Approach of Hybrid Ant Agents and Probabilistic Analysis for Combinatorial Optimization Problems

Dorigo提出的蚂蚁系统算法的思想非常独特。然而，标准类型的蚂蚁系统算法无法针对随机图获得更好的解。因此，我们利用基于集约化和多样化策略的信息素来设计新的智能体，例如应用禁忌搜索，以达到更好的解决方案。我们尝试将基于邻域的方法应用于蚂蚁系统算法，以提高解决方案的质量，因为蚂蚁系统算法不依赖于邻域。并且，通过上述新代理实现并行蚂蚁系统算法以减少计算时间。此外，我们还介绍了如何使用代理技术克服另一种元启发式并行算法所带来的困难。最后，我们讨论这些元启发式方法的特征，试图构建一个模型，为广泛的组合优化问题提供理论概率分析。我们认为该模型可以适应许多问题。在这里，我们引入 AR(1) 模型来数值近似各种邻域，并制定概率模型，计算局部搜索找到的解的成本的平均情况和所需的步骤数。我们使用这种概率分析来讨论元启发式的特征。

The idea of ant system algorithm proposed by Dorigo is very unique. However, the standard type of the ant system algorithm cannot obtain better solutions for random graphs. So, we design new agent by using pheromone based on intensification and diversification strategy, such as the tabu search is applied, in order to reach better solutions. We attempt to apply approach based on neighborhood to the ant system algorithm in terms of improving quality of solutions because the ant system algorithm does not depend on neighborhood. And, parallel ant system algorithm by above-mentioned new agents is implemented to reduce computational time. Furthermore, we present how the difficulty caused in parallel algorithm for another meta-heuristics has been overcome using agent technology. Finally we discuss the characteristics of these meta-heuristics attempting to construct a model which gives theoretical probabilistic analysis for wide class of combinatorial optimization problem. We consider that it is possible to adapt this model to many problems. Here, we introduce AR(1) model to numerically approximate various kinds of neighborhood, and formulate a probabilistic model, which compute the average-case of the costs of the solutions found by local search and the required number of steps. We discuss the characteristics of meta-heuristics using this probabilistic analysis.