Multidisciplinary Optimisation in Mission Analysis and Design Process

1
Multidisciplinary Optimisationin Mission
Analysis andDesign Process

• Gino Bruno Amata, Giorgio Fasano,Alenia Spazio
  S.p.A., Torino
• Luigi Arcaro, Federico Della Croce, Maria Franca
  Norese, Simone Palamara, Silvio Riva, Roberto
  Tadei,
• D.AU.IN. , D.I.S.P.E.A. , Politecnico di Turin
• Franco Fragnelli, D.S.T.A.,Università del
  Piemonte Orientale, Alessandria
• Final Presentation, ESTEC the 9th of November
  2004

2
MDO FINAL PRESENTATION SUMMARY

• INTRODUCTION (G. Fasano)
• THE THEORETICAL APPROACH (R. Tadei)
• THE SOFTWARE PROTOTYPE (S. Palamara)
• CONCLUSIONS AND FUTURE DEVELOPMENTS (G. Fasano)

3
STUDY GOAL

• TO IDENTIFY AN EFFICIENT APPROACH TO TACKLE
  CONFLICTS AT DIFFERENT SUB-SYSTEMS LEVELS ARISING
  IN SPACE ENGINEERING DURING THE WHOLE DESIGN
  ACTIVITY
• TO INTRODUCE AN ADVANCED MULTIDISCIPLINARY
  OPTIMISATION (MDO) METHODOLOGY
• TO ILLUSTRATE THE CONCEPTUAL ASPECTS OF THE
  METHODOLOGY AND POINT OUT THE APPROACH
  APPLICABILITY TO A WIDE CLASS OF CASES ARISING IN
  SPACE ENGINEERING

4
STUDY CONTEXT (basic choices, assumptions and
limitations)

• THE WHOLE STUDY FOCUSES ON METHODOLOGY
• MISSION ANALYSIS, POWER AND PROPULSION
  SUB-SYSTEMS HAVE BEEN SELECTED AS REFERENCE
  DISCIPLINES TO SIMULATE A REALISTIC (EVEN IF
  SIMPLIFIED) SPACE ENGINEERING ENVIRONMENT
• A REDUCED DESCRIPTION OF THE WATS MISSION (ESA)
  HAS BEEN CONSIDERED AS SIMPLIFIED REFERENCE
  PROBLEM TO SET UP THE PROPOSED METHODOLOGY
• THE INTERMARSNET MISSION (ESA) HAS BEEN
  CONDSIDERED (IN A VERY SIMPLIFIED VERSION) AS
  CASE STUDY
• SUB-SYSTEMS PROBLEMATICS ARE NOT THE CORE OF THE
  STUDY AND ARE CONSIDERED WITH THE SOLE SCOPE TO
  INTRODUCE THE PROPOSED METHODOLOGY

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THE WATS MISSION as (simplified) reference
problem

• SCIENTIFIC GOAL
• MONITORING OF WATER VAPOUR AND TEMPERATURE
• IN TROPOSPHE AND STRATOSPHERE
• MISSION GOAL
• SETTING UP OF A LOW EARTH ORBIT (LEO) SATELLITES
  COSTELLATION

6
THE WATS MISSION as (simplified) reference
problem (contd)

• BASIC PRINCIPLE
• MEASUREMENTS ARE PERFORMED
• UNDER OCCULTATION CONDITIONS

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THE WATS MISSION (contd)main conflicts

• SATELLITES/LAUNCHES NUMBER
• MAXIMIZE THE NUMBER OF SATELLITES
• MINIMIZE THE NUMBER OF LAUNCHES
• PAYLOAD/POWER/PROPULSION SUBSYSTEMS
• PAYLOAD AS SIMPLE AND LIGHT AS POSSIBLE
• POWER SUBSYSTEM AS SIMPLE AND LIGHT AS POSSIBLE
• PROPULSION SUBSYSTEM AS SIMPLE AND LIGHT AS
  POSSIBLE

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THE WATS MISSION (contd)conflicts rationale
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THE WATS MISSION (contd)study logic
Mission Analysis
-

Constellation Analysis
Deployment
Power Requirements
Propulsion Requirements
-

P/L Power Budget
-

Budget
-

S/S Power Budget
S/C Configuration and Pointing Strategy
-

P/L Configuration
-

System Budgets
Power Design
Propulsion Design
-

Solar Panel Area
-

Fuel Mass
and Mass
-

Tank Volume
-

Battery Size and
and Mass
Mass
Launcher Selection

Launch Strategy
-

number of launches
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THE WATS MISSION (contd) (non MDO-based)
solution

