Replication Data for : A New Method For Optimizing a Function Over The Efficient Set

This benchmark set is designed to test and evaluate the algorithm from the article "A New Method For Optimizing a Function Over The Efficient Set". It is structured into three main folders: P3, P5, and P8, where the numbers indicate the number of objectives in the problems to be optimized, namely 3, 5, and 8 objectives, respectively.

Each main folder contains subfolders named 'mxn', where:

m represents the number of constraints,

n represents the number of variables.

These subfolders organize the problems based on their dimensions in terms of constraints and variables.

Within each 'mxn' subfolder, several CSV files are present. Each CSV file corresponds to a specific benchmark instance, with the benchmark number indicated in the second part of the file name.

For each benchmark instance, the following data is provided:

c: The matrix of objective coefficients, which defines the objective functions to be optimized. It is typically of dimension k × n, where k is the number of objectives (3, 5, or 8) and n is the number of variables.

population: The matrix of constraint coefficients, which describes the problem’s constraints. It is typically of dimension m × n, where m is the number of constraints and n is the number of variables.

phi: The vector associated with the Phi function, likely used to combine multiple objectives into a single scalar objective function (e.g., a weighted sum or another scalarization method).

b: The right-hand side vector of the constraints (denoted HRS), which contains the constraint constants, typically of length m.

x_optimal: The optimal solution to the scalarized problem obtained by using the Phi function to combine the objectives.

RP: The convergence metric, which can be used to assess the performance of optimization algorithms on this problem.

This data may be contained in a single CSV file per benchmark or distributed across multiple CSV files, depending on the specific organization, with the benchmark number reflected in the file names.

This benchmark set provides a structured and varied collection for testing multi-objective optimization algorithms, covering different combinations of objectives, constraints, and variables, accompanied by known optimal solutions for the scalarized versions of the problems.