Global optimization of complex models has been for several decades approached by means of formal algorithms as well as Mathematical Programming (MP) (often branded as Operations Research, yet strongly rooted at Theoretical CS), and simultaneously has been treated by a wide range of dedicated heuristics (frequently under the label of Soft Computing) – where EC resides. The former is applicable when explicit modeling is available, whereas the latter is typically utilized for simulation- or experimentation-based optimization (but also applicable for explicit models). These two branches complement each other, yet practically studied under two independent CS disciplines. It is widely recognized nowadays that EC scholars become stronger, better-equipped researchers when obtaining knowledge on this so-called "optimization complement". In other words, the claim that our EC education should encompass basic MP is untenable at present times, and this tutorial aims at bridging the gap for our community's scholars.

The tutorial comprises three parts, aiming to introduce basic MP for EC audience.
(*) The first part presents the fundamentals of MP. It overviews mathematical optimization and outlines its taxonomy when classified by the underlying model: convex optimization (linear programs (pure-LP) and non-linear programs), versus combinatorial optimization (integer and mixed-integer linear programs M)ILP), integer quadratic programs (IQP. It then discusses some of the theoretical aspects, such as polyhedra and the duality theorems. It covers selected algorithms for the major classes of problems: Dantzig's Simplex for pure-LP, Ellipsoid for convex models, and Branch-and-Bound for integer programming.
(**) The second part focuses on MP in practice. The tutorial presents the principles of MP modeling, with emphasis on the roles of constraints and auxiliary/dummy decision variables in MP. It is compared to equivalent modeling for bio-inspired heuristics, which is formed differently with respect to such components.
(***) The third part constitutes an interactive demo session of problem-solving. We plan to model in a precept-style, using ILOG Studio's OPL, several ILP benchmark problems, including the basic Knapsack, Markowitz portfolio, N-queens, and the Traveling Salesman Problem – as a demonstration of practical problem-solving by means of mathematical optimization.