In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and several challenges arise in a distributed framework, so that looking for suboptimal solutions is of interest. To achieve this goal, the presence of a linear coupling calls for tailored decomposition approaches. We propose a fully distributed algorithm based on a primal decomposition approach and a suitable tightening of the coupling constraints. Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of an approximate version of the original problem. Based on such allocation vectors, agents are able to (locally) compute a mixed-integer solution, which is guaranteed to be feasible after a sufficiently large time. Asymptotic and finite-time suboptimality bounds are established for the computed solution. Numerical simulations highlight the efficacy of the proposed methodology.

A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

Camisa, Andrea;Notarnicola, Ivano
;
Notarstefano, Giuseppe
2018

Abstract

In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and several challenges arise in a distributed framework, so that looking for suboptimal solutions is of interest. To achieve this goal, the presence of a linear coupling calls for tailored decomposition approaches. We propose a fully distributed algorithm based on a primal decomposition approach and a suitable tightening of the coupling constraints. Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of an approximate version of the original problem. Based on such allocation vectors, agents are able to (locally) compute a mixed-integer solution, which is guaranteed to be feasible after a sufficiently large time. Asymptotic and finite-time suboptimality bounds are established for the computed solution. Numerical simulations highlight the efficacy of the proposed methodology.
2018 IEEE Conference on Decision and Control (CDC)
3391
3396
Camisa, Andrea; Notarnicola, Ivano; Notarstefano, Giuseppe
File in questo prodotto:
File Dimensione Formato  
cdc18.pdf

embargo fino al 21/07/2019

Tipo: Postprint
Licenza: Licenza per accesso libero gratuito
Dimensione 951.81 kB
Formato Adobe PDF
951.81 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/674566
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact