Running time analysis of the (1+1)-EA for robust linear optimization

Running-time analysis of ant colony optimization (ACO) is crucial for understanding the power of the algorithm in computation. This paper conducts a running-time analysis of ant system algorithms (AS) as a kind of ACO for traveling salesman problems (TSP). The authors model the AS algorithm as an absorbing Markov chain through jointly representing the best-so-far solutions and pheromone matrix as a discrete stochastic status per iteration. The running-time of AS can be evaluated by the expected first-hitting time (FHT), the least number of iterations needed to attain the global optimal solution on average. The authors derive upper bounds of the expected FHT of two classical AS algorithms (i.e., ant quantity system and ant-cycle system) for TSP. They further take regular-polygon TSP (RTSP) as a case study and obtain numerical results by calculating six RTSP instances. The RTSP is a special but real-world TSP where the constraint of triangle inequality is stringently imposed. The numerical results derived from the comparison of the running time of the two AS algorithms verify our theoretical findings.

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Running Time Analysis of the ( $$1+1$$ 1 + 1 )-EA for OneMax and LeadingOnes Under Bit-Wise Noise

Algorithmica ◽

10.1007/s00453-018-0488-4 ◽

2018 ◽

Vol 81 (2) ◽

pp. 749-795 ◽

Cited By ~ 9

Author(s):

Chao Qian ◽

Chao Bian ◽

Wu Jiang ◽

Ke Tang

Keyword(s):

Time Analysis ◽

Running Time ◽

Running Time Analysis

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Average running time analysis of an algorithm to calculate the size of the union of Cartesian products

Discrete Mathematics ◽

10.1016/s0012-365x(03)00239-5 ◽

2003 ◽

Vol 273 (1-3) ◽

pp. 211-220

Author(s):

Susumu Suzuki ◽

Toshihide Ibaraki

Keyword(s):

Time Analysis ◽

Cartesian Products ◽

Running Time ◽

Running Time Analysis ◽

Average Running Time

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A General Approach to Running Time Analysis of Multi-objective Evolutionary Algorithms

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/195 ◽

2018 ◽

Cited By ~ 3

Author(s):

Chao Bian ◽

Chao Qian ◽

Ke Tang

Keyword(s):

Evolutionary Algorithms ◽

Optimization Problems ◽

Theoretical Aspect ◽

Combinatorial Problems ◽

Time Analysis ◽

Running Time ◽

Asymptotic Bounds ◽

Multi Objective ◽

Running Time Analysis ◽

Empirical Performance

Evolutionary algorithms (EAs) have been widely applied to solve multi-objective optimization problems. In contrast to great practical successes, their theoretical foundations are much less developed, even for the essential theoretical aspect, i.e., running time analysis. In this paper, we propose a general approach to estimating upper bounds on the expected running time of multi-objective EAs (MOEAs), and then apply it to diverse situations, including bi-objective and many-objective optimization as well as exact and approximate analysis. For some known asymptotic bounds, our analysis not only provides their leading constants, but also improves them asymptotically. Moreover, our results provide some theoretical justification for the good empirical performance of MOEAs in solving multi-objective combinatorial problems.

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Partial Quicksort and Quickpartitionsort

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.2781 ◽

2010 ◽

Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽

Author(s):

Conrado Martínez ◽

Uwe Rösler

Keyword(s):

Lower Bound ◽

Time Analysis ◽

Information Theoretic ◽

Running Time ◽

Running Time Analysis ◽

International Audience

International audience Partial Quicksort sorts the $l$ smallest elements in a list of length $n$. We provide a complete running time analysis for this combination of Find and Quicksort. Further we give some optimal adapted versions, called Partition Quicksort, with an asymptotic running time $c_1l\ln l+c_2l+n+o(n)$. The constant $c_1$ can be as small as the information theoretic lower bound $\log_2 e$.

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