Theoretical Research

Fundamental contributions to optimization theory and algorithms

KKT MINLP Demo

Optimality Conditions for Mixed-Integer Nonlinear Programming

Optimal points in linear optimization problems are known to lie on the boundary of the feasible region, while solutions to continuous nonlinear optimization problems must satisfy the Karush-Kuhn-Tucker (KKT) conditions. However, mixed-integer nonlinear programming (MINLP) problems lack such straightforward and well-defined optimality conditions. In this work, we propose novel optimality conditions for MINLP and present an efficient implementation of new domain reduction techniques based on these conditions.

Zhang, Y., Sahinidis, N.V., Nohra, C. et al. Optimality-based domain reduction for inequality-constrained NLP and MINLP problems J Glob Optim 77, 425–454 (2020).

Applications

Real-world applications of optimization and AI in industry

MARL MAPF Demo

Deep Reinforcement Learning for Online AGV Path Finding

Multi-agent pathfinding (MAPF) naturally arises in applications such as the pick-up and drop-off of parcels by automated guided vehicles (AGVs) in warehouses. We propose a decentralized multi-agent reinforcement learning (MARL) framework combined with a multi-step ahead tree search (MATS) strategy to make efficient decisions. Through experiments on both numerical cases and real-world warehouse scenarios, our proposed MARL policy demonstrates better performance in problem scale, solution time, and length of paths than classical methods.

Software

Software tools and frameworks for large-scale optimization

Distributed Optimization Demo

Optimization in the Cloud for Large-Scale Problems

In many real-world applications, optimization models can scale to over 10 million variables with sparse coefficient matrices, as seen in logistics assignment problems. Traditional optimization solvers, which typically operate in standalone mode, often struggle to handle such memory-intensive cases. To address this challenge, we propose a distributed optimization framework that constructs and presolves models in a streaming mode. This framework decomposes large-scale optimization problems into sub-blocks and solves them in a distributed manner.