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Multi Agents-Multi Tasks Assignment Problem using Hybrid Cross-Entropy Algorithm

혼합 교차-엔트로피 알고리즘을 활용한 다수 에이전트-다수 작업 할당 문제

  • 김광 (조선대학교 경영학부)
  • Received : 2022.06.23
  • Accepted : 2022.07.21
  • Published : 2022.08.30

Abstract

In this paper, a multi agent-multi task assignment problem, which is a representative problem of combinatorial optimization, is presented. The objective of the problem is to determine the coordinated agent-task assignment that maximizes the sum of the achievement rates of each task. The achievement rate is represented as a concave down increasing function according to the number of agents assigned to the task. The problem is expressed as an NP-hard problem with a non-linear objective function. In this paper, to solve the assignment problem, we propose a hybrid cross-entropy algorithm as an effective and efficient solution methodology. In fact, the general cross-entropy algorithm might have drawbacks (e.g., slow update of parameters and premature convergence) according to problem situations. Compared to the general cross-entropy algorithm, the proposed method is designed to be less likely to have the two drawbacks. We show that the performances of the proposed methods are better than those of the general cross-entropy algorithm through numerical experiments.

본 논문에서는 대표적인 조합 최적화(combinatorial optimization) 문제인 다수 에이전트-다수 작업 할당 문제를 제시한다. 할당 문제의 목적은 각 작업의 달성률(achievement rate)의 합을 최대로 하는 에이전트-작업 할당을 결정하는 것이다. 달성률은 각 작업의 할당된 에이전트의 수에 따라 아래 오목 증가(concave down increasing)형태로 다루어지며, 본 할당 문제는 비선형(non-linearity)의 목적함수를 갖는 NP-난해(NP-hard) 문제로 표현된다. 본 논문에서는 할당 문제를 해결하기 위한 효과적이면서 효율적인 문제 해결 방법론으로 혼합 교차-엔트로피 알고리즘(hybrid cross-entropy algorithm)을 제안한다. 일반적인 교차-엔트로피 알고리즘은 문제 상황에 따라 느린 매개변수 업데이트 속도와 조기수렴(premature convergence)이 발생할 수 있다. 본 연구에서 제안하는 문제 해결 방법론은 이러한 단점의 발생 확률을 낮추도록 설계되었으며, 실험적으로도 우수한 성능을 보이는 알고리즘임을 수치실험을 통해 제시한다.

Keywords

References

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