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Xin Yao
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Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2020) 28 (2): 227–253.
Published: 01 June 2020
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The quality of solution sets generated by decomposition-based evolutionary multi-objective optimisation (EMO) algorithms depends heavily on the consistency between a given problem's Pareto front shape and the specified weights' distribution. A set of weights distributed uniformly in a simplex often leads to a set of well-distributed solutions on a Pareto front with a simplex-like shape, but may fail on other Pareto front shapes. It is an open problem on how to specify a set of appropriate weights without the information of the problem's Pareto front beforehand. In this article, we propose an approach to adapt weights during the evolutionary process (called AdaW). AdaW progressively seeks a suitable distribution of weights for the given problem by elaborating several key parts in weight adaptation—weight generation, weight addition, weight deletion, and weight update frequency. Experimental results have shown the effectiveness of the proposed approach. AdaW works well for Pareto fronts with very different shapes: 1) the simplex-like, 2) the inverted simplex-like, 3) the highly nonlinear, 4) the disconnect, 5) the degenerate, 6) the scaled, and 7) the high-dimensional.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2019) 27 (2): 195–228.
Published: 01 June 2019
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Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains—random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2018) 26 (2): 237–267.
Published: 01 June 2018
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In real-world optimization tasks, the objective (i.e., fitness) function evaluation is often disturbed by noise due to a wide range of uncertainties. Evolutionary algorithms are often employed in noisy optimization, where reducing the negative effect of noise is a crucial issue. Sampling is a popular strategy for dealing with noise: to estimate the fitness of a solution, it evaluates the fitness multiple ( ) times independently and then uses the sample average to approximate the true fitness. Obviously, sampling can make the fitness estimation closer to the true value, but also increases the estimation cost. Previous studies mainly focused on empirical analysis and design of efficient sampling strategies, while the impact of sampling is unclear from a theoretical viewpoint. In this article, we show that sampling can speed up noisy evolutionary optimization exponentially via rigorous running time analysis. For the (1 1)-EA solving the OneMax and the LeadingOnes problems under prior (e.g., one-bit) or posterior (e.g., additive Gaussian) noise, we prove that, under a high noise level, the running time can be reduced from exponential to polynomial by sampling. The analysis also shows that a gap of one on the value of for sampling can lead to an exponential difference on the expected running time, cautioning for a careful selection of . We further prove by using two illustrative examples that sampling can be more effective for noise handling than parent populations and threshold selection, two strategies that have shown to be robust to noise. Finally, we also show that sampling can be ineffective when noise does not bring a negative impact.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2007) 15 (4): 435–443.
Published: 01 December 2007
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Various methods have been defined to measure the hardness of a fitness function for evolutionary algorithms and other black-box heuristics. Examples include fitness landscape analysis, epistasis, fitness-distance correlations etc., all of which are relatively easy to describe. However, they do not always correctly specify the hardness of the function. Some measures are easy to implement, others are more intuitive and hard to formalize. This paper rigorously defines difficulty measures in black-box optimization and proposes a classification. Different types of realizations of such measures are studied, namely exact and approximate ones. For both types of realizations, it is proven that predictive versions that run in polynomial time in general do not exist unless certain complexity-theoretical assumptions are wrong.