4. Design Space Exploration of Embedded Systems

Transcription

1 4. Design Space Exploration of Embedded Systems Lothar Thiele ETH Zurich, Switzerland 4-1

2 Contents of Lectures (Lothar Thiele) 1. Introduction to Embedded System Design 2. Software for Embedded Systems 3. Real-Time Scheduling 4. Design Space Exploration 5. Performance Analysis 4-2

3 Topics Multi-Objective Optimization! Introduction! Multi-Objective Optimization! Algorithm Design Design Choices Representation Fitness and Selection Variation Operators! Implementation Design Space Exploration! System Design! Problem Specification! Example 4-3

4 Evolutionary Multiobjective Optimization Algorithms What are Evolutionary Algorithms? randomized, problem-independent search heuristics applicable to black-box optimization problems How do they work? by iteratively improving a population of solutions by variation and selection can find many different optimal solution in a single run 4-4

5 Black-Box Box Optimization Stretch-Module objective function Decision-Module Handling-Module 100 DX lane ψ DV lane v, a a require decision vector x v v=f(t) lane x, v, a t point of gear change n gear 4 R? gear Vehicle-Module α α Br Dr α Dr gear s clutch objective vector f(x) lane, x, v a,gear, n (e.g. simulation model) Optimization Algorithm: only allowed to evaluate f (direct search) 4-5

6 The Knapsack Problem weight = 750g profit = 5 weight = 1500g profit = 8 weight = 300g profit = 7 weight = 1000g profit = 3? Goal: choose subset that maximizes overall profit minimizes total weight 4-6

7 The Solution Space profit g 1000g 1500g 2000g 2500g 3000g 3500g weight 4-7

8 The Trade-off Front Observations: " there is no single optimal solution, but # some solutions ( ) are better than others ( ) profit 20 selecting a solution finding the good solutions 5 500g 1000g 1500g 2000g 2500g 3000g 3500g 4-8 weight

9 Decision Making: Selecting a Solution Approaches: profit more important than cost (ranking) weight must not exceed 2400g (constraint) profit too heavy 5 500g 1000g 1500g 2000g 2500g 3000g 3500g 4-9 weight

10 Optimization Alternatives Use of classical single objective optimization methods simulated annealing, tabu search integer linear program other constructive or iterative heuristic methods Decision making (weighting the different objectives) is done before the optimization. Population based optimization methods evolutionary algorithms genetic algorithms Decision making is done after the optimization. 4-10

11 Optimization Alternatives scalarization weighted sum population-based SPEA2 y2 y2 y1 y1 parameter-oriented scaling-dependent 4-11 set-oriented scaling-independent

12 Scalarization Approach multiple objectives (y1, y2,, yk) parameters transformation single objective y example: weighting approach y2 maximization problem (w1, w2,, wk) y = w 1 y w k y k 4-12 y1

13 A Generic Multiobjective EA population archive evaluate sample vary update truncate new population 4-13 new archive

14 An Evolutionary Algorithm in Action max. y2 hypothetical trade-off front 4-14 min. y1

15 Design Space Exploration Specification Optimization Evaluation Implementation power consumption latency cost 4-15

16 Packet Processing in Networks Embedded Internet Devices UCB Rabaey method (a)(fsd) for I=1 to n do nothing call comm(a,dsf,*e); end for Wearable Computing Access Core Mobile Mobile Internet 4-16

17 Network Processors Network processor = high-performance, programmable device designed to efficiently execute communication workloads [Crowley et al.: 2003] incoming flows (packet streams) routing / forwarding transcoding encryption / decryption outgoing flows (processed packets) e.g., voice e.g., sftp real-time flows non-real-time flows network processor (NP)? 4-17

18 Optimization Scenario: Overview Given: " specification of the task structure (task model) = for each flow the corresponding tasks to be executed # different usage scenarios (flow model) = sets of flows with different characteristics Sought: network processor implementation (resource model) = architecture + task mapping + scheduling Objectives: " maximize performance # minimize cost Subject to: " memory constraint # delay constraints (performance model) 4-18

19 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness and Selection Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-19

20 Dominance, Pareto Points A (design) point J k is dominated by J i, if J i is better or equal than J k in all criteria and better in at least one criterion. A point is Pareto-optimal or a Pareto-point, if it is not dominated. The domination relation imposes a partial order on all design points We are faced with a set of optimal solutions. Divergence of solutions vs. convergence. 4-20

21 Multi-objective Optimization 4-21

22 Multi-objective Optimization Maximize (y1, y2,, yk) = ƒ(x1, x2,, xn) y2 y2 Pareto optimal = not dominated better incomparable dominated worse incomparable y1 y1 Pareto set = set of all Pareto-optimal solutions 4-22

