![]() Some of these are global solvers and therefore not limited to convex problems. These were chosen based on criteria like availability, active development, and support for a file format available in MINLPLib (MINLPLib 2018). ![]() The solvers considered in the numerical comparison are AlphaECP, Antigone, AOA, BARON, BONMIN, Couenne, DICOPT, Juniper, KNITRO, LINDO, Minotaur, Muriqui, Pavito, SBB, SCIP, and SHOT. Several MINLP solvers also offer interfaces to MATLAB, and through OPTI Toolbox it is also possible to access several solvers in MATLAB (Currie et al. 2017), and Pyomo is a similar environment in Python (Hart et al. 2012) JuMP is a modeling environment for optimization embedded in Julia (Dunning et al. In recent years, there has also been a growing interest in optimization modeling in Python and Julia (Bezanson et al. ![]() Most optimization solvers are connected to one or more of the well-established modeling environments for MINLP optimization, such as, AIMMS (Bisschop 2006), AMPL (Fourer et al. The intention of this paper is to give an overview of commonly available deterministic solvers for convex MINLP problems and to present a thorough numerical comparison of the most common solvers. 2018), further motivating the study of efficient methods for convex MINLP. 2009 Lundell and Westerlund 2017 Nowak et al. It is also possible to solve certain classes of nonconvex MINLP problems, such as problems with signomial or general twice-differentiable constraints, by reformulating them into convex MINLP problems (Pörn et al. 2013) which is also reflected onto the field of MINLP since decomposition techniques for MINLP problems often rely on solving these types of subproblems. In recent years there has been significant progress within the field of MILP and NLP (Achterberg and Wunderling 2013 Bazaraa et al. An MINLP problem is often considered as convex when its continuous relaxation yields a convex NLP problem. Here we will focus on convex MINLP, which is a specific subclass with some desirable properties, e.g., it is possible to decompose a convex MINLP problem into a finite sequence of tractable subproblems. However, there has been significant progress in the field during the last twenty years and there are several good solvers for MINLP problems available today (Bussieck and Vigerske 2010). MINLP is often considered as a “difficult” class of optimization problems. For a recent review on MINLP methods see D’Ambrosio and Lodi ( 2013) and Bonami et al. ( 2016) and Trespalacios and Grossmann ( 2014). More of MINLP applications are described by, e.g., Floudas ( 1995), Biegler and Grossmann ( 2004), Boukouvala et al. 1999), pooling problems in the petrochemical industry (Misener and Floudas 2009), and production planning (Sahinidis and Grossmann 1991). 1999), process synthesis (Grossmann et al. 2012), portfolio optimization (Bonami and Lejeune 2009), nuclear reactor core fuel reloading (Quist et al. 2005), cancer treatment planning (Cao and Lim 2011), design of water distribution networks (Bragalli et al. The versatile modeling capabilities of MINLP means there are a wide variety of real-world optimization problems that can be modeled as MINLP problems, e.g., block layout design problems (Castillo et al. Furthermore, by using both linear and nonlinear functions it is possible to accurately model a variety of different phenomena, such as chemical reactions, separations, and material flow through a production facility. By using integer variables, it is possible to incorporate discrete decisions, e.g., to choose between some specific options, into the optimization model. Mixed-integer nonlinear programming (MINLP) combines the modeling capabilities of mixed-integer linear programming (MILP) and nonlinear programming (NLP) into a versatile modeling framework.
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