• OPTIMIZATION CRITERIA
• TO MINIMIZE SYSTEM RESOURCES (MASS, POWER, COST
  OF EACH SATELLITE, SATELLITES/ LAUNCHES NUMBER,
  ...)
• TO MAXIMIZE SYSTEM PERFORMANCES (EVENTS NUMBER,
  ...)
• SOLUTION FOUND
• NUMBER OF SATELLITES 12
• NUMBER OF LAUNCHES 4
• SATELLITE MASS 237 KG
• PROPULSION MONOPROPELLANT N2H4 (SIMPLEST
  SOLUTION)
• POWER SINGLE JUNCTION SOLAR PANNEL (SIMPLEST
  SOLUTION)
• POINTING STRATEGY EARTH POINTING

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THE INTRAMARSNET MISSION a (very simple) case
study

• SCIENTIFIC GOAL
• MARS SURFACE EXPLORATION (BIOLOGY/GEOLOGY) AND
  OUTER ENVIRONMENT EXPLORATION (REMOTE SENSING)
• MISSION GOAL
• PERFORMING SURFACE OPERATIONS (ROVER)/
• ON-ORBIT REMOTE SENSING (ORBITER)

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THE INTRAMARSNET MISSION main conflicts

• ROVER SYSTEM
• MAXIMIZE DATA VOLUME
• MINIMIZE SYSTEM RESOURCES
• ROVER/ORBITER INTERACTION
• MAXIMIZE ROVER/ORBITER CONTACT PERIOD
• MINIMIZE ORBITER OPERATIONS COMPLEXITY

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THE MARS MISSION (non MDO-based) solution

• SELECTION OF A QUASI-CIRCULAR (ORBITER) ORBIT
  THAT
• MINIMIZES THE ROVER SYSTEM RESOURCES
• MAXIMIZES THE ROVER SYSTEM DATA VOLUME
• REDUCING THE ORBITER OPERATIONS COMPLEXITY

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THE PROPOSED APPROACH

• JOINT USE OF THREE METHODOLOGIES
• NEIGHBOURHOOD SEARCH
• GAME THEORY
• MULTICRITERIA DECISION ANALYSIS
• THE NEIGHBOURHOOD APPROACH AIMS AT FINDING A
  SET OF 'PARETIAN' (NON DOMINATED) SOLUTIONS AT
  SYSTEM LEVEL
• THE GAME THEORY AND THE MULTICRITERIA DECISION
  ANALYSIS SELECT A SMALL SUBSET OF
  PARETIANSOLUTIONS MOREADVANTAGEOUS FROM THE
  CONFLICTS REDUCTION POINT OF VIEW

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The theoretical approach
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Proposed methodology innovation

• There exist in literature various approaches to
  solve this kind of problem
• Conventional algorithms arranged to a specific
  mission
• Based on a single discipline
• Proposed methodology is innovative due to
• Joint enforcement of three different disciplines
• Possible generalisation to other test cases
• Different disciplines features
• Each of them is able to manage some aspects of
  the problem, but not all of them
• Their integration allows to overcome their
  respective limitations

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Joint approach (1)

• Combinatorial Optimisation (Neighbourhood
  Search)
• Fitting for complex and non-linear problems
• Includes methodologies independent from problems
  mathematical model
• Solutions quality / computational time
• Not able to manage multi-objective problems
• Multicriteria Decision Analysis
• Fitting for multi-objective problems
• Decisions support
• Game Theory
• Fitting for multi-objective problems
• Based on equilibria search

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Joint approach (2)

• Multicriteria Decision Analysis and Game Theory
  begin their analysis from an alternatives set.
• How can we obtain these alternatives?
• Preliminary role of Combinatorial Optimisation

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Definitions

• Paretian solution
• The concept of Pareto dominance is considered
  where different actions are to be compared on the
  basis of their consequences (minimization)
  problems with multiple objectives do not have a
  unique optimal solution, but a set of
  Pareto-optimal solutions. A vector of decision
  variables is Pareto optimal if does
  not exist another such that for all i
  and for at
  least one j. Here, F denotes the feasible region
  of the problem.

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Definitions (2)

• Nash equilibrium
• Nash (1950) formally defined an equilibrium of a
  non-cooperative game to be a profile of
  strategies, one for each player in the game, such
  that each player's strategy maximizes his
  expected utility payoff against the given
  strategies of the other players. If we can
  predict the behaviour of all the players in such
  a game, then our prediction must be a Nash
  equilibrium, or else it would violate the
  assumption of intelligent rational individual
  behaviour.

