Russell Ainslie | Searcharxiv

arXiv2024

Mining Potentially Explanatory Patterns via Partial Solutions

Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of confidence in the results. To mitigate this issue, explainability aims to give insight to the user by presenting them with the knowledge obtained by the algorithm. In this paper we introduce Partial Solutions in order to improve the explainability of solutions to combinatorial optimization problems. Partial Solutions represent beneficial traits found by analyzing a population, and are presented to the user for explainability, but also provide an explicit model from which new solutions can be generated. We present an algorithm that assembles a collection of Partial Solutions chosen to strike a balance between high fitness, simplicity and atomicity. Experiments with standard benchmarks show that the proposed algorithm is able to find Partial Solutions which improve explainability at reasonable computational cost without affecting search performance.

cs.NE↗

arXiv2022

Distributionally Robust Resource Planning Under Binomial Demand Intakes

In this paper, we consider a distributionally robust resource planning model inspired by a real-world service industry problem. In this problem, there is a mixture of known demand and uncertain future demand. Prior to having full knowledge of the demand, we must decide upon how many jobs we plan to complete on each day in the planning horizon. Any jobs that are not completed by the end of their due date incur a cost and become due the following day. We present two distributionally robust optimisation (DRO) models for this problem. The first is a non-parametric model with a phi-divergence based ambiguity set. The second is a parametric model, where we treat the number of uncertain jobs due on each day as a binomial random variable with an unknown success probability. We reformulate the parametric model as a mixed integer program and find that it scales poorly with the sizes of the ambiguity and uncertainty sets. Hence, we make use of theoretical properties of the binomial distribution to derive fast heuristics based on dimension reduction. One is based on cutting surface algorithms commonly seen in the DRO literature. The other operates on a small subset of the uncertainty set for the future demand. We perform extensive computational experiments to establish the performance of our algorithms. We compare decisions from the parametric and non-parametric models, to assess the benefit of including the binomial information.

math.OC↗