Optimisation Algorithms for Problems with Changeable Parameters

Summary

The mainstream research in combinatorial optimisation deals with well-defined problems where all problem parameters are known in advance. In real-world scenarios, there is always some degree of uncertainty and variability in problem input. The existing techniques for handling such problems often deal with stability, sensitivity and robustness. Such methods are interesting from the theoretical viewpoint, but their application is usually quite limited due to their complexity.

A new approach to dealing with uncertainty, recently proposed in our preliminary research, is to produce a promising (probably non-optimal) solution in advance based on parameters' estimates. That solution should keep its quality even if actual values of parameters would differ significantly from the original estimates. The new concept of solution stability offers a powerful mathematical tool with a wider scope of problems that can be handled efficiently. Future work is needed to elaborate the new methodology and to explore its capabilities/limitations considering applications in various problem specific areas, such as scheduling, optimal assignment and resource allocation.

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