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# Multi-Objective Evolutionary Algorithms

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### Multi-Objective Evolutionary Algorithms

1. 1. Introduction to Multi-Objective Evolutionary Algorithms<br />
2. 2. Table of Content<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />Multi-Objective Problems<br />MOEA’s Difference from Single-Objective EA<br />Selection: Non-Dominated Sorting <非劣排序><br />MOEA solving Knapsack<br />Problem Description<br />A Test Case<br />MOEA Application: Automated Antenna Design<br />
3. 3. Multi-Objective Problems<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Multi-Objective Problems<br />MOEA‘s Difference from Single-Objective EA<br />Selection: Non-Dominated Sorting <非劣排序><br />With multiple objectives<br />Examples:<br />- Minimize y,z<br /><ul><li> 凤姐征婚：Maximize[学历，相貌，国际视野，……]
4. 4. Knapsack with multiple values
5. 5. TSP<旅行商问题> Minimize [Time, Distance, Cost, Risk]
6. 6. 选修课：Minimize [所花精力] Maximize [最终得分]</li></li></ul><li>Solution methods for Multi-Objective problems<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Multi-Objective Problems<br />MOEA‘s Difference from Single-Objective EA<br />Selection: Non-Dominated Sorting <非劣排序><br />Constructing a single aggregate objective function (AOF) <聚合为单目标><br />Normal Boundary Intersection (NBI) method<br />Normal Constraint (NC) method<br />Successive Pareto Optimization (SPO) method<br />Multiobjective Optimization using Evolutionary Algorithms (MOEA).<br />PGEN (Pareto surface generation for convex multiobjective instances)<br />IOSO (Indirect Optimization on the basis of Self-Organization)<br />Reference: Wikipedia[Multiobjective optimization] - http://en.wikipedia.org/wiki/Multiobjective_optimization<br />
7. 7. General Framework of Evolutionary Algorithms<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Multi-Objective Problems<br />MOEA‘s Difference from Single-Objective EA<br />Selection: Non-Dominated Sorting <非劣排序><br />Initialize Population<br />Evaluation<br />Randomly create a certain number of solutions(individuals)<br />Breeding Operation<br />Apply breeding operators on individuals in the population, producing a group of new individuals.<br />Evaluation<br />Crossover, Mutation, etc.<br />Calculate the objective value based on decision variables of a individual.<br />Apply selection operator on individuals in the population, shrink the population size to the initial size.<br />Selection<br />Termination Conditions?<br />Termination(Output)<br />
8. 8. MOEA’s Difference from Single-Objective EA<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Multi-Objective Problems<br />MOEA‘s Difference from Single-Objective EA<br />Selection: Non-Dominated Sorting <非劣排序><br />Initialize Population<br />Evaluation<br />Breeding Operation<br />Single Objective  Multiple Objectives<br />double Evaluate(vector<double> dna)<br />vector<double> Evaluate(vector<double> dna)<br />Crossover, Mutation, etc.<br />Normal Sorting Non-Dominated Sorting <非劣排序><br />Producing a group of Pareto Fronts <Pareto 前沿><br />Selection<br />Termination Conditions?<br />内涵在这里！<br />Termination(Output)<br />Optimization Result: one optimal solution a group of non-dominated solutions<br />
9. 9. Selection: Non-Dominated Sorting<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Multi-Objective Problems<br />MOEA‘s Difference from Single-Objective EA<br />Selection: Non-Dominated Sorting <非劣排序><br />Non-dominated comparison<br />对于给定的两个非全等向量:A(x1, x2, …, xn), B(y1, y2, …, yn)<br />当且仅当∀i: xi ≥ yi，有A 大于B<br />当且仅当∀i: xi ≤ yi， 有B大于A<br />其余情况，即<br />∃i, ∃j: i≠j AND xi > yi AND xj < yj<br />则A与B不可比<br />学历<br />(2, 3)<br />(3, 2)<br />国际视野<br />
10. 10. Knapsack with Multiple Values<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Problem Description<br />A Test Case<br />Definition<br />Given a set of items<br />each with a set of costs [e.g. Weight, Volume, etc. ]<br />and a set of values<br />determine the number of each item to include in a collection, so that the total costs are less than given limits and the total values are as large as possible.<br />给定一组物品<br />每种物品有确定的 {<br />数量<br />成本[重量，体积，神秘成本]<br />价值[价值1，价值2]<br />}<br />确定每种物品的选取数量，在满足总成本在给定的限定范围之内的前提下，极大化总价值[价值1，价值2]<br />
11. 11. Parameters & Knapsack Data<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Problem Description<br />A Test Case<br />Total Evaluation Used: 240300<br />Properties<br />Algorithm<br />Objectives<br />Problem<br />Constraints<br />
12. 12. Knapsack - Result<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Problem Description<br />A Test Case<br />Distribution of Objectives<br />Generation = 0<br />Generation = 100<br />Generation = 200<br />Generation = 400<br />Generation = 600<br />Generation = 800<br />
13. 13. Knapsack - Result<br />Evolutionary progress of average value of each objective<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />Problem Description<br />A Test Case<br />Objectives’ evolutionary progress in same scale <br />
14. 14. Demand of Micro Antennas<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />用于微型卫星<br />空间和能量都十分宝贵<br />对天线各种性能要求极高<br />
15. 15. Objectives and Contraints of X-Band 5<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br /><ul><li>VSWR(Objectives)
16. 16. Minimize: T_VSWR(r0, r1, …, r4, x1, y1, z1, …, x4, y4, z4)
17. 17. Minimize: R_VSWR(r0, r1, …, r4, x1, y1, z1, …, x4, y4, z4)
18. 18. Gain(Objectives)
19. 19. Maximize: T_Gainθ,φ(r0, r1, …, r4, x1, y1, z1, …, x4, y4, z4)
20. 20. Maximize: R_Gainθ,φ(r0, r1, …, r4, x1, y1, z1, …, x4, y4, z4)
21. 21. Constraints
22. 22. T_Gainθ,φ≥ 0
23. 23. R_Gainθ,φ ≥ 0
24. 24. T_VSWR < 1.5
25. 25. R_VSWR < 1.5
26. 26. Diameter < 15.24cm
27. 27. Height < 15.24cm
28. 28. Antenna Mass < 165g
29. 29. Θ= 5.0i, i = 8,9,…,16
30. 30. φ = 5.0j, j = 0,1,…,71</li></ul>变量维数:17<br />目标个数:1298<br />约束条件个数:1301<br />问题规模庞大<br />
31. 31. Designing with MOEA<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />MOEA<br />chromosome : vector<double><br />Evaluator<br />Encoding<br />Electromagnetic Simulator<br />{NEC, HFSS, etc.}<br />
32. 32. Comparison between traditional and evolvable Antenna<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />QHAHandmade Antenna<br />NASAX-Band 5 Antenna designed by EA<br />
33. 33. Resources<br />Multi-Objective Evolutionary Algorithms(MOEA)<br />MOEA solving Knapsack<br />MOEA Application: Automated Antenna Design<br />MOEA Competition @ CEC 2009<br />http://dces.essex.ac.uk/staff/qzhang/moeacompetition09.htm<br />Knapsack problem<br />http://en.wikipedia.org/wiki/Knapsack_problem<br />NASA – Evolvable Systems<br />http://www.nasa.gov/centers/ames/research/exploringtheuniverse/exploringtheuniverse-evolvablesystems.html<br />