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Combinatorial Optimisation methodology
considerations

• Feature when dealing with real missions, the
  large size of the solution space does not allow
  an exhaustive exploration.
• Goal find the best possible solution in a
  reasonable computational time
• Meta-heuristic methodologies
• No need of model in terms of mathematical
  programming
• Promising solution space subset exploration
• good solutions
• reasonable computational time
• Capacity of escaping from local minima

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Combinatorial Optimisation approach

• Hybrid algorithm based on
• Tabu Search
• Iterative Local Search methodology
• Short term memory to avoid local minima
  entrapments
• Efficient solutions space exploration
• Path Re-linking
• Basic idea probably in the path connecting two
  Paretian solutions do exist other Paretian or,
  even better, dominant ones

23
Combinatorial Optimisation approach (2)
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Game Theory general concepts

• Game Theory studies how strategic interactions
  among rational agents produce outcomes with
  respect to the preferences (or utilities) of the
  agents.
• Agents involved in games are referred to as
  players.
• We need a device for thinking of utility
  maximisation in mathematical terms such a device
  is called utility function.
• Each player in a game faces a choice among two or
  more possible alternatives, called strategies.
• Game theorists refer to the solutions of games as
  equilibria here we are interested in the Nash
  equilibrium of the game.

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Game Theory approach

• Non-cooperative game and cooperative game without
  side payments.
• Three players (apogee altitude, data volume and
  solar array size).
• In order to define the utility of each player,
  two steps were performed
• the utility for apogee altitude and solar array
  size are reversed in the sense that the lower is
  the value the higher is the utility
• the utilities are normalized in the interval 0,
  1000.
• The computation of Nash equilibria was omitted as
  starting from a set of Paretian solutions (quite)
  all of them result in Nash equilibria.
• Nash (N) and Kalay-Smorodinsky (K) solutions,
  being considered promising results for
  cooperative games without side payments, are
  computed by implementing special purpose
  algorithms, instead of conventional ones.

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Example
Consider the number of satellites, 4, 8, 10, 12
and 16, and the number of launches, up to 1, 2,
3, 4 and 5.

• The payoff are computed referring to the
  following hypotheses
• A satellite weights about 350 Kg. and the cost is
  17 M
• Rockot can be used up to 3 satellites, with a
  cost of 15 M.
• Tzyklon can be used up to 4 satellites, with a
  cost of 25 M.
• The benefit (see table below) is shared among the
  two players proportionally as two thirds to
  satellite and one third to launcher.

The relation among benefit (B) and number of
events (E) is expressed as B 8.6vE 27
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Example


Non-cooperative approachThe Nash equilibria (in
bold) correspond to situations in which no player
can improve his utility, when he is the only one
changing his own strategy
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Example
Cooperative approachThe Nash solution (N)
maximizes the Nash product (x1d1)(x2d2)
x?FThe Kalai-Smorodinsky solution (K) is the
intersection of the boundary of the set F with
the line connecting the point d and the utopia
point (u) of theoretical maximal utility for the
players
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Multicriteria Decision Analysis approach

• Able to evaluate a set of alternatives on the
  basis of properly defined criteria.
• Alternatives provided by Combinatorial
  Optimisation.
• Criteria (apogee altitude, data volume, solar
  array dimension, efficiency index), weights and
  thresholds defined by analysing the considered
  mission.
• We used an MCDA software package (ELECTRE III) to
  return a rank of promising solutions.

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Multicriteria Decision Analysis simple example

• Seven alternatives are provided by Combinatorial
  Optimisation.
• Three criteria (apogee altitude, data volume,
  solar array dimension) and several scenarios
  (weights) for the sensitivity analysis of the
  results 0.30-0.40-0.30 / 0.27-0.37-0.36 /
  0.33-0.37-0.30 / 0.35-0.30-0.35 / 0.28-0.44-0.28
• Always these results
  Robust
  conclusions

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Problem Structuring and Modelling for MCDA

• The alternatives and the criteria, to evaluate
  the alternatives, are not defined because the
  problem is complex and at least partially
  unstructured (i.e WATS mission).
• A methodology (Strategic Choice Approach) is used
  to identify Decision Options and combine them in
  a finite set of alternatives.
• The Compatibility of the alternatives is tested
  and an evaluation model is defined by a cyclic
  development of the methodology in relation to the
  considered mission.
• Criteria (such as costs, time, number of events)
  are defined and used to compare alternatives.
  Some local decisions are made and the worst
  alternatives are eliminated.
• An MCDA software package (ELECTRE III) is used to
  rank the most promising solutions, on the basis
  of the defined criteria.

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The software prototype
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Mars mission structure
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Mars mission conflicts

• The first conflict is inner to the rover
  structure
• RF subsystem wants to have the highest data
  volume per orbit, that in turn means it wants to
  have RF power peak as high as possible but, on
  the other hand, Power subsystem prefers small
  solar panel, that means to give to RF subsystem
  as low power peak as possible.
•  
• The second conflict arises between the rover and
  the orbiter
• The rover RF subsystem wants to have the data
  volume per orbit as high as possible, that in
  turn means it wants to have orbiter/rover contact
  period as long as possible. The orbiter, instead,
  wants to perform simple operations, so it prefers
  to stay on a circular orbit.

