as the number of scenarios grows. Motivated by this, we propose TULIP, a modular and easy-to-implement three-step warm-start framework for two-stage stochastic (mixed-)integer programs with an exponential number of cuts separated during branch-and-cut. TULIP (a) builds a cheap surrogate of the full problem by reducing the scenario set or by decoupling the two stages, (b) solves it up to a first incumbent to collect the tight cuts separated along the way, and (c) injects them to warm-start the original problem. In short: we use less (a cheaper surrogate) for more (the original problem). Using this modular setup, we propose four methods within this framework, each with a slightly different setting. Across four case studies, we show that this acceleration is governed by a single mechanism, the root cut loop, and we specify it through a closed-form equation. This TULIP speedup model predicts a speedup when the time saved in the root cut loop exceeds the surrogate overhead. In our experiments, a TULIP variant achieves mean speedups of up to 2.56, with gains increasing with the scenario count. In the remaining case studies, TULIP provides little or no runtime benefit, which the TULIP speedup model mostly explains through insufficient root cut loop savings compared to the surrogate overhead.

math.OC↗

arXiv2026

A Fast Heuristic for Stochastic Steiner Tree Problems

Network design under uncertainty arises in countless real-world settings and can be captured by the Stochastic Steiner Tree Problem (SSTP). Although there are a few approaches specifically tailored to this stochastic optimization problem, there are considerably more state-of-the-art heuristics for its deterministic variant, the Steiner Tree Problem (STP). In this work, we show how to leverage an existing STP heuristic in building a novel method for solving its stochastic variant, the SSTP. This approach is a powerful, yet simple and easy-to-implement way of solving this complex problem. We test our method using benchmark instances from the literature. Numerical results show considerably faster computation times compared to the state-of-the-art, with a gap of approximately 5%.

math.OC↗

arXiv2025

PyJobShop: Solving scheduling problems with constraint programming in Python

This paper presents PyJobShop, an open-source Python library for solving scheduling problems with constraint programming. PyJobShop provides an easy-to-use modeling interface that supports a wide variety of scheduling problems, including well-known variants such as the flexible job shop problem and the resource-constrained project scheduling problem. PyJobShop integrates two state-of-the-art constraint programming solvers: Google's OR-Tools CP-SAT and IBM ILOG's CP Optimizer. We leverage PyJobShop to conduct large-scale numerical experiments on more than 9,000 benchmark instances from the machine scheduling and project scheduling literature, comparing the performance of OR-Tools and CP Optimizer. While CP Optimizer performs better on permutation scheduling and large-scale problems, OR-Tools is highly competitive on job shop scheduling and project scheduling problems--while also being fully open-source. By providing an accessible and tested implementation of constraint programming for scheduling, we hope that PyJobShop will enable researchers and practitioners to use constraint programming for real-world scheduling problems.

math.OC↗

arXiv2024

Feature-Based Network Construction: From Sampling to What-if Analysis

Networks are characterized by structural features, such as degree distribution, triangular closures, and assortativity. This paper addresses the problem of reconstructing instances of continuously (and non-negatively) weighted networks from given feature values. We introduce the gradient-based Feature-Based Network Construction (FBNC) framework. FBNC allows for sampling networks that satisfy prespecified features exactly (hard constraint sampling). Initializing the FBNC gradient descent with a random graph, FBNC can be used as an alternative to exponential random graphs in sampling graphs conditional on given feature values. We establish an implicit regularization approach to the original feature-fitting loss minimization problem so that FBNC achieves a parsimonious change in the underlying graph, where the term "implicit" stems from using appropriate norms in the very construction of the FBNC gradient descent. In constructing the implicit regularization, we distinguish between the case where weights of a link can be chosen from a bounded range, and, the more demanding case, where the weight matrix of the graph constitutes a Markov chain. We show that FBNC expands to "what-if analysis" of networks, that is, for a given initial network and a set of features satisfied by this network, FBNC finds the network closest to the initial network with some of the feature values adjusted or new features added. Numerical experiments in social network management and financial network regulation demonstrate the value of FBNC for graph (re)construction and what-if analysis.

physics.soc-ph↗

arXiv2024

A Pseudo-Gradient Approach for Model-free Markov Chain Optimization

We develop a first-order (pseudo-)gradient approach for optimizing functions over the stationary distribution of discrete-time Markov chains (DTMC). We give insights into why solving this optimization problem is challenging and show how transformations can be used to circumvent the hard constraints inherent in the optimization problem. The optimization framework is model-free since no explicit model of the interdependence of the row elements of the Markov chain transition matrix is required. Upon the transformation we build an extension of Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, called stochastic matrix SPSA (SM-SPSA) to solve the optimization problem. The performance of the SM-SPSA gradient search is compared with a benchmark commercial solver. Numerical examples show that SM-SPSA scales better which makes it the preferred solution method for large problem instances. We also apply the algorithm to the maximization of web-page rankings in web-graphs based on a real-life data set. As we explain in the paper, when applying a first-order gradient search one typically encounters a phenomenon which we call ``infliction points," that is, jumps in the optimization trajectories between periods of almost stationary behavior that slow down the optimization. We propose a heuristic for avoiding such infliction points and present a metastudy on a wide range of networks showing the positive effect of our heuristic on the convergence properties of SM-SPSA gradient search.

math.OC↗

arXiv2024

A new Simheuristics procedure for stochastic combinatorial optimization

Ignoring uncertainty in combinatorial optimization leads to suboptimal decisions in practice. Nevertheless, the focus is often on deterministic combinatorial optimization problems, mainly because they are already challenging enough without stochasticity. To make it easier to address stochasticity in combinatorial optimization, Simheuristics have been developed that allow solving stochastic combinatorial optimization problems. We propose a new Simheuristic procedure that dynamically changes the optimization focus between a deterministic and stochastic perspective based upon a statistical model. By doing so, an adequate trade-off is made between exploration and exploitation of the solution space during the optimization. We numerically show that the new Simheuristic procedure solves real-life stochastic scheduling problems more efficiently than standard Simheuristics strategies.

math.OC↗

arXiv2024

Future-proof ship pipe routing: navigating the energy transition

The maritime industry must prepare for the energy transition from fossil fuels to sustainable alternatives. Making ships future-proof is necessary given their long lifetime, but it is also complex because the future fuel type is uncertain. Within this uncertainty, one typically overlooks pipe routing, although it is a crucial driver for design time and costs. Therefore, we propose a mathematical approach for modeling uncertainty in pipe routing with deterministic, stochastic, and robust optimization. All three models are based on state-of-the-art integer linear optimization models for the Stochastic Steiner Forest Problem and adjusted to the maritime domain using specific constraints for pipe routing. We compare the models using both artificial and realistic instances and show that considering uncertainty using stochastic optimization and robust optimization leads to cost reductions of up to 22% in our experiments.

math.OC↗

arXiv2016

A Critical Account of Perturbation Analysis of Markov Chains

Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite and denumerable Markov chains and introduces new bounds based on series expansions. We discuss a series of examples to illustrate the applicability and numerical efficiency of the various bounds. Specifically, we address the question on how the bounds developed for finite Markov chains behave as the size of the system grows. In addition, we provide for the first time an analysis of the relative error of these bounds. For the case of a scaled perturbation we show that perturbation bounds can be used to analyze stability of a stable Markov chain with respect to perturbation with an unstable chain.

math.PR↗