Collaborative Research: Next Generation Solvers for Mixed Integer Nonlinear Programs: Structure, Search, and Implementation

合作研究：混合整数非线性程序的下一代求解器：结构，搜索和实现许多科学，工程和公共部门的应用涉及影响最终设计最优性的离散决策和非线性系统动力学。混合整数非线性规划（MINLP）优化问题将优化过离散变量集的困难与处理非线性函数的挑战结合起来。MINLP是最灵活的建模范例之一，越来越多的研究人员和实践者，包括计算机科学家、工程师、经济学家、统计学家和运营经理，都对解决大规模的MINLP感兴趣。不幸的是，可以通过使用MINLP精确建模的应用程序的财富还没有与可用的算法和软件的能力相匹配。本研究将解决自然优化模型和可用的鲁棒优化求解器之间的不匹配，开发和提供强大的新求解器用于混合整数非线性程序。研究重点主要分为三大类。在第一部分中，研究人员研究了基本MINLP模型的结构，开发了预处理技术和强有效不等式。第二步，搜索，利用结构分析的结果来设计算法的搜索和划分策略。第三个要点是实现，重点是在现代计算资源上有效地实现生成的算法框架。该项目的变革目标是使MINLP成为一个研究人员和实践者可以使用强大的工具和方法来解决广泛的重要的、经常发生的决策支持问题的领域。

Collaborative Research: Next-Generation Solvers for Mixed-Integer Nonlinear Programs: Structure, Search, and ImplementationMany scientific, engineering, and public sector applications involveboth discrete decisions and nonlinear system dynamics that affect theoptimality of the final design. Mixed-integer nonlinear programming(MINLP) optimization problems combine the difficulty of optimizing overdiscrete variable sets with the challenges of handling nonlinearfunctions. MINLP is one of the most flexible modeling paradigmsavailable, and an expanding body of researchers and practitioners,including computer scientists, engineers, economists, statisticians, andoperations managers, are interested in solving large-scale MINLPs.Unfortunately, the wealth of applications that can be accurately modeledby using MINLP is not yet matched by the capability of availablealgorithms and software. This research will address the mismatchbetween natural optimization models and available robust optimizationsolvers, developing and delivering powerful new solvers formixed-integer nonlinear programs. The research thrusts are in three main categories. In the first thrust,the investigators study the structure of fundamental MINLP models,developing preprocessing techniques and strong valid inequalities. Thesecond thrust, search, leverages the results of the structural analysesto design search and partitioning strategies for algorithms. The thirdthrust, implementation, focuses on implementing the resultingalgorithmic frameworks efficiently on modern computational resources.The project has the transformative goal of making MINLP into an area inwhich researchers and practitioners can access robust tools and methodscapable of solving a wide range of important, commonly occurringdecision support problems.