178 Appendixtion given by the gap between best possible solution found and the overall optimal solution.The described optimization usually starts out with a heuristic search algorithm thatuses a Branch and Cut method. Branching, which means defining the tree structure andcutting, to safely “cut” away the nodes not representing an optimal solution, and thusprune the solution outcome. It is often the case, that a single MIT problem can generatea great amount of sub-problems, which quickly turns the modeling into a compute intensiveprocess that requires a great amount of physical memory as well (GAMS 2007).11.3.3. GAMS/CPLEXAs mentioned in chapter 5, the mathematical tools used in this project for solving theunit commitment problem is a combination of the modeling language GAMS and theMIP solver Cplex, respectively. Regarding the model language, GAMS operates in generalwith sets, indigenously and endogenously sizes which in normal terms best can beinterpret as indexes, variables and scalar items, respectively. One of the greatest advantagesof this particular tool, in connection with the current project, is that it from thebeginning has build in different types of variables such as positive variables, integersand binary variables. Especially the use of positive variables is a factor that trims downthe programming language as well as heavy computing processes. Another advantage isthe rather easy use of tables and vectors in combination between indexes (for example(i,t)) and input parameters (scalars).Since GAMS is mostly a programming language, the code is also used for “calling” thespecific solver to perform the desired optimization. This way, GAMS translates thestated mathematical problem for the user into the solver’s language. When it comes topicking out an appropriate solver for a specific assignment a great selection of differenttools is presented - varying from simple linear programming-solvers (LP) to more advancedones. When choosing the solver, it is important to carefully consider what particulartype of problem is to be optimized, avoiding greater complexity than necessary 38 –especially since the solvers more often than not are quite expensive (although GAMS asa tool is free of charge).The solver chosen for this project is Cplex, due to its efficient MIP optimizing, and thefact, that an academic software license for Cplex already was available through the university.38Sometimes, a small simplification can mean the difference between a simple linear problem (LP), andan advanced non-linear (NLP) or a NLPEC, MPEC, MSNLP and so on.
AppendixNomenclature 17911.4. Optimal GAB sizes from GAMS/CPLEXIn this section further tables on the necessary limitation of the solving process given bythe solution gaps are presented.Solution Gaps on the modeledreference systemGABS 2008 2017 2025January 0 0 0.005February 0 0.02 0.005March 0 0 0.005April 0 0 0May 0.02 0.001 0.005June 0.015 0.03 0.005July 0.025 0.09 0.025August 0.025 0.02 0.015September 0.00015 0.01 0.005October 0.005 0.01 0.005November 0 0.01 0December 0 0 0.005Solution Gaps on the modeledbypass system (single unit)GABS 2008 2017 2025January 0.75 1.41 1.32February 1.48 1.44 1.47March 1.29 1.42 1.47April 1.47 1.5 1.49May 1.33 1.49 1.45June 0.79 1.11 1.15July 1.26 1.05 1.20August 1.05 1.38 1.36September 0.86 1.45 1.23October 1.32 1.39 1.47November 1.47 1.47 1.41December 1.43 2.48 4.2211.1, Gap sizes restraining the optimal solution in the reference and the bypass scenario.