Address Non-constrained Multi-objective Design Problem using Layered Pareto Frontiers: A Case Study of a CubeSat Design

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1 Address Non-constrained Multi-objective Design Problem using Layered Pareto Frontiers: A Case Study of a CubeSat Design Never Stand Still UNSW Canberra School of Engineering and Information Telecommunication Lily Qiao l.qiao@adfa.edu.au Capability Systems Centre School of Engineering and IT UNSW, Canberra

2 What s the problem? Objective space Design problem: Treated as multi-objective optimization (MOP) problem Traditional optimization-based design approach: 1) formulate the design problem 2) develop analysis models 3) execute an optimization algorithm Results: A set of non-dominated solutions or Pareto frontier. (not a single optimal solution) Concept of Pareto-optimality 2 objective functions Every point in objective/ criterion space has a corresponding point in design space Shortcomings: However, in the early phase design, it usually lefts designers unsatisfied with their results. 2

3 Why? The optimization problem is usually improperly formulated. Not well defined. Designers only have some rough description of the design objectives. Not clear in terms of preference and priorities. The objectives and constraints were not what the owners and stakeholders really wanted in many cases. Relying solely on Pareto-optimal solutions is a not desirable. The size of the Pareto-optimal sets increases rapidly with the number of objectives Some non-pareto solution might still be desirable. Not helpful in decision making. 3

4 What we should do? In the start-up s strategy People don t know what they really want until they see some designs. Deciding objectives and constraints prematurely may lead to many infeasible solutions and difficulties to reach agreements. Preferred to treat all the objectives simultaneously and equally. Find some accepted designs to reveal the customer s real preference are important. How to provide decision makers an understanding of the choices of candidate system component? 4

5 Our approach Start Tradespace modelling Architecture Design Space Generate all possible design alternatives Layered Pareto Analysis Individual 2D objective space Clustering Analysis Objective Space 2D view for Layer k (k=1,2,...) of fi fj Clustering design alternatives Tradespace Exploration Pareto front interactions and visualization Reach agreement? No Yes Individual Pareto Layer Find possible accepted solutions(interactions)? Similar design near Pareto and near- Pareto solutions Find close-to-the-wanted designs? Yes No No Layer = Layer +1 Yes Similar designs Reach agreement? Yes Stop No Flexible and fully controlled by the users. 5

6 Internal Analysis Algorithms Pareto-Font sorting Concept of Union of the bi-objective Pareto fronts Layered Pareto Frontiers A solution with a lower-numbered rank is assigned a higher fitness than that of a solution with a higher-numbered rank. Find the intersection using pairwise Pareto front layers via iteration. 6

7 Study case: Problem Description CubeSat: Board-level subsystem CubeSat bus = A combination of 6 boards This results in a 1296 design alternatives. minimize Communication Power Supply Satellite bus system Attitude determination and Control Command Data Handling Structure Solar Panel 7

8 Results: Six objective spaces with Pareto front via Iterations Iteration 1 Iteration 4 Iteration 10 Following iterations product more intersections. 8

9 Results: Choices of subsystems for iteration 4 to 11 1 design 2 designs 3 designs 4 designs 5 designs 6 designs 7 designs 8 designs 9

10 Results: The combination of subsystems for iteration 4 to 11 1 design 2 designs 3 designs 4 designs 5 designs 6 designs 7 designs 8 designs 10

11 Results: Similar designs to Design 217 Design space Decision space Similar designs to Design 217 ( 1,, 6) (1,3,1,1,1,1) (1,3,1,1,3,1) (1,3,2,1,1,1) (1,3,2,1,3,1) (1,3,3,1,1,1) (1,3,3,1,3,1) Iteration 9, 6 solutions. The combination of subsystems for similar designs to Design 217 Objective values for similar designs to Design 217 Choices of subsystems for similar designs to Design

12 Results: Pareto front solutions vs. pairwise Pareto solutions Shows the Pareto fronts (red) pairwise Pareto solution (green) of the CubeSat example 102 solutions when the four objectives are considered together. Some red points are highly undesirable solutions. Layered Pairwise Pareto produces fewer useful solutions. 12

13 Conclusion Suitable for decision making in the early phases. Objectives are not clear, and constraints should not be set. It is preferred to treat all the objectives simultaneously and equally. MOP using bi-objective pair-wise Pareto fronts. Produces few useful solutions combined with a decomposition based method to find neighbouring solutions to the Pareto solutions for further consideration Li (Lily) Qiao L.qiao@adfa.edu.au Capability Systems Centre School of Engineering and Information Technology UNSW, Canberra 13