Integer Optimization Never Dies: From Evolution Strategies to Quantum Annealing

Optimization across combinatorial domains remains a fundamental hurdle for science and engineering, both of which face a stubbornly discrete reality. But even as theoretical advancements push the boundaries of what we can formally solve, heuristics continue to be the primary workhorses for these NP-hard challenges. This talk argues that integer optimization is far from a "solved" classical relic; it is undergoing a renaissance fueled by non-classical solvers and a shift toward experimental methodologies.

We first explore the intersection of evolutionary computation and discrete spaces via modern Evolution Strategies (ES). Characterized by small-population search and effective self-adaptation, this branch of randomized search heuristics is underpinned by a surge in research activity in which our group takes part. However, theoretical and simulation-based objective functions tell only part of the story. In the realm of Experimental Combinatorial Optimization, we shift the focus to "zero-presumption" black-box problems, reporting on case studies from Postharvest and Food Tech that benefit from having experimental evolution directly in the loop.

Finally, we look toward the horizon: Quantum Annealing. We discuss our work in mapping combinatorial challenges to quantum hardware via QUBO formulations. By treating the optimization landscape as a physical system, we explore both the potential and the current boundaries of quantum speedups for NP-hard integer problems.

Whether through biological metaphors, experimental rigor, or quantum physics, the quest to solve integer problems continues to evolve. We conclude by discussing how these three seemingly disparate paths converge to define the future of integer metaheuristics.