Mingxin Liang

Solving NP-Hard Problems with Physarum -Based Ant Colony System

NP-hard problems exist in many real world applications. Ant colony optimization (ACO) algorithms can provide approximate solutions for those NP-hard problems, but the performance of ACO algorithms is significantly reduced due to premature convergence and weak robustness, etc. With these observations in mind, this paper proposes a Physarum-based pheromone matrix optimization strategy in ant colony system (ACS) for solving NP-hard problems such as traveling salesman problem (TSP) and 0/1 knapsack problem (0/1 KP). In the Physarum-inspired mathematical model, one of the unique characteristics is that critical tubes can be reserved in the process of network evolution. The optimized updating strategy employs the unique feature and accelerates the positive feedback process in ACS, which contributes to the quick convergence of the optimal solution. Some experiments were conducted using both benchmark and real datasets. The experimental results show that the optimized ACS outperforms other meta-heuristic algorithms in accuracy and robustness for solving TSPs. Meanwhile, the convergence rate and robustness for solving 0/1 KPs are better than those of classical ACS.

Multi-objective ant colony optimization based on the Physarum-Inspired mathematical model for bi-objective traveling salesman problems

Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs.

A new multi-agent system to simulate the foraging behaviors of Physarum

Physarum Polycephalum is a unicellular and multi-headed slime mold, which can form high efficient networks connecting spatially separated food sources in the process of foraging. Such adaptive networks exhibit a unique characteristic in which network length and fault tolerance are appropriately balanced. Based on the biological observations, the foraging process of Physarum demonstrates two self-organized behaviors, i.e., search and contraction. In this paper, these two behaviors are captured in a multi-agent system. Two types of agents and three transition rules are designed to imitate the search and the contraction behaviors of Physarum based on the necessary and the sufficient conditions of a self-organized computational system. Some simulations of foraging process are used to investigate the characteristics of our system. Experimental results show that our system can autonomously search for food sources and then converge to a stable solution, which replicates the foraging process of Physarum. Specially, a case study of maze problem is used to estimate the path-finding ability of the foraging behaviors of Physarum. What’s more, the model inspired by the foraging behaviors of Physarum is proposed to optimize meta-heuristic algorithms for solving optimization problems. Through comparing the optimized algorithms and the corresponding traditional algorithms, we have found that the optimization strategies have a higher computational performance than their corresponding traditional algorithms, which further justifies that the foraging behaviors of Physarum have a higher computational ability.

A new genetic algorithm based on modified Physarum network model for bandwidth-delay constrained least-cost multicast routing

A mobile ad hoc network is a kind of popular self-configuring network, in which multicast routing under the quality of service constraints, is a significant challenge. Many researchers have proved that such problem can be formulated as a NP-complete problem and proposed some swarm-based intelligent algorithms to solve the optimal solution, such as the genetic algorithm (GA), bees algorithm. However, a lower efficiency of local search ability and weak robustness still limit the computational effectiveness. Aiming to those shortcomings, a new hybrid algorithm inspired by the self-organization of Physarum, is proposed in this paper. In our algorithm, an updating scheme based on Physarum network model (PM) is used for improving the crossover operator of traditional GAs, in which the same parts of parent chromosomes are reserved and the new offspring by the PM is generated. In order to estimate the effectiveness of our proposed optimized scheme, some typical genetic algorithms and their updating algorithms (PMGAs) are compared for solving the multicast routing on four different datasets. The simulation experiments show that PMGAs are more efficient than original GAs. More importantly, the PMGAs are more robustness that is very important for solving the multicast routing problem. Moreover, a series of parameter analyses is used to find a set of better setting for realizing the maximal efficiency of our algorithm.

