Instruction Scheduling Using Max-Min Ant System Optimization

1. Instruction Scheduling Using Max-Min Ant System Optimization Gang Wang, Wenrui Gong, and Ryan Kastner Dept. of Electrical and Computer Engineering University of California, Santa Barbara GLSVLSI’2005, Chicago, April 18, 2005

2. Instruction Scheduling • Instruction Scheduling is a fundamental synthesis problem • Software - compilers for microprocessors • Hardware - behavioral synthesis for ASIC, FPGA • Requisite Moore’s Law reference • Moore transistors = moore computational resources • Larger applications = moore operations • How to best utilize the resources?

3. Instruction Scheduling Definition Auto Regressive Filter • Given a set of instructions and collection of computational units • Instruction modeled using data flow graph (DFG) • Directed acyclic graph • Each node is instruction • Each edge is a data dependence • Find schedule for instructions to minimize some function (latency, area, power, …) • We focus on resource constrained problem, i.e. minimize latency given a set of resources.

4. start 1     +   + < 2 - 3 - 4 end Instruction Scheduling • NP-hard • Fundamental problem - many different heuristic methods have been developed • ILP • Force directed • Genetic algorithm • Path based • Graph theoretic • Computational geometry • List scheduling v1 v2 v6 v8 v10 v3 v7 v9 v11 v4 v5 vn

5. List Scheduling • Simple and effective • Greedy strategy • Operation selection decided by criticality • O(n) time complexity • Make a priority list of the instructions based on some measure (mobility, instruction depth, number of successors, etc.) • No single priority function works well over all applications • Highly dependent on problem instance • Solution quality varies greatly across different functions

6. start 1     +   + < 2 - 3 - 4 end List Scheduling • Procedure ListScheduling(G, R, L) • Input: DFG(V,E), resource set R, priority list L • Output: instruction schedule • cycle 0 • ReadyList  successors of start • While node end is not scheduled do • for op in ReadyList in decending priority do • if resource exists for op to start then • schedule op at time cycle • end if • Update ReadyList • end for • cycle  cycle + 1 • end while • return schedule v1 v2 v6 v8 v10 v3 v7 v9 v11 v4 v5 vn

7. Our approach – Ant System Heuristic • Inspired by ethological study on the behavior of ants [Goss et al. 1989] • A meta heuristic • A multi-agent cooperative searching method • A new way for combining global/local heuristics • Extensible and flexible

8. Ant System Heuristic

9. Ant System Heuristic

10. Ant System Heuristic

11. Ant System Heuristic

12. Ant System Heuristic

13. Ant System Heuristic

14. Ant System Heuristic

15. Ant System Heuristic

16. Ant System Heuristic

17. Autocatalytic Effect

18. Formulating Problems Using Ant Search • Problem model – define search space, create decision variables • Pheromone model – used as a global heuristic, distribution of pheromones, evaporation and strengthening strategies • Ant search strategy – local heuristics and solution space traversal • Solution construction – method of creating an answer from decision variables • Feedback – provide assessment of solution quality and adjust pheromones accordingly

19. Hybrid Ants with Lists • Combine Ant System Optimization and List Scheduling • Ants determine priority list • List scheduling framework evaluates the “goodness” of the list • Iterative approach

20. op1 1 op2 2 op3 3 op4 4 op5 5 op6 6 Instructions Priority List Pheromone Model For Instruction Scheduling Each instruction opi  Iassociated with n pheromone trails where j = 1, …, n which indicate the favorableness of assign instruction i to position j Each instruction also has a dynamic local heuristic

21. 1 2 3 4 5 6 Priority List Ant Search Strategy • Multiple ants independently create their own priority list • Fill one instruction at a time • Iterative process op1 op1 op4 op2 op2 op1 op3 op3 op5 op4 op4 op6 op5 op5 op2 op6 op6 op3 Instructions

22. Ant Search Strategy • Each ant has memory about instructions already selected • At step j ant has already selected j-1 instructions • jth instruction selected probabilistically op1 op1 op4 1 op2 op2 2 op1 op3 op3 op5 3 op4 op4 4 op5 op5 5 op6 op6 6 Instructions Priority List

23. Ant Search Strategy • ij(k) : global heuristic (pheromone) for selecting instruction i at j position • j(k) : local heuristic – can use different properties • Instruction mobility (IM) • Instruction depth (ID) • Latency weighted instruction depth (LWID) • Successor number (SN) • ,  control influence of global and local heuristics

24. Pheromone Update • Priority lists evaluated using list scheduling • Latency Lh for the result from ant h • Evaporation – prevent stigmergy and punish “useless” trails • Reinforcement – award trails with better quality

25. 1 2 3 4 5 6 Priority List Pheromone Update • Evaporation happens on all trails • Reward the used trails based on the solution’s quality op1 op1 op4 op2 op2 op1 op3 op3 op5 op4 op4 op6 op5 op5 op2 op6 op6 op3 Instructions

26. Max-Min Ant System (MMAS) • Risks of Ant System optimization • Too much feedback • Dynamic range of pheromone trails can increase rapidly • Limited search of solution space • Unused trails can be repetitively punished, therefore certain schedules may never be selected • Premature convergence • MMAS is designed to address this problem • Built upon original AS • Idea is to limit the pheromone trails within an evolving bound so that more broader exploration is possible • Better balance the exploration and exploitation • Prevent premature convergence

27. Max-Min Ant System (MMAS) • Limit (t) within min(t) and max(t) • Sgbis the best global solution found so far at t-1 • f(.) is the quality evaluation function, e.g. latency in our case • avg is the average size of decision choices • Pbest  (0,1]is the controlling parameter • Smaller Pbest  tighter range for  more emphasis on exploration • When Pbest  0, we setmin  max

28. Other Algorithmic Refinements • Dynamically evolving local heuristics • Example: dynamically adjust instruction mobility • Benefit: dynamic search space reduction • Taking advantage of topological sorting of DFG when constructing priority list • Each step ants select from the ready instructions instead from all unscheduled instructions • Benefit: greatly reduce the search space

29. MMAS Instruction Scheduling Algorithm

30. ARF Pheromones

31. Experimental Results • ILP (optimal) using CPLEX • List scheduling • Instruction mobility (IM), instruction depth (ID), latency weighted instruction depth (LWID), successor number (SN) • Ant scheduling results using different local heuristics (Averaged over 5 runs, each run 100 iteration with 5 ants)

32. Conclusion • Proposed a novel heuristic method for resource-constrained instruction scheduling problem • Hybrid MMAS and List Scheduling • Create a mathematic model for combining global and local heuristics • Experiment results are promising • Near optimal results • Outperforms widely used force-directed approach • More stable and insensitive to choice of application/local heuristics • Thanks! Questions?

33. Extra Slides

34. DFG Size Distribution

35. Auto Regressive Filter