# Solving a Continuous Multifacility Location Problem by DC Algorithms

## TL;DR

This paper introduces a novel DC algorithm with Nesterov's smoothing to efficiently solve complex multifacility location problems reformulated as continuous optimization tasks.

## Contribution

It develops a new DC-based algorithm for multifacility location problems, addressing their nonconvex and nondifferentiable challenges with a reformulation and smoothing techniques.

## Key findings

- Algorithm successfully solves artificial and real data instances.
- Reformulation improves computational efficiency.
- Demonstrates effectiveness of DC algorithms in location problems.

## Abstract

The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) functions. The main challenges for solving the multifacility location problems under consideration come from their intrinsic discrete, nonconvex, and nondifferentiable nature. We provide a reformulation of these problems as those of continuous optimization and then develop a new DC type algorithm for their solutions involving Nesterov's smoothing. The proposed algorithm is computationally implemented via MATLAB numerical tests on both artificial and real data sets.