Artificial Immune Systems can Beat Evolutionary Algorithms in Combinatorial Optimisation

Artificial immune systems (AIS) are randomised search heuristics that can be applied to any kind of optimisation problem just like evolutionary algorithms (EAs). Unlike EAs their inception stems from a different natural paradigm: the immune system of vertebrates instead of natural evolution. While AIS proved to be highly efficient in several application areas, so far for no classic optimisation problem it could be rigorously proven that AIS outperform EAs. We consider the B-Cell Algorithm (BCA) as an example of an artificial immune system and compare its performance with that of the (1+1) EA on a classic combinatorial op- timisation problem, interval scheduling. We show that for the natural binary encoding both heuristics are not able to efficiently find an optimal solution for all instances. The (1+1) EA has exponential expected optimisation time and the BCA may never find an optimal solution. However, we also show that a natural preprocessing changes the situation dramatically. If we remove beforehand all intervals strictly containing another one, then the BCA always finds an optimal solution in polynomial expected optimisation time. The (1+1) EA remains inefficient in the worst case, still having exponential expected optimisation time. It can, however, find a 2-approximation of an optimal solution very quickly.

[1]  Pietro Simone Oliveto,et al.  On the runtime analysis of stochastic ageing mechanisms , 2014, GECCO.

[2]  Thomas Jansen,et al.  Analysis of Randomised Search Heuristics for Dynamic Optimisation , 2015, Evolutionary Computation.

[3]  Thomas Jansen,et al.  On the Analysis of the Immune-Inspired B-Cell Algorithm for the Vertex Cover Problem , 2011, ICARIS.

[4]  Andrew M. Sutton.  Superpolynomial Lower Bounds for the $$(1+1)$$(1+1) EA on Some Easy Combinatorial Problems , 2015, Algorithmica.

[5]  Ingo Wegener,et al.  Evolutionary Algorithms and the Maximum Matching Problem , 2003, STACS.

[6]  Jonathan Timmis,et al.  Immune Inspired Somatic Contiguous Hypermutation for Function Optimisation , 2003, GECCO.

[7]  Thomas Jansen,et al.  On the role of age diversity for effective aging operators , 2011, Evol. Intell..

[8]  Jonathan Timmis,et al.  A Markov Chain Model of the B-Cell Algorithm , 2005, ICARIS.

[9]  Thomas Jansen,et al.  Reevaluating Immune-Inspired Hypermutations Using the Fixed Budget Perspective , 2014, IEEE Transactions on Evolutionary Computation.

[10]  Thomas Jansen,et al.  Understanding randomised search heuristics lessons from the evolution of theory: A case study , 2014 .

[11]  Thomas Jansen,et al.  Analyzing Evolutionary Algorithms , 2015, Natural Computing Series.

[12]  Thomas Jansen,et al.  Analyzing Evolutionary Algorithms: The Computer Science Perspective , 2012 .

[13]  Jonathan Timmis,et al.  Artificial Immune Systems: A New Computational Intelligence Approach , 2003 .

[14]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[15]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[16]  Éva Tardos,et al.  Algorithm design , 2005 .

[17]  Fernando José Von Zuben,et al.  Learning and optimization using the clonal selection principle , 2002, IEEE Trans. Evol. Comput..

[18]  Thomas Jansen,et al.  On benefits and drawbacks of aging strategies for randomized search heuristics , 2011, Theor. Comput. Sci..

[19]  Thomas Jansen,et al.  On Easiest Functions for Somatic Contiguous Hypermutations And Standard Bit Mutations , 2015, GECCO.

[20]  Christine Zarges,et al.  On the utility of the population size for inversely fitness proportional mutation rates , 2009, FOGA '09.

[21]  Thomas Jansen,et al.  Variation in Artificial Immune Systems: Hypermutations with Mutation Potential , 2011, ICARIS.

[22]  Thomas Jansen,et al.  Maximal age in randomized search heuristics with aging , 2009, GECCO.

[23]  Thomas Jansen,et al.  Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods Evolutionary Algorithms-How to Cope With Plateaus of Constant Fitness and When to Reject Strings of the Same Fitness , 2001 .

[24]  Christine Zarges,et al.  Rigorous Runtime Analysis of Inversely Fitness Proportional Mutation Rates , 2008, PPSN.

[25]  Vincenzo Cutello,et al.  Exploring the Capability of Immune Algorithms: A Characterization of Hypermutation Operators , 2004, ICARIS.

[26]  Thomas Jansen,et al.  Analyzing different variants of immune inspired somatic contiguous hypermutations , 2011, Theor. Comput. Sci..

[27]  Thomas Jansen,et al.  Computing Longest Common Subsequences with the B-Cell Algorithm , 2012, ICARIS.

[28]  Carsten Witt,et al.  Tight Bounds on the Optimization Time of a Randomized Search Heuristic on Linear Functions† , 2013, Combinatorics, Probability and Computing.

[29]  Pietro Simone Oliveto,et al.  On the Convergence of Immune Algorithms , 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.