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Software prototype concept
36
Parameters setting

• Contact Time Transmitting Bit Rate
• Starting solution 7.5 min 4000 bps
  
• Final solution 34.5 min 8000
  bps
• Ranges Contact Time 7.5 34.5 min
• Transmitting Bit Rate 2000 10000 bps
• Steps Contact Time 0.5 min
• Transmitting Bit Rate 100 bps

37
Combinatorial Optimisation approach
38
Multicriteria Decision Analysis methodology

• Phase I MCDA parameters definition
• Model obtained by defining criteria and by
  setting MCDA specific parameters (veto,
  preference and indifference thresholds, weights).
• where q is the indifference threshold
• s is the preference threshold
• v is the veto threshold
• Phase II alternatives analysis
• Performed by Electra III.

39
Game Theory approach

• Three players (apogee altitude, data volume and
  solar array size).
• In order to define the utility for each player,
  two steps were performed
• the utility for apogee altitude and solar array
  size are reversed in the sense that the lower is
  the value the higher is the utility
• the utilities are normalised in the interval 0,
  1000.
• The Nash solution takes into account what is
  given to the players.
• The Kalai-Smorodinsky solution, instead,
  considers not only what is given to the players
  but also what they could be given, looks for a
  Paretian solution that leads all the players
  towards their maximal utility, instead to ask a
  small sacrifice to one player if the other two
  can greatly increase their utilities.

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Computational results

• We obtained different solutions ranks according
  to the three scenarios defined.
• General considerations
• The Nash solution results as a good quality
  solution also according to the multicriteria
  approach.
• The Kalai-Smorodinsky solution, instead,
  according to MCDA results, it is only in the mid
  ranking.

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Software Prototype demonstration

• Starting values setting
• Default starting and final solutions (file1.txt)
• Default input parameters ranges and steps
  (file2.txt)
• Combinatorial Optimisation (search of paretian
  solutions)
• NS.EXE
• Results (OOCIGT.txt)
• Game Theory (search of Nash and Kalai-Smorodinsky
  solutions)
• GT.EXE
• Results (memo.txt)
• Multicriteria Decision Analysis
• III scenario

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CONCLUSION AND FUTURE DEVELOPMENTS

• INTRODUCTION OF AN ADVANCED AND INNOVATIVE
  METHODOLOGY TO TACKLE CONFLICTS ARISING IN ANY
  PHASE OF A SPACE PROGRAM
• POSSIBLE FUTURE ACTIVITY
• INCLUSION OF FURTHER SUBSYSTEMS
• (E.G. THERMAL OR STRUCTURAL SUBSYSTEM)
• DEVELOPMENT OF A COMPREHENSIVE DECISION SUPPORT
  SYSTEM ADDRESSED TO EFFICIENTLY SUPPORT THE WHOLE
  LIFE CYCLE OF A SPACE PROGRAM

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REFERENCE DOCUMENTS AND BIBLIOGRAPPHY

• Multidisciplinary Optimisation (MDO) - Problem
  Architecture Definition, Final Report
• Multidisciplinary Optimisation (MDO) -
  Executive summary
• WATS - Water Vapour and Temperature in the
  Troposphere and Stratosphere, SP-1257 (3).
• Rayward-Smith, V.J., Osman, I.H., Reeves, C.R.
  and Smith G.D. eds., Modern Heuristic Search
  Methods, Wiley, 1996.
• Glover, F., Laguna, M. and Martì, R.
  Fundamentals of scatter search and path
  relinking, Control and Cybernetics, 39, 2000,
  653-684.
• G.Owen, G., Game Theory, Third Ed., Academic
  Press, 1994.
• Myerson, R. B., Game Theory, Harvard University
  Press, 1991.
• Belton, V. and Stewart, T.J., Multiple criteria
  decision analysis an integrated approach, Kluwer,
  Dordrecht, 2002.
• Roy, B., Multicriteria methodology for Decision
  Aiding, Kluwer, Dordrecht, 1996.
• Vincke, P., Multicriteria decision-aid, Wiley,
  Chichester, 1992.
• Roy B. The outranking approach and the
  foundations of ELECTRE methods. In Bana CA, ed.
  Readings in Multiple Criteria Decision Aid,
  Springer-Verlag, Heidelberg, 1990, 115-184.
  
  
  
  
  INTERMARSNET RF COMMUNICATION, IMN-ALS-TN-1540-167
  0.

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ACKNOWLEDGEMENTS

• THIS WORK WAS FULLY FUNDED BY
  THE EUROPEAN SPACE
  AGENCY
• AUTHORS ARE VERY GRATEFUL TO
• DR. A. GALVEZ AND DR. D. IZZO