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  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. Auto Regressive Filter

4. 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 + start   +< - - end 1 2 3 4 v2v1 v3 v4 v5 vn v6 v7 v8 v9 v10 v11

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. List Scheduling + start   +< - - end 1 2 3 4 v2v1 v3 v4 v5 vn v6 v7 v8 v9 v10 v11 Procedure ListScheduling(G, R, L) Input: DFG(V,E), resource set R, priority list L Output: instruction schedule 1.cycle  0 2.ReadyList  successors of start 3.While node end is not scheduled do 4. for op in ReadyList in decending priority do 5. if resource exists for op to start then 6. schedule op at time cycle 7. end if 8. Update ReadyList 9. end for 10. cycle  cycle + 1 11.end while 12.return schedule

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

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. Pheromone Model For Instruction Scheduling op1 op2 op3 op4 op5 op6 Instructions 1 2 3 4 5 6 Priority List Each instruction opi  I associated 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. Ant Search Strategy op1 op2 op3 op4 op5 op6 Instructions 1 2 3 4 5 6 Priority List  Multiple ants independently create their own priority list  Fill one instruction at a time  Iterative process op1 op2 op3 op4 op5 op6 op5 op4 op1 op6 op2 op3

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 op2 op3 op4 op5 op6 Instructions 1 2 3 4 5 6 Priority List op1 op2 op3 op4 op5 op6 op5 op4 op1

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 L h for the result from ant h  Evaporation – prevent stigmergy and punish “useless” trails  Reinforcement – award trails with better quality

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

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)  S gb is 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  P best  (0,1] is the controlling parameter  Smaller P best  tighter range for   more emphasis on exploration  When P best  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) Benchmark (nodes/edges) ResourcesCPLEX (latency /runtime) Force Directed List SchedulingMMAS-IS (average over 5 runs) IMIDLWIDSNIMIDLWIDSN HAL(21/25)la, lfm, lm, 3i, 3o8/32888988888 ARF(28/30)2a, lfm, 2m11/2211 13 11 EWF(34/47)la, lfm, lm27 /2400028 31 2827.2 2727.2 FIR1 (40/39)2a, 2m, 3i, 3o13/23219 1817.2 1717.8 FIR2(44/43)la, lfm, lm, 3i, 3o14/1156019 21 16.216.416.217 COSINE 1(66/76)2a,2m, lfm, 3i, 3o  18192018 17.418.217.6 COSINE2(82/91)2a,2m, lfm, 3i, 3o  23 21.2 Average1818.219.320.518.516.817.016.917.1

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