###### Abstract  
While network path generation has been one of the representative Non-deterministic Polynomial-time (NP)-hard problems, changes of network topology invalidate the effectiveness of the existing metaheuristic algorithms. This research proposes a new and efficient path generation framework that considers dynamic topology changes in a complex network. In order to overcome this issue, Multi-directional and Parallel Ant Colony Optimization (MPACO) is proposed. Ant agents are divided into several groups and start at different positions in parallel. Then, Gaussian Process Regression (GPR)-based pheromone update method makes the algorithm more efficient. While the proposed MPACO algorithm is more efficient than the existing ACO algorithm, it is limited in a network with topological changes. In order to overcome the issue, the MPACO algorithm is modified to the Convolution MPACO (CMPACO) algorithm. The proposed algorithm uses the pheromone convolution method using a discrete Gaussian distribution. The proposed pheromone updating method enables the generation of a more efficient network path with comparatively less influence from topological network changes. In order to show the effectiveness of CMPACO, numerical networks considering static and dynamic conditions are tested and compared. The proposed CMPACO algorithm is considered a new and efficient parallel metaheuristic method to consider a complex network with topological changes.  
metaheuristics; Gaussian Process Regression (GPR); dynamic network topology; discrete pheromone convolution +
Footnote †: journal: Applied  
used an ACO algorithm to search parallel routes by introducing a parameter matrix design method, in order to produce fast escape routes from a maze. [PERSON] and [PERSON] [3] developed faster routes using the modification of the pheromone renewal rule, by minimizing the pheromone concentration in a blind spot, whenever an ant agent in the maze reached the blind spot. Moreover, [PERSON] and [PERSON] [4] generated a more efficient route using an exchange of messages among various ant agents. [PERSON] and [PERSON] [5] conducted a study to limit ant agents that suddenly behave in an unusual way, minimizing deviations in route production. Moreover, [PERSON] and [PERSON] [6] presented a study that aimed to limit the possibility of an ant agent being trapped in a dead end. [PERSON] and [PERSON] [7] minimized the escape time using the cooperation of multiple agents to avoid consequent congestion. In the studies mentioned above, all agents used a unidirectional direction-based strategy [1; 2; 3; 4; 5; 6] to produce routes from the start point to the terminal point, in the escape from a maze or large network. However, as the network becomes more complex, more time and computational loads are added to this strategy.  
In order to overcome this issue, this research study uses a new and efficient strategy, the \"Multi-directional and Parallel Ant Colony Optimization (MPACO)\" algorithm, to start agents at any number of points simultaneously, not simply from the start point to the terminal point. The MPACO algorithm supports parallel searches of agents, and uses a Gaussian Processes Regression (GPR)-based pheromone updating method. Specifically, the proposed algorithm generates evacuation routes faster than the previous algorithms in a dynamic network where the topology of the network is transformed due to several reasons, such as traffic congestion or construction.  
Section 2 of this research study examines the current ACO algorithms and relevant studies. Section 3 proposes the MPACO framework in a static environment. Section 4 proposes the Convolution-based Multi-directional and Parallel Ant Colony Algorithm (CMPACO) framework that is effective in a dynamic environment. Section 5 analyzes the effectiveness of the proposed framework with the experimental results of ACO, MPACO algorithm, and CMPACO algorithm.