Automatic Generation of Combinatorial Reoptimisation Problem Specifications: A Vision

2025-10-02

AI Summary

Dynamic optimization environments necessitate rapid re-optimization following environmental changes, yet existing approaches lack systematic support for maintaining solution consistency, preserving irreversible constraints, and ensuring traceability during adaptation. Method: This paper proposes a model-driven engineering (MDE)-based methodology: the original combinatorial optimization problem is formally specified using a declarative modeling language; environment-induced changes—such as constraint updates, variable freezing, or objective shifts—are classified systematically, and corresponding model transformation rules automatically generate re-optimization specifications satisfying minimality, irreversible-constraint preservation, and change traceability requirements. Contribution/Results: It pioneers the application of MDE to combinatorial re-optimization, enabling fully automated derivation of re-optimization models from initial problem models. A prototype system built upon the GIPS framework validates the approach’s effectiveness and feasibility in a real-world teaching assistant course scheduling scenario.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Automatically generate combinatorial reoptimisation problem specifications
• Minimise solution changes when contextual factors shift
• Derive reoptimisation problems from original optimisation specifications

Innovation

• Model-Driven Engineering for reoptimisation problem derivation
• Declarative modelling languages specify optimisation problems
• Graph-Based Integer Programming tool for resource allocation