arXiv subjects

Weijie Zheng

Publications and source records attributed to Weijie Zheng.

23 records · Page 2Linked to original sources

arXiv2023

Theoretical Analyses of Evolutionary Algorithms on Time-Linkage OneMax with General Weights

Evolutionary computation has shown its superiority in dynamic optimization, but for the (dynamic) time-linkage problems, some theoretical studies have revealed the possible weakness of evolutionary computation. Since the theoretically analyzed time-linkage problem only considers the influence of an extremely strong negative time-linkage effect, it remains unclear whether the weakness also appears in problems with more general time-linkage effects. Besides, understanding in depth the relationship between time-linkage effect and algorithmic features is important to build up our knowledge of what algorithmic features are good at what kinds of problems. In this paper, we analyze the general time-linkage effect and consider the time-linkage OneMax with general weights whose absolute values reflect the strength and whose sign reflects the positive or negative influence. We prove that except for some small and positive time-linkage effects (that is, for weights $0$ and $1$), randomized local search (RLS) and (1+1)EA cannot converge to the global optimum with a positive probability. More precisely, for the negative time-linkage effect (for negative weights), both algorithms cannot efficiently reach the global optimum and the probability of failing to converge to the global optimum is at least $1-o(1)$. For the not so small positive time-linkage effect (positive weights greater than $1$), such a probability is at most $c+o(1)$ where $c$ is a constant strictly less than $1$.

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arXiv2021

From Understanding Genetic Drift to a Smart-Restart Parameter-less Compact Genetic Algorithm

One of the key difficulties in using estimation-of-distribution algorithms is choosing the population size(s) appropriately: Too small values lead to genetic drift, which can cause enormous difficulties. In the regime with no genetic drift, however, often the runtime is roughly proportional to the population size, which renders large population sizes inefficient. Based on a recent quantitative analysis which population sizes lead to genetic drift, we propose a parameter-less version of the compact genetic algorithm that automatically finds a suitable population size without spending too much time in situations unfavorable due to genetic drift. We prove a mathematical runtime guarantee for this algorithm and conduct an extensive experimental analysis on four classic benchmark problems both without and with additive centered Gaussian posterior noise. The former shows that under a natural assumption, our algorithm has a performance very similar to the one obtainable from the best problem-specific population size. The latter confirms that missing the right population size in the original cGA can be detrimental and that previous theory-based suggestions for the population size can be far away from the right values; it also shows that our algorithm as well as a previously proposed parameter-less variant of the cGA based on parallel runs avoid such pitfalls. Comparing the two parameter-less approaches, ours profits from its ability to abort runs which are likely to be stuck in a genetic drift situation.

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arXiv2021

When Non-Elitism Meets Time-Linkage Problems

Many real-world applications have the time-linkage property, and the only theoretical analysis is recently given by Zheng, et al. (TEVC 2021) on their proposed time-linkage OneMax problem, OneMax$_{(0,1^n)}$. However, only two elitist algorithms (1+1)EA and ($μ$+1)EA are analyzed, and it is unknown whether the non-elitism mechanism could help to escape the local optima existed in OneMax$_{(0,1^n)}$. In general, there are few theoretical results on the benefits of the non-elitism in evolutionary algorithms. In this work, we analyze on the influence of the non-elitism via comparing the performance of the elitist (1+$λ$)EA and its non-elitist counterpart (1,$λ$)EA. We prove that with probability $1-o(1)$ (1+$λ$)EA will get stuck in the local optima and cannot find the global optimum, but with probability $1$, (1,$λ$)EA can reach the global optimum and its expected runtime is $O(n^{3+c}\log n)$ with $λ=c \log_{\frac{e}{e-1}} n$ for the constant $c\ge 1$. Noting that a smaller offspring size is helpful for escaping from the local optima, we further resort to the compact genetic algorithm where only two individuals are sampled to update the probabilistic model, and prove its expected runtime of $O(n^3\log n)$. Our computational experiments also verify the efficiency of the two non-elitist algorithms.

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arXiv2021

Analysis of Evolutionary Algorithms on Fitness Function with Time-linkage Property

In real-world applications, many optimization problems have the time-linkage property, that is, the objective function value relies on the current solution as well as the historical solutions. Although the rigorous theoretical analysis on evolutionary algorithms has rapidly developed in recent two decades, it remains an open problem to theoretically understand the behaviors of evolutionary algorithms on time-linkage problems. This paper takes the first step to rigorously analyze evolutionary algorithms for time-linkage functions. Based on the basic OneMax function, we propose a time-linkage function where the first bit value of the last time step is integrated but has a different preference from the current first bit. We prove that with probability $1-o(1)$, randomized local search and $(1+1)$ EA cannot find the optimum, and with probability $1-o(1)$, $(μ+1)$ EA is able to reach the optimum.

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arXiv2018

Working Principles of Binary Differential Evolution

We conduct a first fundamental analysis of the working principles of binary differential evolution (BDE), an optimization heuristic for binary decision variables that was derived by Gong and Tuson (2007) from the very successful classic differential evolution (DE) for continuous optimization. We show that unlike most other optimization paradigms, it is stable in the sense that neutral bit values are sampled with probability close to $1/2$ for a long time. This is generally a desirable property, however, it makes it harder to find the optima for decision variables with small influence on the objective function. This can result in an optimization time exponential in the dimension when optimizing simple symmetric functions like OneMax. On the positive side, BDE quickly detects and optimizes the most important decision variables. For example, dominant bits converge to the optimal value in time logarithmic in the population size. This enables BDE to optimize the most important bits very fast. Overall, our results indicate that BDE is an interesting optimization paradigm having characteristics significantly different from classic evolutionary algorithms or estimation-of-distribution algorithms (EDAs). On the technical side, we observe that the strong stochastic dependencies in the random experiment describing a run of BDE prevent us from proving all desired results with the mathematical rigor that was successfully used in the analysis of other evolutionary algorithms. Inspired by mean-field approaches in statistical physics we propose a more independent variant of BDE, show experimentally its similarity to BDE, and prove some statements rigorously only for the independent variant. Such a semi-rigorous approach might be interesting for other problems in evolutionary computation where purely mathematical methods failed so far.

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