mathematical modeling language

Zimpl, which stands for the Zuse Institute Mathematical Programming Language, is an open-source, algebraic modeling language designed to translate high-level mathematical optimization models into solver-readable formats. Developed by Thorsten Koch at the Zuse Institute Berlin (ZIB), it serves as a lightweight, flexible alternative to commercial languages like AMPL and GAMS. Core Function and Purpose

Zimpl allows you to write down complex optimization problems using natural mathematical notation (such as sets, summations, and indices) instead of manually building massive constraint matrices.

The Process: You write a model file (typically a .zpl file). Zimpl compiles it and exports it into standard .lp or .mps file formats.

The Solvers: Those exported files are then fed into standalone optimization solvers like SCIP, CPLEX, Gurobi, or lp_solve to compute the actual solution. Key Features of Zimpl

Infinite-Precision Rational Arithmetic: Unlike many modeling languages that use floating-point math, Zimpl performs its internal calculations using exact rational arithmetic via the GNU Multiple Precision (GMP) library. This completely eliminates rounding errors during model generation.

Clean Code Separation: It strictly separates the abstract mathematical model structure from the underlying data, making it easy to run the exact same model code against different data sets.

Platform Independence & Open Source: Zimpl is written in pure C, distributed under the GNU LGPL license, and runs seamlessly across Linux, macOS, and Windows. It is officially bundled as a core component of the widely used SCIP Optimization Suite. Structure of a Zimpl (.zpl) File

A standard Zimpl program relies on five foundational statements, each ending with a semicolon (;): Sets set

Defines the indexing dimensions (like products, factories, or time steps). set Plants := { “Berlin”, “Sydney” }; Parameters param

Holds the fixed numerical data or strings used by the model. param Capacity[Plants] := <“Berlin”> 500, <“Sydney”> 750; Variables var

Defines the unknown decision values the solver must determine. var ship[Plants] integer >= 0; Objective maximize / minimize The mathematical function you want to optimize. minimize cost: sum

in Plants : ship[p]10; Constraints subto The boundaries and rules the variables must obey.

subto CapLimit: forall

in Plants : ship[p] <= Capacity[p]; Example: A Simple Production Model

To illustrate how clean the language is, here is how a tiny production constraint looks in a Zimpl script:

# Define indices and raw data set Products := { “A”, “B” }; param profit[Products] := <“A”> 30, <“B”> 40; param hours[Products] := <“A”> 2, <“B”> 3; param MaxHours := 120; # Decision variables var x[Products] integer >= 0; # Objective function maximize TotalProfit: sum

in Products : hours[p] * x[p]) <= MaxHours; Use code with caution.

If you are working on a specific math modeling assignment, let me know: ZIMPL User Guide