# Scherer Multidemand Multidimensional KP Instances

## Description

Test instance data for the 0-1 multidemand multidimensional knapsack problem (MDMKP) from the Primal Problem Instance Generator (PPIG) from Scherer et al. 2023. The instances allow for a greater range of correlation values between the profit coefficients and the coefficients for the knapsack and demand constraints. The test instances also flex the constraint tightness across each dimension. Providing a different structure than existing instances. The first 45 instances do not obey a predetermined correlation structure, while the remaining 135 instances are defined through an explicit predetermined correlation structure (Uniform(-1,1)) for each dimension of each coefficient used in the MDMKP. The .txt file attached obeys the following structure, by line. Problem number and best found objective value number of variables, number of knapsack constraints, number of covering constraints objective function coefficients right hand side values knapsack constraints right hand side values covering constraints m rows of left hand side knapsack coefficients n rows of left hand side covering coefficients For any inquires contact the author at matthewescherer97@gmail.com

## Files

## Steps to reproduce

PPIG is a sampling-based instance generation method which begins in the primal feasible space. The method involves generating a set of k solutions where each decision variable is set active (i.e., to a value of 1) with probability p. The instance's left-hand-side coefficients for each constraint are generated in some predetermined fashion to obtain the problem meta-features desired. Each of the k solutions, when applied to the constraint coefficients, yield the required right-hand-side values for each of the k instances, providing an empirical distribution of right-hand-side values, which is then used to set the final right-hand-side values for each constraint for the problem instance.