Advances in Combinatorial Optimization and Machine Learning

The field of combinatorial optimization and machine learning is rapidly evolving, with a focus on developing innovative methods for solving complex problems. Recent research has explored the use of large language models (LLMs) with reasoning to generate search heuristics for combinatorial design problems, resulting in the solution of long-standing open instances. Additionally, there is a growing interest in developing efficient instruction evolving methods, such as Tag-Evol, which utilizes diverse and specific knowledge tags to achieve controlled evolution. The development of standardized evaluation frameworks, such as EVA-MILP, is also crucial for assessing the fidelity and utility of synthetic Mixed-Integer Linear Programming (MILP) instances. Furthermore, the integration of instance generation with solver design is becoming increasingly important, with frameworks like EALG providing a seamless pipeline for generating challenging instances and synthesizing adaptive heuristic algorithms. Noteworthy papers include Using Reasoning Models to Generate Search Heuristics, which successfully solved open instances of combinatorial design problems using LLMs with reasoning, and Tag-Evol, which demonstrated significant improvements in instruction evolving. EALG is also noteworthy for its ability to generate significantly harder instances than current benchmarks and synthesize effective solvers.

Sources

Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems

Tag-Evol: Achieving Efficient Instruction Evolving via Tag Injection

EVA-MILP: Towards Standardized Evaluation of MILP Instance Generation

EALG: Evolutionary Adversarial Generation of Language Model-Guided Generators for Combinatorial Optimization

Agnostic Learning under Targeted Poisoning: Optimal Rates and the Role of Randomness

Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees

An Expansion-Based Approach for Quantified Integer Programming

On Top-Down Pseudo-Boolean Model Counting

Conservative classifiers do consistently well with improving agents: characterizing statistical and online learning

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