Abstract
A simple immune-based multi-objective optimizer (IBMO) is proposed, and a rigorous running time analysis of IBMO on three proposed bi-objective pseudo-Boolean functions (Bi-Trap, Bi-Plateau and Bi-Jump) is presented. The running time of a global simple evolutionary multi-objective optimizer (GSEMO) using standard bit mutation operator with IBMO using somatic contiguous hypermutation (CHM) operator is compared with these three functions. The results show that the immune-based hypermutation can significantly beat standard bit mutation on some well-known multi-objective pseudo-Boolean functions. The proofs allow us to understand the relationship between the characteristics of the problems and the features of the algorithms more deeply. These analysis results also give us a good inspiration to analyze and design a bio-inspired search heuristics.
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References
HANNE T. Global multiobjective optimization with evolutionary algorithms: Selection mechanisms and mutation control [C]//Evolutionary Multi-Criterion Optimization. Ouro Preto, Brazil: EMO, 2001: 197–212.
LAUMANNS M, THIELE L, ZITZLER E. Archiving with guaranteed convergence and diversity in multiobjective optimization [C]//Genetic and Evolutionary Computation Conference. New York, USA: Morgan Kaufmann Publishers, 2002: 439–447.
LAUMANNS M, THIELE L, ZITZLER E. Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions [J]. IEEE Transaction on Evolutionary Computation, 2004, 8(2): 170–182.
LAUMANNS M, THIELE L, ZITZLER E. Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem [J]. Natural Computing, 2004, 3(1): 37–51.
SCHARNOW J, TINNEFELD K, WEGENER I. Fitness landscapes based on sorting and shortest paths problems [C]//International Conference on Parallel Problem Solving from Nature. Berlin, Germany: Springer-Verlag, 2002: 54–63.
QIAN C, YU Y, ZHOU Z H. An analysis on recombination in multi-objective evolutionary optimization [J]. Artificial Intelligence, 2013, 204: 99–119.
PENG X, XIA X Y, LIAO W Z, et al. Running time analysis of the Pareto archived evolution strategy on pseudo-Boolean functions [J]. Multimedia Tools and Applications, 2018, 77(9): 11203–11217.
XIA X Y, PENG X, DENG L Y, et al. Performance analysis of evolutionary optimization for the bank account location problem [J]. IEEE Access, 2018, 6: 17756–17767.
KELSEY J, TIMMIS J. Immune inspired somatic contiguous hypermutations for function optimisation [C]//Genetic and Evolutionary Computation Conference. Chicago, IL, USA: Springer-Verlag, 2003: 207–218.
XIA X Y, ZHOU Y R. On the effectiveness of immune inspired mutation operators in some discrete optimization problems [J]. Information Sciences, 2018, 426: 87–100.
JANSEN T, ZARGES C. Analysis of randomised search heuristics for dynamic optimization [J]. Evolutionary Computation, 2015, 23(4): 513–541.
JANSEN T, ZARGES C. Computing longest common subsequences with the B-cell algorithm [C]//International Conference on Artificial Immune Systems. Taormina, Italy: Springer-Verlag, 2012: 111–124.
JANSEN T, ZARGES C. Re-evaluating immuneinspired hypermutations using the fixed budget perspective [J]. IEEE Transactions on Evolutionary Computation, 2014, 18(5): 674–688.
XIA X Y, ZHOU Y R. Performance analysis of immune inspired B-cell algorithm for the SAT problem [J]. Microelectronics and Computer, 2016, 33(7): 5–10 (in Chinese).
NEUMANN F. Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem [J]. European Journal of Operational Research, 2007, 181(3): 1620–1629.
NEUMANN F, WEGENER I. Minimum spanning trees made easier via multi-objective optimization [J]. Natural Computing, 2006, 5 (3): 305–319.
LAI X S, ZHOU Y R, HE J, et al. Performance analysis of evolutionary algorithms for the minimum label spanning tree problem [J]. IEEE Transactions on Evolutionary Computation, 2014, 18(6): 860–872.
FRIEDRICH T, HEBBINGHAUS N, NEUMANN F, et al. Approximating covering problems by randomized search heuristics using multi-objective models [C]//Genetic and Evolutionary Computation Conference. London, UK: ACM, 2007: 797–804.
JANSEN T, ZARGES, C. Analyzing different variants of immune inspired somatic contiguous hypermutations [J]. Theoretical Computer Science, 2011, 412(6): 517–533.
MITZENMACHER M, UPFAL E. Propability and computing: Randomized algorithms and probabilistic analysis [M]. Cambridge, UK: Cambridge University Press, 2005.
JANSEN T, WEGENER I. Evolutionary algorithms: How to cope with plateaus of constant fitness and when to reject strings of the same fitness [J]. IEEE Transactions on Evolutionary Computation, 2001, 5(6): 589–599.
DROSTE S, JANSEN T, WEGENER I. A rigorous complexity analysis of the (1+1) evolutionary algorithm for separable functions with Boolean inputs [J]. Evolutionary Computation, 1998, 6(2): 185–196.
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Foundation item: the National Natural Science Foundation of China (Nos. 61703183, 61773410, 61375053), and the Public Welfare Technology Research Plan of Zhejiang Province (No. LGG19F030010)
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Zhou, S., Peng, X., Wang, Y. et al. Rigorous Running Time Analysis of a Simple Immune-Based Multi-Objective Optimizer for Bi-Objective Pseudo-Boolean Functions. J. Shanghai Jiaotong Univ. (Sci.) 23, 827–833 (2018). https://doi.org/10.1007/s12204-018-2004-z
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DOI: https://doi.org/10.1007/s12204-018-2004-z