Tabu Search Vignette on Fred GLover's web pag

Sevaux, Marc

HAL-Université de Bretagne Occidentale

Tabu search for high level synthesis from [3]Marc Sevaux ∗July 26, 20101 Background and description of the problemElectronic chip design is of widespread importance throughout the electronics industry, constitut-ing an essential underpinning of computer-based applications. A critical problem in chip designis that of High Level Synthesis (HLS) [2], which consists of minimizing the total cost of an archi-tecture that is required for implementing a particular application in an embedded system (e.g. amp3 decoder device).A classical way to approach such a problem, which involves discrete sequencing requirements,is by means of an integer linear programming (ILP) model, and this approach has been gainingincreased favor with recent advances in the software for solving ILP models. A key finding ofour present study is that our tabu search (TS) approach, as described below, is dramaticallysuperior to solving the problem by integer linear programming, which always fails for large reallife problem instances. Consequently, we find that our TS method has special merit for practicalproblems faced in the electronics field.The High Level Synthesis problem can be model as a particular scheduling problem where theobjective, contrary to classical scheduling objectives related to jobs completion, is to minimize thenumber of resources used for scheduling the jobs in their time windows.More formally, a list of n jobs is to be scheduled on identical parallel processors, and for eachjob i, a release date ri, a due date di, a processing time pi and a set of predecessors PREDiare given. Let si be the starting time of job i that has to be determined. Apart from satisfyingprecedence constraints, job i cannot start before its release date (si ≥ ri) and has to be completedbefore its due date (si + pi ≤ di). The objective is to minimize the number of processors usedwhile respecting all the constraints. This problem is NP-hard.2 Application of Tabu Search for HLSSevaux and So¨rensen [4] proposed a tabu search method for the problem without precedenceconstraints. This method begins by computing a lower bound m on the number of processorsand then solves the classical Pm|ri|∑Ui scheduling problem using tabu search. The tabu searchprocedure consists of either inserting a late job between two early jobs or replacing a late job witha selected subset of consecutive early jobs. This method uses the sum of processing times of latejobs as a tabu criterion.The method is designed to handle precedence constraints as well. A preprocessing phase isperformed in order to tighten both release dates and due dates based on implications of precedenceconstraints by computing latest starting times and earliest due dates. Moreover, the methodfollows a reverse approach in comparison to [4]. From an initial feasible solution withm processors,the number of resources is decreased. The initial feasible solution to the problem withm processors∗Universite´ de Bretagne-Sud, UEB – Lab-STICC – CNRS, Centre de recherche, BP 92116, 56321 Lorient Cedex,France, marc.sevaux@univ-ubs.fr1is obtained by scheduling jobs as early as possible on processors where the remaining idle time onthe current processor is smallest (taking into account predecessors).The method perturbs the solution (removing some processors) to create a set of unallocatedjobs. These unallocated jobs are randomly tested for allocation on processors by tabu search.A reallocation step is undertaken by inserting the jobs on some processors by shifting theposition of others (i.e., by rescheduling jobs on the same processor either earlier or later withoutchanging their order). Among many possible insertion positions, a job is inserted at a place whereidle time left after insertion is the smallest. After inserting the job, all jobs that are scheduledbefore it on the same processor are rescheduled so that they can be finished by their earliestcompletion time and all jobs that are scheduled after it are delayed only by the required minimumamount. This is done following the policy of scheduling the jobs as early as possible.If it is not possible to insert the job on available processors then the method seeks to reallocatethe job by exchanging this job with those consecutively allocated jobs whose schedules overlapwith it. By consecutively allocated jobs, we mean those jobs, which are allocated one after theother on the same processor. However, unlike [4], the exchange operation is performed only whenthe processing time of each consecutively allocated job is less than the unallocated job. Amongall possible exchanges, the exchange that leaves the shortest period of idle time is selected. Thisnewly allocated job is assigned a tabu status to prevent it from being removed again for a specificduration.If a solution with m or less than m processors is obtained then it becomes the new initialsolution and the whole process is repeated, otherwise the new solution is discarded and the originalsolution is perturbed again.3 Successful experimentsExperiments were conducted on instances without precedence constraints to provide a comparisonto the TS-SS method from [4]. A large set of instances with precedence constraints were alsogenerated and used for additional experiments. Instances were also taken from the design of real-life embedded systems. Since our work is the first to address the problem as an optimizationproblem in the electronic community, in order to be able to carry out benchmark comparisonsto establish the quality of our outcomes we have developed an integer linear programming (ILP)model and solved it with the GLPK open source software.On the instances without precedence constraints (from 20 to 100 jobs), our TS-PRED methodclearly shows its superiority over the earliest TS-SS procedure. TS-PRED not only returns betterquality solutions but is also much faster than TS-SS. Our ILP formulation also proved to be quiteeffective for these problems, making possible to find all optimal solutions in 600 seconds whichwas nearly as fast as our TS-PRED method.On randomly generated instances with precedence constraints (from 25 to 1000 jobs), TS-PRED is able to find almost all optimal solutions when known, while running several times fasterthan the ILP model.Results for more challenging real-life instances (from 26 to 4040 jobs) demonstrated a moredramatic superiority for TS-PRED. The ILP model always fails for large instances, while TS-PRED was able to find efficient solutions in 20 seconds on average. Preliminary experiments witha commercial ILP software like Xpress-MP from FICO discloses continued advantages for TS-PRED, where large instances can require more than one hour of running time with the commercialsoftware.Interest from the electronic community for this kind of approach is increasing based on ourfinding that results can be obtained very rapidly and can be used in an interactive decision process.Decision makers are currently preparing to integrate this approach in CAD software dedicated toHLS like Gaut [1].2References[1] C. Chavet, C. Andriamisaina, P. Coussy, E. Casseau, E. Juin, P. Urard, and E. Martin. A designflow dedicated to multi-mode architectures for dsp applications. In International Conferenceon Computer Aided Design 2007 – ICCAD’07, San Jose, USA, November 2007.[2] D.D. Gajski, N.D. Dutt, A.C-H. Wu, and S.Y-L. Lin. High-level synthesis: introduction tochip and system design. Kluwer Academic Publishers, Norwell, MA, USA, 1992.[3] M. Sevaux, A. Singh, and A. Rossi. Tabu search for multiprocessor scheduling: application tohigh level synthesis. Asia-Pacific Journal of Operational Research, 2010. To appear.[4] M. Sevaux and K. So¨rensen. A tabu search method for high level synthesis. In Confe´renceconjointe Francoro V – Roadef 2007, pages 395–396, Grenoble, France, 20-23 February 2007.3

Tabu search for high level synthesis

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Tabu search for high level synthesis

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