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A class of iterative refined Max-sum algorithms via non-consecutive value propagation strategies

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Abstract

As an important technique to solve distributed constraint optimization problems, Max-sum has drawn a lot of attention and successfully been deployed in real applications. Unfortunately, Max-sum fails to converge in cyclic problems and usually traverses states with low quality. Max-sum_AD and Max-sum_ADVP were proposed to guarantee the single phase convergence and the cross phase convergence respectively, and greatly improve the solution quality of Max-sum. However, the solution quality is closely related to the timing for starting value propagation in Max-sum_ADVP. In other words, low-quality initial assignments will lead to a poor result. In this paper, we prove that value propagation could restrict the exploration ability brought by Max-sum and eventually makes Max-sum_ADVP equivalent to a sequential greedy local search algorithm. For getting a balance between exploration and exploitation, several non-consecutive value propagation strategies are proposed to relax the restriction caused by value propagation: single-side value propagation which executes value propagation and Max-sum_AD in an interleaved way, probabilistic value propagation which performs value propagation stochastically and hybrid belief/value propagation where agents perform Max-sum_AD and value propagation in one round. We illustrate that agents in our algorithms can make decisions beyond local functions. Our empirical evaluations demonstrate the superiority of our methods over Max-sum and its variants. It also can be found that our methods are independent of the value propagation timing which is a major concern in Max-sum_ADVP.

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Notes

  1. We describe Max-sum as a minimization version to cope with the objective of DCOPs.

  2. For sake of clarity and simplicity, we only show stable and unchanging outgoing messages here. In fact, nodes in Max-sum_AD perform concurrently and each node sends messages to its downstream neighbors every iteration. Besides, we also ignore the normalization to messages to make the trace more clear.

  3. In fact, Standard Max-sum without personal preferences cannot solve graph-coloring problem for the same reason.

  4. Since Lemma 1 has demonstrated that the global beliefs have no influence on the algorithm after enabling value propagation, we hereafter drop the global beliefs in response messages and only present exactly local functions in value propagation phases.

  5. We notice that in the method value propagation is no longer always performed in a direction, and thus the name is somewhat misleading. However, since the paper is an extension to our AAMAS paper [3], we inherit the naming convention from [3].

  6. https://github.com/czy920/DCOPSovler

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  1. College of Computer Science, Chongqing University, Chongqing, 400044, China

    Ziyu Chen, Yanchen Deng, Tengfei Wu & Zhongshi He

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  1. Ziyu Chen
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  2. Yanchen Deng
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  3. Tengfei Wu
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  4. Zhongshi He
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Correspondence to Ziyu Chen or Yanchen Deng.

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The paper is an extension to our AAMAS paper [3]. Beside execution examples and an extension to Max-sum_ADSSVP, we also present three algorithms that can substantially suppress the cost fluctuation.

This research is funded by Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2017jcyjAX0030), Fundamental Research Funds for the Central Universities (No. 2018CDXYJSJ0026) and Graduate Research and Innovation Foundation of Chongqing, China (Grant No. CYS18047).

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Chen, Z., Deng, Y., Wu, T. et al. A class of iterative refined Max-sum algorithms via non-consecutive value propagation strategies. Auton Agent Multi-Agent Syst 32, 822–860 (2018). https://doi.org/10.1007/s10458-018-9395-y

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