Subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models

This project is based on the paper Statistical performance of subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models by C. Ritter and B. Singh published in the Lecture Notes in Computer Science (LNCS) series. There, using different computational experiments and statistical tests on two example instances of chance-constrained optimization problems, we investigate whether particular choices of the step-size rules are better suited for solving the Lagrangian relaxation via the subgradient method for these kinds of models in practice. We present the results of those tests and several additional investigations related to bounding techniques. We refer to the paper for further information on methods and conclusions: https://doi.org/10.1007/978-3-031-47859-8_26.

Repository content

The repository contains the following content:

• Code contains all the GAMS code one needs to run the algorithms presented in the paper. Please refer to the subfolders for a specific instance of the desired model. Starter files for the different algorithms are included. main_for_naive.gms for the naive solution method, main_for_lr1.gms up to main_for_lr6.gms for the Lagrangian relaxation algorithm (Alg. 1) using step-size rule one to six, SAA.gms as part 1 of Algorithm 2 and fixed_problem.gms as part 2 of Algorithm 2. Analogously, SAA_hi.gms as part 1 of Algorithm 3 and fixed_problem_hi.gms as part 2 of Algorithm 3. We also have a starter file MainHeuristic.gms for Algorithm 4. For Model I, that is also included and put out in the Lagrangian relaxation.
• Results contains the Excel tables and figures visualizing the results, some of which are also included in the paper. We differentiate between the Example_Instances and Samples for each model instance. The Example_Instances include the 16 instances we presented separately in the paper for Model I and Model II, respectively. The Samples include all 20 batches of each scenario-size regime for Model I and Model II, respectively. For Model II, the example instances can be found in a subfolder of Model II in Code. For Model I, the example instances are part of the 20 batches of each regime. Which of those we used as the example instances can be read in Example_instance_Model_I.txt in the Model I subfolder of Code.

Requirements to run code

The code uses the optimization solver Gurobi and the modeling language GAMS which are therefore required to run it.