Benders output trace

The Benders decomposition algorithm generates a CSV trace file to track iteration progress and results. By default, this file is named benders_output_trace.csv and is located in the output directory specified by the OUTPUTROOT option (default: current directory).

The filename can be customized via the CSV_NAME option in the option.json file.

File structure

The CSV file uses semicolons (;) as delimiters and contains one header row followed by data rows. Each iteration of the Benders algorithm produces:

• One Master row with information about the master problem
• Multiple Subproblem rows (one per subproblem) with information about each subproblem

Columns

Column	Master Row	Subproblem Row	Description
Ite	Iteration number	Iteration number	Current iteration counter (1-indexed)
Worker	Master	Subproblem	Type of worker/row
Problem	Master problem name (from MASTER_NAME, default: master)	Subproblem name	Identifier for the problem
Id	Total number of subproblems	Subproblem index	For master: count of subproblems. For subproblem: its unique identifier
UB	Upper bound (trace._ub)	Subproblem cost (subproblem_data.subproblem_cost)	Upper bound of the master problem / Cost of the subproblem
LB	Lower bound (trace._lb)	-	Lower bound of the master problem
bestUB	Best upper bound (trace._best_ub)	-	Best upper bound found so far
simplexiter	-	Simplex iterations (subproblem_data.simplex_iter)	Number of simplex iterations for the subproblem
jump	Cut distance (norm_point(x_cut, trace.get_x_cut()))	-	Euclidean distance between current and previous cut points
single_subpb_costs_under_approx	-	Approximation cost (alpha_i)	Subproblem cost under current approximation
time	Master duration (trace._master_duration)	Subproblem timer (subproblem_data.subproblem_timer)	Wall-clock time spent solving in seconds
basis	-	-	Reserved for basis information (currently unused)

Example

Ite	Worker	Problem	Id	UB	LB	bestUB	simplexiter	jump	single_subpb_costs_under_approx	time	basis
1	Master	master	5	1000.5	950.2	1000.5	0.123			0.25
1	Subproblem	sub-1	0					150	450.5	0.1
1	Subproblem	sub-2	1					200	350.2	0.08
2	Master	master	5	980.1	975.3	980.1	0.087			0.30
2	Subproblem	sub-1	0					120	445.2	0.09
2	Subproblem	sub-2	1					180	348.5	0.07

Notes

• The file is created at the start of the Benders run and appended to if RESUME mode is enabled
• Empty cells in the CSV represent values that are not applicable for that row type
• The jump column for master rows indicates how much the solution has changed between iterations
• The single_subpb_costs_under_approx column for subproblem rows shows the contribution of each subproblem to the overall approximation