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Chao Bian

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12 papers

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AIJ Journal 2025 Journal Article

Stochastic population update can provably be helpful in multi-objective evolutionary algorithms

Chao Bian
Yawen Zhou
Miqing Li
Chao Qian

Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update, a key component in multi-objective EAs (MOEAs), is usually performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the best solutions from the current population and newly-generated solutions (irrespective of the selection criteria used such as Pareto dominance, crowdedness and indicators). In this paper, we analytically present that stochastic population update can be beneficial for the search of MOEAs. Specifically, we prove that the expected running time of two well-established MOEAs, SMS-EMOA and NSGA-II, for solving two bi-objective problems, OneJumpZeroJump and bi-objective RealRoyalRoad, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed population update method. This work is an attempt to show the benefit of introducing randomness into the population update of MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.

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IJCAI Conference 2024 Conference Paper

An Archive Can Bring Provable Speed-ups in Multi-Objective Evolutionary Algorithms

Chao Bian
Shengjie Ren
Miqing Li
Chao Qian

In the area of multi-objective evolutionary algorithms (MOEAs), there is a trend of using an archive to store non-dominated solutions generated during the search. This is because 1) MOEAs may easily end up with the final population containing inferior solutions that are dominated by other solutions discarded during the search process and 2) the population that has a commensurable size of the problem's Pareto front is often not practical. In this paper, we theoretically show, for the first time, that using an archive can guarantee speed-ups for MOEAs. Specifically, we prove that for two well-established MOEAs (NSGA-II and SMS-EMOA) on two commonly studied problems (OneMinMax and LeadingOnesTrailingZeroes), using an archive brings a polynomial acceleration on the expected running time. The reason is that with an archive, the size of the population can reduce to a small constant; there is no need for the population to keep all the Pareto optimal solutions found. This contrasts existing theoretical studies for MOEAs where a population with a commensurable size of the problem's Pareto front is needed. The findings in this paper not only provide a theoretical confirmation for an increasingly popular practice in the design of MOEAs, but can also be beneficial to the theory community towards studying more practical MOEAs.

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IJCAI Conference 2024 Conference Paper

Maintaining Diversity Provably Helps in Evolutionary Multimodal Optimization

Shengjie Ren
Zhijia Qiu
Chao Bian
Miqing Li
Chao Qian

In the real world, there exist a class of optimization problems that multiple (local) optimal solutions in the solution space correspond to a single point in the objective space. In this paper, we theoretically show that for such multimodal problems, a simple method that considers the diversity of solutions in the solution space can benefit the search in evolutionary algorithms (EAs). Specifically, we prove that the proposed method, working with crossover, can help enhance the exploration, leading to polynomial or even exponential acceleration on the expected running time. This result is derived by rigorous running time analysis in both single-objective and multi-objective scenarios, including (mu+1)-GA solving the widely studied single-objective problem, Jump, and NSGA-II and SMS-EMOA (two well-established multi-objective EAs) solving the widely studied bi-objective problem, OneJumpZeroJump. Experiments are also conducted to validate the theoretical results. We hope that our results may encourage the exploration of diversity maintenance in the solution space for multi-objective optimization, where existing EAs usually only consider the diversity in the objective space and can easily be trapped in local optima.

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AAAI Conference 2024 Conference Paper

Towards Running Time Analysis of Interactive Multi-Objective Evolutionary Algorithms

Tianhao Lu
Chao Bian
Chao Qian

Evolutionary algorithms (EAs) are widely used for multi-objective optimization due to their population-based nature. Traditional multi-objective EAs (MOEAs) generate a large set of solutions to approximate the Pareto front, leaving a decision maker (DM) with the task of selecting a preferred solution. However, this process can be inefficient and time-consuming, especially when there are many objectives or the DM has subjective preferences. To address this issue, interactive MOEAs (iMOEAs) combine decision making into the optimization process, i.e., update the population with the help of the DM. In contrast to their wide applications, there has existed only two pieces of theoretical works on iMOEAs, which only considered interactive variants of the two simple single-objective algorithms, RLS and (1+1)-EA. This paper provides the first running time analysis (the essential theoretical aspect of EAs) for practical iMOEAs. Specifically, we prove that the expected running time of the well-developed interactive NSGA-II (called R-NSGA-II) for solving the OneMinMax, OneJumpZeroJump problems are all asymptotically faster than the traditional NSGA-II. Meanwhile, we present a variant of OneMinMax, and prove that R-NSGA-II can be exponentially slower than NSGA-II. These results provide theoretical justification for the effectiveness of iMOEAs while identifying situations where they may fail. Experiments are also conducted to validate the theoretical results.

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IJCAI Conference 2023 Conference Paper

Stochastic Population Update Can Provably Be Helpful in Multi-Objective Evolutionary Algorithms

Chao Bian
Yawen Zhou
Miqing Li
Chao Qian

Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update is a key component in multi-objective EAs (MOEAs), and it is performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the first population-size ranked solutions (based on some selection criteria, e. g. , non-dominated sorting, crowdedness and indicators) from the collections of the current population and newly-generated solutions. In this paper, we question this practice. We analytically present that introducing randomness into the population update procedure in MOEAs can be beneficial for the search. More specifically, we prove that the expected running time of a well-established MOEA (SMS-EMOA) for solving a commonly studied bi-objective problem, OneJumpZeroJump, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed stochastic population update method. This work is an attempt to challenge a common practice for the population update in MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.

