Mathematical Optimisation in Rust: A Complete Guide to good_lp + HiGHS (Production Ready with Axum)

Modern backend systems often need to make optimal decisions under constraints . Examples: Allocate limited resources Minimize operational cost Select optimal product mix Plan logistics efficiently Build smart pricing engines This is where mathematical optimization becomes powerful. In Rust, two tools make this practical: good_lp → Modeling layer (DSL for optimization problems) HiGHS → High-performance optimization solver This guide covers: Mathematical foundations What good_lp and HiGHS are When to use them Rust examples Production-ready Axum backend integration Scaling considerations 1. Mathematical Optimization (Concept) Optimization problems look like this: Minimize or Maximize: f(x) Subject to: g1(x) ≤ b1 g2(x) = b2 x ∈ feasible set Where: x = decision variables f(x) = objective function g(x) = constraints 2. LP vs MIP Linear Programming (LP) All expressions are linear. Example: Maximize: 3x + 2y Subject to: x + y ≤ 10 x ≥ 0 y ≥ 0 LP problems are solved efficiently using simplex or