TY - JOUR
T1 - Extension of Stochastic Point Location for Multimodal Problems
AU - Zhang, Junqi
AU - Qiu, Pengzhan
AU - Zhou, Mengchu
N1 - Funding Information:
This work was supported in part by the Innovation Program of Shanghai Municipal Education Commission under Grant 202101070007E00098; in part by the National Natural Science Foundation of China under Grant 51775385, Grant 61703279, Grant 62073244, and Grant 61876218; in part by the Shanghai Innovation Action Plan under Grant 20511100500; and in part by Fundo para o Desenvolvimento das Ciencias e da Tecnologia under Grant 0047/2021/A1.
Publisher Copyright:
© 2013 IEEE.
PY - 2023/9/1
Y1 - 2023/9/1
N2 - Stochastic point location (SPL) involves a learning mechanism (LM) determining an optimal point on the line when the only inputs LM receives are stochastic information about the direction in which LM should move. The complexity of SPL comes from the stochastic responses of the environment, which may lead LM completely astray. SPL is a fundamental problem in optimization and was studied by many researchers during the last two decades, including improvement of its solution and all-pervasive applications. However, all existing SPL studies assume that the whole search space contains only one optimal point. Since a multimodal optimization problem (MMOP) contains multiple optimal solutions, it is significant to develop SPL's multimodal version. This article extends it from a unimodal problem to a multimodal one and proposes a parallel partition search (PPS) solution to address this issue. The heart of the proposed solution involves extracting the feature of the historical sampling information to distinguish the subintervals that contain the optimal points or not. Specifically, it divides the whole search space into multiple subintervals and samples them parallelly, then utilizes the feature of the historical sampling information to adjust the subintervals adaptively and to find the subintervals containing the optimal points. Finally, the optimal points are located within these subintervals according to their respective sampling statistics. The proof of the ϵ-optimal property for the proposed solution is presented. The numerical testing results demonstrate the power of the scheme.
AB - Stochastic point location (SPL) involves a learning mechanism (LM) determining an optimal point on the line when the only inputs LM receives are stochastic information about the direction in which LM should move. The complexity of SPL comes from the stochastic responses of the environment, which may lead LM completely astray. SPL is a fundamental problem in optimization and was studied by many researchers during the last two decades, including improvement of its solution and all-pervasive applications. However, all existing SPL studies assume that the whole search space contains only one optimal point. Since a multimodal optimization problem (MMOP) contains multiple optimal solutions, it is significant to develop SPL's multimodal version. This article extends it from a unimodal problem to a multimodal one and proposes a parallel partition search (PPS) solution to address this issue. The heart of the proposed solution involves extracting the feature of the historical sampling information to distinguish the subintervals that contain the optimal points or not. Specifically, it divides the whole search space into multiple subintervals and samples them parallelly, then utilizes the feature of the historical sampling information to adjust the subintervals adaptively and to find the subintervals containing the optimal points. Finally, the optimal points are located within these subintervals according to their respective sampling statistics. The proof of the ϵ-optimal property for the proposed solution is presented. The numerical testing results demonstrate the power of the scheme.
KW - Learning mechanism (LM)
KW - machine learning
KW - multimodal optimization problems (MMOPs)
KW - stochastic point location (SPL)
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U2 - 10.1109/TCYB.2021.3119591
DO - 10.1109/TCYB.2021.3119591
M3 - Article
C2 - 35139033
AN - SCOPUS:85124751013
SN - 2168-2267
VL - 53
SP - 5403
EP - 5413
JO - IEEE Transactions on Cybernetics
JF - IEEE Transactions on Cybernetics
IS - 9
ER -