Juniper: An Open-Source Nonlinear Branch-and-Bound Solver in Julia (1804.07332v1)

Abstract: Nonconvex mixed-integer nonlinear programs (MINLPs) represent a challenging class of optimization problems that often arise in engineering and scientific applications. Because of nonconvexities, these programs are typically solved with global optimization algorithms, which have limited scalability. However, nonlinear branch-and-bound has recently been shown to be an effective heuristic for quickly finding high-quality solutions to large-scale nonconvex MINLPs, such as those arising in infrastructure network optimization. This work proposes Juniper, a Julia-based open-source solver for nonlinear branch-and-bound. Leveraging the high-level Julia programming language makes it easy to modify Juniper's algorithm and explore extensions, such as branching heuristics, feasibility pumps, and parallelization. Detailed numerical experiments demonstrate that the initial release of Juniper is comparable with other nonlinear branch-and-bound solvers, such as Bonmin, Minotaur, and Knitro, illustrating that Juniper provides a strong foundation for further exploration in utilizing nonlinear branch-and-bound algorithms as heuristics for nonconvex MINLPs.

Juniper: An Open-Source Nonlinear Branch-and-Bound Solver in Julia

The paper "Juniper: An Open-Source Nonlinear Branch-and-Bound Solver in Julia" presents an open-source solution addressing the challenges associated with nonconvex mixed-integer nonlinear programs (MINLPs). These programs are crucial in engineering and scientific applications, where they often manifest in infrastructure network optimization problems but present formidable difficulties due to their nonconvex nature. The authors propose Juniper, a nonlinear branch-and-bound (NLBB) solver, leveraging the Julia programming language to adapt quickly to algorithmic modifications, emphasizing its ease in extending functionality such as branching heuristics, feasibility pumps, and parallelization.

The primary contribution of the paper is the presentation of Juniper, designed for rapid exploration of NLBB algorithms. The use of Julia, along with JuMP, provides an intuitive platform for this optimization exploration, allowing seamless solver integration and algorithm experimentation. This flexible architecture supports the rapid testing of novel NLBB heuristics, emphasizing the adaptability of Juniper in incorporating various NLP and MIP solvers efficiently.

The paper details extensive experiments, showcasing Juniper's competitive performance in comparison with established NLBB solvers like BonMin and Minotaur, and other global optimization methods like Couenne and SCIP. The results from solving 298 challenging nonconvex MINLP instances highlight Juniper's robust solution capability, often revealing superior solution quality within permissible optimality gaps, notwithstanding a slight increased execution time in simpler models. As described, the default configuration of Juniper demonstrates parity with other NLBB implementations, offering reliable results across a variety of problem sizes and complexities.

A salient feature of Juniper is its capability to utilize different sub-solvers, which it demonstrates through performance metrics indicating a non-significant difference when employing varied NLP and MIP solvers like GLPK, Cbc, and Gurobi. The solver's configurability illustrates its strength in addressing the feasibility pump efficiency, highlighting the effectiveness of Cbc over other alternatives due to its balanced computation performance within defined time limits.

The paper further explores algorithmic improvements achieved through parallel tree search strategies facilitated by Julia's native parallel processing support. The experimental results document notable speedup, suggesting an efficient exploitation of parallelism, marking Juniper's significant advantage in solving large-scale MINLPs quicker than sequential methods.

Juniper sets a foundation for further research into NLBB algorithm enhancements, potentially inspiring other open-source contributions and extending its application in real-world optimization challenges. As nonconvex constraints increasingly appear in diverse industrial optimization scenarios, Juniper’s flexible, Julia-centric platform may serve a pivotal role in advancing the mathematical strategies employed by researchers and facilitating progressive theoretical inquiries into heuristic designs in nonconvex MINLPs.

Conclusively, this paper invites the research community to build upon Juniper, exploring the vast possibilities in refining NLBB algorithms and deploying this tool on broader scales in complex infrastructural systems. Given the compelling empirical results and its modular architecture, Juniper remains a valuable reference for ongoing development efforts and collaborative interactions in the field of open-source optimization methodologies.