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AAAI Conference 2023 Conference Paper

Submodular Maximization under the Intersection of Matroid and Knapsack Constraints

Yu-Ran Gu
Chao Bian
Chao Qian

Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of constraint, while many real-world problems often involve several constraints. In this paper, we consider the problem of submodular maximization under the intersection of two commonly used constraints, i.e., k-matroid constraint and m-knapsack constraint, and propose a new algorithm SPROUT by incorporating partial enumeration into the simultaneous greedy framework. We prove that SPROUT can achieve a polynomial-time approximation guarantee better than the state-of-the-art algorithms. Then, we introduce the random enumeration and smooth techniques into SPROUT to improve its efficiency, resulting in the SPROUT++ algorithm, which can keep a similar approximation guarantee. Experiments on the applications of movie recommendation and weighted max-cut demonstrate the superiority of SPROUT++ in practice.

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IJCAI Conference 2022 Conference Paper

Robust Subset Selection by Greedy and Evolutionary Pareto Optimization

Chao Bian
Yawen Zhou
Chao Qian

Subset selection, which aims to select a subset from a ground set to maximize some objective function, arises in various applications such as influence maximization and sensor placement. In real-world scenarios, however, one often needs to find a subset which is robust against (i. e. , is good over) a number of possible objective functions due to uncertainty, resulting in the problem of robust subset selection. This paper considers robust subset selection with monotone objective functions, relaxing the submodular property required by previous studies. We first show that the greedy algorithm can obtain an approximation ratio with respect to the correlation and submodularity ratios of the objective functions; and then propose EPORSS, an evolutionary Pareto optimization algorithm that can utilize more time to find better subsets. We prove that EPORSS can also be theoretically grounded, achieving a similar approximation guarantee to the greedy algorithm. In addition, we derive the lower bound of the correlation ratio for the application of robust influence maximization, and further conduct experiments to validate the performance of the greedy algorithm and EPORSS.

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IJCAI Conference 2021 Conference Paper

Fast Pareto Optimization for Subset Selection with Dynamic Cost Constraints

Chao Bian
Chao Qian
Frank Neumann
Yang Yu

Subset selection with cost constraints is a fundamental problem with various applications such as influence maximization and sensor placement. The goal is to select a subset from a ground set to maximize a monotone objective function such that a monotone cost function is upper bounded by a budget. Previous algorithms with bounded approximation guarantees include the generalized greedy algorithm, POMC and EAMC, all of which can achieve the best known approximation guarantee. In real-world scenarios, the resources often vary, i. e. , the budget often changes over time, requiring the algorithms to adapt the solutions quickly. However, when the budget changes dynamically, all these three algorithms either achieve arbitrarily bad approximation guarantees, or require a long running time. In this paper, we propose a new algorithm FPOMC by combining the merits of the generalized greedy algorithm and POMC. That is, FPOMC introduces a greedy selection strategy into POMC. We prove that FPOMC can maintain the best known approximation guarantee efficiently.

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AAAI Conference 2020 Conference Paper

An Efficient Evolutionary Algorithm for Subset Selection with General Cost Constraints

Chao Bian
Chao Feng
Chao Qian
Yang Yu

In this paper, we study the problem of selecting a subset from a ground set to maximize a monotone objective function f such that a monotone cost function c is bounded by an upper limit. State-of-the-art algorithms include the generalized greedy algorithm and POMC. The former is an efﬁcient ﬁxed time algorithm, but the performance is limited by the greedy nature. The latter is an anytime algorithm that can ﬁnd better subsets using more time, but without any polynomial-time approximation guarantee. In this paper, we propose a new anytime algorithm EAMC, which employs a simple evolutionary algorithm to optimize a surrogate objective integrating f and c. We prove that EAMC achieves the best known approximation guarantee in polynomial expected running time. Experimental results on the applications of maximum coverage, inﬂuence maximization and sensor placement show the excellent performance of EAMC.

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TCS Journal 2020 Journal Article

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

Chao Bian
Chao Qian
Ke Tang
Yang Yu

Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization, while another common type of uncertain optimization, i. e. , robust optimization, has been rarely touched. In this paper, we analyze the expected running time of the (1+1)-EA solving robust linear optimization problems (i. e. , linear problems under robust scenarios) with a cardinality constraint k. Two common robust scenarios, i. e. , deletion-robust and worst-case, are considered. Particularly, we derive tight ranges of the robust parameter d or budget k allowing the (1+1)-EA to find an optimal solution in polynomial running time, which disclose the potential of EAs for robust optimization.

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AAAI Conference 2020 Conference Paper

Subset Selection by Pareto Optimization with Recombination

Chao Qian
Chao Bian
Chao Feng

Subset selection, i. e. , to select a limited number of items optimizing some given objective function, is a fundamental problem with various applications such as unsupervised feature selection and sparse regression. By employing a multi-objective evolutionary algorithm (EA) with mutation only to optimize the given objective function and minimize the number of selected items simultaneously, the recently proposed POSS algorithm achieves state-of-the-art performance for subset selection. In this paper, we propose the PORSS algorithm by incorporating recombination, a characterizing feature of EAs, into POSS. We prove that PORSS can achieve the optimal polynomial-time approximation guarantee as POSS when the objective function is monotone, and can ﬁnd an optimal solution efﬁciently in some cases whereas POSS cannot. Extensive experiments on unsupervised feature selection and sparse regression show the superiority of PORSS over POSS. Our analysis also theoretically discloses that recombination from diverse solutions can be more likely than mutation alone to generate various variations, thereby leading to better exploration; this may be of independent interest for understanding the inﬂuence of recombination.

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IJCAI Conference 2018 Conference Paper

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

Chao Bian
Chao Qian
Ke Tang

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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