Automatic Generation of Combinatorial Reoptimisation Problem Specifications: A Vision
Maximilian Kratz, Steffen Zschaler, Jens Kosiol, Gabriele Taentzer
TL;DR
The paper tackles automatic generation of reoptimisation problem specifications for combinatorial optimization by leveraging Model-Driven Engineering with declarative metamodels and transformations. It introduces a taxonomy of contextual changes, two core strategy classes (plaster-based local repair and full recomputation), and a GIPS-based proof-of-concept applied to TA allocation, demonstrating feasibility and guidance on when different strategies are appropriate. The contributions include a formalization of Problem Change Specifications, a spectrum of plaster-rule varieties (basic, smart, plaster sets), and an approach to derive reoptimisation problems from the original specification and solution. This work lays groundwork for automated, minimal-perturbation reoptimisation workflows with potential impact across scheduling, healthcare, and resource allocation domains.
Abstract
Once an optimisation problem has been solved, the solution may need adaptation when contextual factors change. This challenge, also known as reoptimisation, has been addressed in various problem domains, such as railway crew rescheduling, nurse rerostering, or aircraft recovery. This requires a modified problem to be solved again to ensure that the adapted solution is optimal in the new context. However, the new optimisation problem differs notably from the original problem: (i) we want to make only minimal changes to the original solution to minimise the impact; (ii) we may be unable to change some parts of the original solution (e.g., because they refer to past allocations); and (iii) we need to derive a change script from the original solution to the new solution. In this paper, we argue that Model-Driven Engineering (MDE) - in particular, the use of declarative modelling languages and model transformations for the high-level specification of optimisation problems - offers new opportunities for the systematic derivation of reoptimisation problems from the original optimisation problem specification. We focus on combinatorial reoptimisation problems and provide an initial categorisation of changing problems and strategies for deriving the corresponding reoptimisation specifications. We introduce an initial proof-of-concept implementation based on the GIPS (Graph-Based (Mixed) Integer Linear Programming Problem Specification) tool and apply it to an example resource-allocation problem: the allocation of teaching assistants to teaching sessions.