A new modeling approach for the biobjective exact optimization of satellite payload configuration

• DOI: http://doi.org/10.1111/itor.12386
• Date: 01 January 2019
• Author: Grégoire Danoy,Emmanuel Kieffer,Anass Nagih,Pascal Bouvry
• Published date: 01 January 2019

Intl. Trans. in Op. Res. 26 (2019) 180–199

DOI: 10.1111/itor.12386

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A new modeling approach for the biobjective exact

optimization of satellite payload configuration

Emmanuel Kieffera,Gr

´

egoire Danoyb, Pascal Bouvryband Anass Nagihc

aInterdisciplinary Centre forSecurity, Reliability, and Trust (SnT), Universityof Luxembourg, Luxembourg

bCSC Research Unit, Universityof Luxembourg, Luxembourg

cLCOMS Laboratory, Decision & Optimization Research Group, University of Lorraine,France

E-mail: emmanuel.kieffer@uni.lu [Kieffer]; gregoire.danoy@uni.lu[Danoy]; pascal.bouvry@uni.lu [Bouvry];

anass.nagih@univ-lorraine.fr [Nagih]

Received 20 May2015; received in revised form 6 September 2016; accepted 24 November 2016

Abstract

Communication satellites have the crucial role to forward signals to customers. They filter and amplify

uplink signals coming from Earth stations to improve the signal quality before reaching customers. These

operations are performed by the payload component of the satellite that embeds reconfigurable components

(e.g., switches).These components route signals to appropriate signal processing components (e.g.,amplifiers,

filters) and lead amplified signals to the output antenna. In order to route the channels that compose

signals, satellite engineers can remotely modify switch states. These are typically updated when one or more

new channels must be connected or when failures occur. However, satellites embed always more switches

to answer customer demands, which makes their reconfiguration time consuming and error prone without

appropriate decision aid tools. Power transmission is a crucial objective to ensure a maximum quality of

service at reasonable cost. This is why satellite operators aim at minimizing incoming power signals while

guaranteeing a maximum factor of amplification at the output antenna. This problem is referred to as the

“satellite payload powerproblem.” Previous works haveoutlined the difficulty to solve exactly large instances

of this problem. This workproposes to improve the existing mathematical formulation of the switch network.

We show that it can be modeled as a static network and switch states can be deduced after optimization,

thus limiting the combinatorial explosion. Computational experiments on different sizes of realistic instances

using the adaptive ε-constraint method demonstrate the computational time gain with this new model and

the possibility to solve larger instances.

Keywords:bi-objective optimization; integer linear programming; adaptive ε-constraint; satellite payloadoptimization

1. Introduction

Communication satellitesare nowadays essential for communication over long distances. Since their

birth in the 1960s, they have become more complex and keep embedding more components. The

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E. Kieffer et al. / Intl. Trans.in Op. Res. 26 (2019) 180–199 181

exponential growth of the market demands demands more flexibility and redundancy to ensure that

signals are reliably forwarded to customers (Hoeber and Kim, 2000). The market competition also

motivates satellite operators to request more power, longer lifetime (up to 15 years), and reliability

(redundant systems). These are crucial to ensure the quality of service (QoS).

A communicationsatellite is mainly composed of two distinct modules.The first is the payload that

receives uplink signals fromEarth stations, filters, amplifies,and finally forwards the modified signals

back to Earth. Components embedded in the payload are multiplexers, switches, and amplifiers.The

second module, the platform, embeds all subsystems required for the functioning of the satellite

in space, regardless of the satellite’s mission. Such subsystems include power provisioning and

propulsion. This work is focused on the payload module, which contains some reconfigurable

components, that is, switches. Indeed, engineers are nowadays able to remotely modify the state of

these switches,which allow to connect or disconnect channels that compose input signals. Designing

such payloads is an optimization problem for the satellite manufacturer point of view (Havet, 2002)

in which the best network topologymust be found while minimizing the number of components, due

to their high cost. This work focuses on a later stage, when the satellite operator faces configuration

and reconfiguration problems during the lifetime of such satellites. The problem can be divided into

three main categories:

rThe initialization problemwhere no channels are preconnected. The goal is to configure the payload

for the first time. This is the hardest and most sensitive task because the initial configuration

determines future reconfigurations.

rThe reconfiguration problem where a predefined set of channels is already connected and new

channels have to be added without interrupting the pre-connected channels.

rThe restoration problemwhere component failures may appear and paths need to be reconnected.

For each of these previous problem categories, different objectives can be defined. For example,

Stathakis et al. (2012a) minimized the number of switch changes for the reconfiguration problem.

Kieffer et al. (2014) tackled for the first time the biobjective power initialization problem by mod-

ifying the original model developed by Stathakis et al. in order to include power parameters.

Optimizing input and output power is a real and key problem for satellite providers since signals

have to be routed and amplified inside the satellite. These operations are achieved by the payload

module that contains different passive components inducing attenuations. All these characteristics

motivate the development and usage of efficient optimization procedures to ensure the satellite

operator that routing choices are the closest to the optimal ones in terms of signal power. In this

work, the problem consists inoptimizing the input signals power beforeamplification while keeping

a maximal output power after amplification. The goal is to find efficient alternatives representing

optimal power paths since these two objectives are conflicting. Results obtained in Kieffer et al.

(2014) show the difficulty to solve the biobjective satellite payload power optimization problem. In

this article, an improved model is proposed to tackle larger instances and provide faster solutions.

Instead of focusing on new algorithms, a new formulation for the switch representation is adopted

in order to provide better relaxations for exact algorithms. It also avoids the drawback of finding

relevant switches needed for the configuration and is based exclusively on a flow model. Once paths

delivering the flows are known then the state of the crossed switches is updated.

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2017 The Authors.

International Transactionsin Operational Research C

2017 International Federation of OperationalResearch Societies