Computational experiments

To test our proposed variant of SDDiP we conducted experiments on two different test problems:

• a capacitated lot-sizing problem (CLSP)
• a capacitated facility location problem (CFLP)

For CLSP we performed tests for two different problem sizes, with 3 state variables (folder CLSP) and with 10 state variables (folder CLSP_Large).

For each example, the code consists of the following files:

• A starter file (e.g. starter.jl): This file is used to run one or several experiments for the test problem.
• A config file (algo_config.jl) setting up the parameters for SDDiP.
• A model file (e.g. model.jl) in which the multistage optimization problem is defined.
• A scenario file (e.g. scenario_tree.jl) preparing the scenarios for the model.
• A simulation file (simulation.jl) required for simulations after SDDiP has terminated.

Note that for CLSP we ran tests with a static binary approximation of the state space (CLSP-Bin; files model.jl and starter.jl) and with the original state space (CLSP; model_no_bin.jl, starter_no_bin.jl). Therefore, the corresponding folders contain different model and starter files.

The starter file

In the starter file, the user can start a specific test run by calling the model_starter function (or det_equiv_starter if the deterministic equivalent should be solved).

The function comes with several arguments that can be specified by the user and (for the most part) are passed to the algo_params struct later. They allow to define several model runs (e.g. for different cut or normalization techniques) at once and run them after each other.

For each run, the following steps are executed:

• The algorithm is configured by calling the algo_config function from algo_config.jl. This yields a struct of type AlgoParams that is passed to the algorithm.
• The model_set_up function from model.jl is called to create the multistage optimization problem. It also contains the data (except for the scenario data) for the model.
• A seed for the forward pass sampling is specified.
• The solve function from algorithm.jl is called.
• The policy obtained with SDDiP is simulated on in-sample or out-of-sample data.

The config file

Most of the model parameter choices are hard-coded in function algo_config, as they do not change much between different runs of our experiments. Others which change more frequently between runs are passed to this function as arguments from the starter file.

using DynamicSDDiP
function algo_config(
    duality_regime_sym::Symbol,
    normalization_regime::DynamicSDDiP.AbstractNormalizationRegime,
    cut_aggregation_regime::DynamicSDDiP.AbstractCutAggregationRegime,
    cut_selection_regime::DynamicSDDiP.AbstractCutSelectionRegime,
    log_file::String,
    time_limit::Int,
    forward_seed::Int,
    )
end

algo_config (generic function with 1 method)

Note that all the parameters for a given are also stored in the log-file of this run, see Understanding the logging output. We also describe the runs in a bit more detail below.

For explanations of the parameters that can be set in algo_config.jl see Setting algorithmic parameters.

The results

The full results of our experiments are provided in folder results of this repository. For each run presented in the paper, there is a dedicated logging file which contains the parameter configuration of the run as well as the results. To understand the logging files, please see the description in Understanding the logging output.

Reproducing the results

CFLP

To reproduce the results from our experiments for CFLP, use the starter.jl file in folder CFLP with the pre-defined runs. The algo_config.jl file also contains the exact configuration to reproduce our results.

For runs in combination with SB cuts, make sure to change the algo_config.jl file by uncommenting iteration_to_start = 21 for cut_generation_regime_2 and by replacing cut_generation_regimes = [cut_generation_regime_2] with cut_generation_regimes = [cut_generation_regime_1, cut_generation_regime_2].

If you want to use different logging files for different runs, the file name arguments in starter.jl should be adjusted.

CLSP with Binarization

To reproduce the results from our experiments for CLSP with binarization, use the starter.jl file in folder CLSP with the pre-defined runs. The algo_config.jl file also contains the exact configuration to reproduce our results.

For 4 or 10 stages, make sure to adjust the variables stages and time_limit accordingly.

For runs in combination with SB cuts, make sure to change the algo_config.jl file by uncommenting iteration_to_start = 21 for cut_generation_regime_2 and by replacing cut_generation_regimes = [cut_generation_regime_2] with cut_generation_regimes = [cut_generation_regime_1, cut_generation_regime_2].

If you want to use different logging files for different runs, the file name arguments in starter.jl should be adjusted.

CLSP without Binarization

To reproduce the results from our experiments for CLSP without binarization, use the starter_no_bin.jl file in folder CLSP_Large with the pre-defined runs. The algo_config.jl file also contains the exact configuration to reproduce our results.

For runs in combination with SB cuts, make sure to change the algo_config.jl file by uncommenting iteration_to_start = 21 for cut_generation_regime_2 and by replacing cut_generation_regimes = [cut_generation_regime_2] with cut_generation_regimes = [cut_generation_regime_1, cut_generation_regime_2].

If you want to use different logging files for different runs, the file name arguments in starter_no_bin.jl should be adjusted.

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