23 Randomized (Black Box) Search Algorithms Idea: find good solutions without investigating all solutions Assumptions:better solutions can be found in the neighborhood of good solutions information available only by function evaluations Randomized search algorithm t = 1: (randomly) choose a solution x 1 to start with ƒ t t+1: (randomly) choose a solution x t+1 using solutions x 1,, x t 4-23

24 Types of Randomized Search Algorithms memory selection variation mating selection environmental selection EA 1 both evolutionary algorithm TS tabu search 1 no mating selection SA simulated annealing 1 no mating selection 4-24

25 Limitations of Randomized Search Algorithms The No-Free-Lunch Theorem All search algorithms provide in average the same performance on a all possible functions with finite search and objective spaces. Remarks: [Wolpert, McReady: 1997] Not all functions equally likely and realistic We cannot expect to design the algorithm beating all others Ongoing research: which algorithm suited for which class of problem? 4-25

26 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness and Selection Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-26

27 Design Choices representation fitness assignment mating selection parameters environmental selection variation operators 4-27

28 Issues in Multi-Objective Optimization y2 Diversity How to maintain a diverse Pareto set approximation? # density estimation How to prevent nondominated solutions from being lost? $ environmental selection y1 Convergence How to guide the population towards the Pareto set? " fitness assignment 4-28

29 Comparison of Three Implementations 2-objective knapsack problem SPEA2 VEGA extended VEGA Trade-off between distance and diversity? 4-29

30 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-30

31 Representation search space decoder solution space objectives objective space m ƒ solutions encoded by vectors, matrices, trees, lists,... Issues: 4-31 fixed length variable length completeness (each solution has an encoding) uniformity (all solutions are represented equally) redundancy (cardinality of search space vs. solution space) feasibility (each encoding maps to a feasible solution)

32 Example: Binary Vector Encoding Given: graph Goal: find minimum subset of nodes such that each edge is connected to at least one node of this subset (minimum vertex cover) A B C D E nodes selected? A 1 B 0 C 1 D 1 E 1 F

33 Example: Integer Vector Encoding Given: graph, k colors Goal: assign each node one of the k colors such that the number of connected nodes with the same color is minimized (graph coloring problem) A B C D E nodes colors A 1 B 2 C 1 D 3 E 1 F

34 Example: Real Vector Encoding parameters values [Michalewicz, Fogel: How to Solve it. Springer 2000] x 1 x 2 x 3 x x n 9.83

35 Tree Example: Parking a Truck steering angle u dock trailer cab d position (x,y) t constant speed 4-35 Goal: find function c with u = c(x, y, d, t)

36 Operators: Search Space for the Truck Problem Arguments: X position x Y position y DIFF cab angle d TANG trailer angle t Search space :set of symbolic expression using the above operators and arguments 4-36

37 Example Solution: Tree Representation MULT MINUS PLUS X DIFF Y TANG encodes the function (symbolic expression): u = (x d) * (y + t) 4-37

38 A Solution Found by an EA truck simulation encoded tree 4-38

39 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness and Selection Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-39

40 Fitness Assignment Fitness = scalar value representing quality of an individual (usually). Used for mating and environmental selection F i = f ( m (i) ) Difficulties: multiple objectives have to be considered (Pareto set is sought) multiple optima need to be approximated (how to consider diversity?) constraints are involved which have to be met 4-40

41 Example Pareto Ranking Fitness function: execution time F (1) = F F F (2) (3) (4) = 1 = 1 = 2 4 F (5) = 1 F 5 (6) 0 = cost 4-41

42 Constraint Handling feasible Constraint = g(x1, x2,, xn) 0 g 0 infeasible g < 0 Approaches: construct initialization and variation such that infeasible solutions are not generated (resp. not inserted) representation is such that decoding always yields a feasible solution calculate constraint violation (- g(x1, x2,, xn) ) and incorporate it into fitness, e.g., F i = f ( m (i) ) - g(x1, x2,, xn) (fitness to be maximized) code constraint as a new objective 4-42

43 Selection Two conflicting goals: exploitation (converge fast) trade-off exploration (avoid getting stuck) Two types of selection: mating selection = select for variation environmental selection = select for survival 4-43

44 Example: Tournament Selection = integrated sampling rate assignment and sampling population mating pool " uniformly choose T individuals at random independently of fitness # compare fitness and copy best individual in mating pool T = tournament size (binary tournament selection means T=2) 4-44

45 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness and Selection Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-45

46 Example: Vector Mutation Bit vectors: each bit is flipped with probability 1/6 Permutations: swap rearrange 4-46

47 Example: Vector Recombination Bit vectors: Permutations: parents child

48 Example: Recombination of Trees MULT PLUS MINUS PLUS TANG MINUS MINUS DIFF Y TANG PLUS DIFF X Y MULT DIFF exchange Y TANG 4-48

