Modeling overview and implemented solvers

AMPL’s newly extended C++ solver interface library, MP, is publicly available in the ampl/mp repository. Solver interfaces built with MP are able to handle a significantly expanded range of model expressions. Currently available MP-based solvers include:

• gurobi, an interface to the Gurobi solver

• cplex, an interface to the IBM ILOG CPLEX solver

• copt, an interface to Cardinal Optimizer

• xpress, an interface to FICO Xpress

• mosek, an interface to the MOSEK solver

• baronmp, an interface to the BARON solver

• highs, an interface to the open-source HiGHS solver

• cuopt, an interface to the open-source NVIDIA cuOpt solver

• cbc, an enhanced interface to the open-source CBC solver

• scip, an interface to the open-source SCIP solver

• gcg, an interface to the open-source GCG solver

• A meta-solver MP2NL translating MP to any AMPL solver.

Binaries for these solvers can be downloaded, in distribution bundles and individually, through the AMPL Portal. Solver options and features are described at Feature guide for MP-based AMPL solvers and, for concrete solvers, at AMPL Development.

The expanded MP solver interface library offers new support for the following categories of operators and expressions:

• Conditional operators: if-then-else; ==>, <==, <==>

• Logical operators: or, and, not; exists, forall

• Piecewise linear functions: abs; min, max; <<breakpoints; slopes>>

• Counting operators: count; atmost, atleast, exactly; numberof

• Relational and comparison operators: >(=), <(=), (!)=; alldiff

• Complementarity operator: complements

• Nonlinear operators and functions: *, /, ^; exp, log; sin, cos, tan; sinh, cosh, tanh

• Set membership operator: in

Modeling details and examples are given in the Expressions supported section below. Technical details, configuration settings, and tools are in the Tools & details section. See also the individual solvers’ documentation at AMPL Development for more details of solver-specific features:

• Choice between linearization in the interface and native solver support for some operations

• Handling of AMPL suffixes on constraints that are transformed by the interface

The slides from our presentation on Advances in Model-Based Optimization provide overview of the MP interface library in the context of AMPL applications, including comments on implementation and efficiency issues.