# Robust Approach to Restricted Items Selection Problem

## TL;DR

This paper addresses a complex robust item selection problem, proving its computational hardness, identifying solvable cases, and developing an exact algorithm with experimental validation.

## Contribution

It introduces a robust version of the items selection problem, proves NP-hardness, explores special cases, and proposes an exact solution method with computational results.

## Key findings

- NP-hardness of the deterministic problem
- Polynomially solvable special cases identified
- An exact solution algorithm with computational experiments

## Abstract

We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version, and establish polynomially solvable special cases. Next, we consider the robust version in which we aim at minimizing the maximum regret of the solution under interval parameter uncertainty. We show that this problem is hard for the second level of polynomial-time hierarchy. We develop an exact solution algorithm for the robust problem, based on cut generation, and present the results of computational experiments.