49 Step 1: Generate initial population P0 and empty archive (external set) A 0. Set t = 0. Step 2: Calculate fitness values of individuals in P t and A t. Step 3: A t+1 = nondominated individuals in P t and A t. If size of A t+1 > N then reduce A t+1, else if size of A t+1 < N then fill A t+1 with dominated individuals in P t and A t. Step 4: If t > T then output the nondominated set of A t+1. Stop. Step 5: Fill mating pool by binary tournament selection. Step 6: Example: SPEA2 Algorithm Apply recombination and mutation operators to the mating pool and set P t+1 to the resulting population. Set t = t + 1 and go to Step

50 SPEA2 Fitness Assignment Idea (Step 2): calculate dominance rank weighted by dominance count y non-dominated solutions: F = #dominated solutions dominated solutions F = # of non-pareto solutions + strengths of dominators y1 Note: lower raw fitness = better quality 4-50

51 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness and Selection Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-51

52 A framework that What Is Needed Provides ready-to-use modules (algorithms / applications) Is simple to use Is independent of programming language and OS Comes with minimum overhead Idea: separate problem-dependent from problemindependent part cut Selection Fitness assignment Archiving Representation Recombination Mutation Objective functions 4-52

53 PISA: Implementation shared file file system selector process text files variator process application independent: mating / environmental selection individuals are described by IDs and objective vectors handshake protocol: state / action individual IDs objective vectors parameters 4-53 application dependent: variation operators stores and manages individuals

54 PISA Installation 4-54

55 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness and Selection Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-55

56 Design Space Exploration Application Architecture Mapping Estimation 4-56

57 Embedded System Design evaluation architecture template task graph binding restrictions allocation bindings performance / cost vector construct architecture map application estimate performance multiobjective optimization architecture performance 4-57

58 Example: System Synthesis Given: algorithm mappings architectures f 1, f 2,K Goal: schedule mapping architecture Objectives: cost, latency, power consumption 4-58

59 Evolutionary Algorithms for DSE individual EA " selection # recombination $ mutation allocation binding decode allocation decode binding scheduling chromosome = encoded allocation + binding design point (implementation) fitness fitness evaluation user constraints 4-59

60 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness and Selection Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-60

61 Basic Model Problem Graph Problem graph G P (V P,E P ): Interpretation: V P consists of functional nodes V f P (task, procedure) and communication nodes V c P. E P represent data dependencies 4-61

62 Basic model architecture graph Architecture graph G A (V A,E A ): RISC HWM1 RISC HWM1 shared bus HWM2 Architecture PTP bus shared bus HWM2 Architecture graph PTP bus V A consists of functional resources V A f (RISC, ASIC) and bus resources V A c. These components are potentially allocatable. E A model directed communication. 4-62

63 Basic model specification graph Definition: Aspecification graph is a graph G S =(V S,E S ) consisting of a problem graph G P, an architecture graph G A, and edges E M.In particular, V S =V P V A, E S =E P E A E M G P E M G A RISC SB HWM1 PTP HWM2 4-63

64 Basic model - synthesis Three main tasks of synthesis: Allocation α is a subset of V A. Binding β is a subset of E M, i.e., a mapping of functional nodes of V P onto resource nodes of V A. Schedule τ is a function that assigns a number (start time) to each functional node. 4-64

65 Basic model - implementation Definition: Givena specification graph G S an implementation is a triple (α,β,τ), where α is a feasible allocation, β is a feasible binding, and τ is a schedule τ α β RISC HWM1 shared bus HWM2 RISC SB HWM1 PTP bus 4-65

66 Example P 4-66

67 Challenges Encoding of (allocation+binding) simple encoding eg. one bit per resource, one variable per binding easy to implement many infeasible partitionings encoding + repair eg. simple encoding and modify such that for each v p V P there exists at least one v a V A with a β(v p ) = v a reduces number of infeasible partitionings Generation of the initial population, mutation Recombination 4-67

68 Topics Multi-Objective Optimization Introduction Multi-Objective Optimization Algorithm Design Design Choices Representation Fitness and Selection Variation Operators Implementation Design Space Exploration System Design Problem Specification Example 4-68

69 Exploration - Case Study (1) 4-69

70 Exploration - Case Study (2) 4-70

71 Exploration - Case Study (3) frame memory dual ported frame memory block matching module input module subtract/add module DCT/IDCT module Huffman encoder output module 4-71

72 EA Case Study - Design Space power consumption latency cost

73 Exploration Case Study - Solution 1 INM OUTM FM RISC2 SBS 4-73

74 Exploration Case Study - Solution 2 INM OUTM DPFM HC DCTM BMM SAM SBF 4-74