Saeideh Shirinzadeh
Daniel Große
Rolf Drechsler
ABSTRACT
Approximate computing is an emerging methodology that allows to increase efficiency in a range of resilient applications for an affordable loss of precision or quality. In this paper, we exploit approximation in a multi-criteria optimization approach for the widely used data structure Binary Decision Diagram (BDD) to achieve higher efficiency besides lowering the inaccuracy. For this purpose, we utilize an ε-preferred evolutionary algorithm giving a higher priority to minimize BDD sizes as well as maintaining certain error constraints. In particular, we propose an adaptive ε-setting method which adds an automated factor to the algorithm based on the behavior of the function under approximation. This improves the performances of the algorithm by correcting the effect of the user set error constraints which can restrict the dimensions of the search and can lead to immature convergence.
In comparison with the non-optimized BDDs, the proposed algorithm achieves a high gain of 68.02% at a low cost of 2.12% inaccuracy for the whole benchmark set. The experimental results also reveal a considerable improvement of 25.19% in the average value of error rate besides reduction in BDD sizes compared to the manual ε-setting approach.
- Beate Bollig, Martin Löbbing, and Ingo Wegener. 1995. Simulated Annealing To Improve Variable Orderings For OBDDs. In International Workshop on Logic Synth.Google Scholar
- Beate Bollig and Ingo Wegener. 1996. Improving the Variable Ordering of OBDDs Is NP-Complete. IEEE Trans. Comput. 45, 9 (1996), 993--1002. Google ScholarDigital Library
- Franc Brglez, David Bryan, and Krzysztof Kozminski. 1989. Combinational Profiles of Sequential Benchmark Circuits. In International Symposium on Circuits and Systems. 1929--1934.Google Scholar
- Randal E. Bryant. 1995. Binary Decision Diagrams and Beyond: Enabling Technologies for Formal Verification. In International Conference on Computer-Aided Design. 236--243. Google ScholarDigital Library
- Vinay K. Chippa, Srimat T. Chakradhar, Kaushik Roy, and Anand Raghunathan. 2013. Analysis and Characterization of Inherent Application Resilience for Approximate Computing. In Design Automation Conference. 113:1--113:9. Google ScholarDigital Library
- Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, and T. Meyarivan. 2002. A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 2 (2002), 182--197. Google ScholarDigital Library
- Nicole Drechsler, Rolf Drechsler, and Bernd Becker. 2001. Multiobjective Optimisation Based on Relation Favour. In International Conference on Evolutionary Multi-Criterion Optimization, Vol. 1993. 154--166. Google ScholarDigital Library
- Nicole Drechsler, André Sülflow, and Rolf Drechsler. 2015. Incorporating User Preferences in Many-Objective Optimization Using Relation ε-Preferred. Natural Computing 14, 3 (2015), 469--483. Google ScholarDigital Library
- Rolf Drechsler, Bernd Becker, and Nicol Göckel. 1996. A Genetic Algorithm for Variable Ordering of OBDDs. In IEE Proceedings of Computers and Digital Techniques, Vol. 143(6). 364--368.Google ScholarCross Ref
- Rolf Drechsler and Detlef Sieling. 2001. Binary decision diagrams in theory and practice. Software Tools for Technology Transfer 3, 2 (2001), 112--136.Google ScholarCross Ref
- Rüdiger Ebendt, Görschwin Fey, and Rolf Drechsler. 2005. Advanced BDD Optimization. Springer.Google Scholar
- Rüdiger Ebendt, Wolfgang Günther, and Rolf Drechsler. 2003. An Improved Branch and Bound Algorithm for Exact BDD Minimization. IEEE Transactions on CAD of Integrated Circuits and Systems 22, 12 (2003), 1657--1663. Google ScholarDigital Library
- Görschwin Fey and Rolf Drechsler. 2006. Minimizing the Number of Paths in BDDs: Theory and Algorithm. IEEE Transactions on CAD of Integrated Circuits and Systems 25, 1 (2006), 4--11. Google ScholarDigital Library
- Jie Han and Michael Orshansky. 2013. Approximate Computing: An Emerging Paradigm for Energy-Efficient Design. In IEEE European Test Symposium. 1--6.Google Scholar
- Mario Hilgemeier, Nicole Drechsler, and Rolf Drechsler. 2003. Minimizing the Number of One-Paths in BDDs by an Evolutionary Algorithm. In IEEE Congress on Evolutionary Computation. 1724--1731.Google ScholarCross Ref
- Nagisa Ishiura, Hiroshi Sawada, and Shuzo Yajima. 1991. Minimazation of Binary Decision Diagrams Based on Exchanges of Variables. In International Conference on Computer-Aided Design. 472--475.Google Scholar
- Kavita Ravi and Fabio Somenzi. 1995. High-density Reachability Analysis. In International Conference on Computer-Aided Design. 154--158. Google ScholarDigital Library
- Richard Rudell. 1993. Dynamic Variable Ordering for Ordered Binary Decision Diagrams. In International Conference on Computer-Aided Design. 42--47. Google ScholarDigital Library
- Frank Schmiedle, Nicole Drechsler, and Rolf Drechsler. 2001. Priorities in Multi-Objective Optimization for Genetic Programming. In Genetic and Evolutionary Computation Conference. 129--136. Google ScholarDigital Library
- Doochul Shin and Sandeep K. Gupta. 2010. Approximate Logic Synthesis for Error Tolerant Applications. In Design, Automation and Test in Europe. 957--960. Google ScholarDigital Library
- Saeideh Shirinzadeh, Mathias Soeken, and Rolf Drechsler. 2015. Multi-Objective BDD Optimization with Evolutionary Algorithms. In Genetic and Evolutionary Computation Conference. 751--758. Google ScholarDigital Library
- Saeideh Shirinzadeh, Mathias Soeken, Daniel Große, and Rolf Drechsler. 2016. Approximate BDD Optimization with Prioritized ε-Preferred Evolutionary Algorithm. In Genetic and Evolutionary Computation Conference. 79--80. Google ScholarDigital Library
- Mathias Soeken, Daniel Große, Arun Chandrasekharan, and Rolf Drechsler. 2016. BDD Minimization for Approximate Computing. In Asia and South Pacific Design Automation Conference. 474--479.Google Scholar
- Fabio Somenzi. 2012. CUDD: CU Decision Diagram Package Release 2.5.0. University of Colorado at Boulder.Google Scholar
- André Sülflow, Nicole Drechsler, and Rolf Drechsler. 2007. Robust Multi-Objective Optimization in High Dimensional Spaces. In International Conference on Evolutionary Multi-Criterion Optimization. 715--726. Google ScholarDigital Library
- Swagath Venkataramani, Amit Sabne, Vivek J. Kozhikkottu, Kaushik Roy, and Anand Raghunathan. 2012. SALSA: Systematic Logic Synthesis of Approximate Circuits. In Design Automation Conference. 796--801. Google ScholarDigital Library
Index Terms
- An adaptive prioritized ε-preferred evolutionary algorithm for approximate BDD optimization
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