A New Physarum Network Based Genetic Algorithm for Bandwidth-Delay Constrained Least-Cost Multicast Routing

Bandwidth-delay constrained least-cost multicast routing is a typical NP-complete problem. Although some swarm-based intelligent algorithms (e.g., genetic algorithm (GA)) are proposed to solve this problem, the shortcomings of local search affect the computational effectiveness. Taking the ability of building a robust network of Physarum network model (PN), a new hybrid algorithm, Physarum network-based genetic algorithm (named as PNGA), is proposed in this paper. In PNGA, an updating strategy based on PN is used for improving the crossover operator of traditional GA, in which the same parts of parent chromosomes are reserved and the new offspring by the \(Physarum\) network model is generated. In order to estimate the effectiveness of our proposed optimized strategy, some typical genetic algorithms and the proposed PNGA are compared for solving multicast routing. The experiments show that PNGA has more efficient than original GA. More importantly, the PNGA is more robustness that is very important for solving the multicast routing problem.

A Physarum-Inspired Vacant-Particle Model with Shrinkage for Transport Network Design

Physarum can form a higher efficient and stronger robust network in the processing of foraging. The vacant-particle model with shrinkage VP-S model, which captures the relationship between the movement of Physarum and the process of network formation, can construct a network with a good balance between exploration and exploitation. In this paper, the VP-S model is applied to design a transport network. We compare the performance of the network designed based on the VP-S model with the real-world transport network in terms of average path length, network efficiency and topology robustness. Experimental results show that the network designed based on the VP-S model has better performance than the real-world transport network in all measurements. Our study indicates that the Physarum-inspired model can provide useful suggestions to the real-world transport network design.

Network Community Detection based on the Physarum-inspired Computational Framework

Community detection is a crucial and essential problem in the structure analytics of complex networks, which can help us understand and predict the characteristics and functions of complex networks. Many methods, ranging from the optimization-based algorithms to the heuristic-based algorithms, have been proposed for solving such a problem. Due to the inherent complexity of identifying network structure, how to design an effective algorithm with a higher accuracy and a lower computational cost still remains an open problem. Inspired by the computational capability and positive feedback mechanism in the wake of foraging process of Physarum, a kind of slime, a general Physarum-based computational framework for community detection is proposed in this paper. Based on the proposed framework, the inter-community edges can be identified from the intra-community edges in a network and the positive feedback of solving process in an algorithm can be further enhanced, which are used to improve the efficiency of original optimization-based and heuristic-based community detection algorithms, respectively. Some typical algorithms (e.g., genetic algorithm, ant colony optimization algorithm, and Markov clustering algorithm) and real-world datasets have been used to estimate the efficiency of our proposed computational framework. Experiments show that the algorithms optimized by Physarum-inspired computational framework perform better than the original ones, in terms of accuracy and computational cost.

A Physarum -Inspired Ant Colony Optimization for Community Mining

Community mining is a powerful tool for discovering the knowledge of networks and has a wide application. The modularity is one of very popular measurements for evaluating the efficiency of community divisions. However, the modularity maximization is a NP-complete problem. As an effective optimization algorithm for solving NP-complete problems, ant colony based community detection algorithm has been proposed to deal with such task. However the low accuracy and premature still limit its performance. Aiming to overcome those shortcomings, this paper proposes a novel nature-inspired optimization for the community mining based on the Physarum, a kind of slime molds cells. In the proposed strategy, the Physarum-inspired model optimizes the heuristic factor of ant colony algorithm by endowing edges with weights. With the information of weights provided by the Physarum-inspired model, the optimized heuristic factor can improve the searching abilities of ant colony algorithms. Four real-world networks and two typical kinds of ant colony optimization algorithms are used for estimating the efficiency of proposed strategy. Experiments show that the optimized ant colony optimization algorithms can achieve a better performance in terms of robustness and accuracy with a lower computational cost.

A bio-inspired genetic algorithm for community mining

The community structure as a vital property for complex networks contributes a lot for understanding and detecting inherent functions of real networks. However, existing algorithms which are ranging from the optimization-based to model-based strategies still need to be strengthened further in terms of their robustness and accuracy. In this paper, a kind of multi-headed slime molds, Physarum, is used for optimizing genetic algorithm (GA), due to its intelligence of generating foraging networks based on bioresearches. Thus, a Physarum-based Network Model (PNM) is proposed based on the Physarum-based Model, which shows an ability of recognizing inter-community edges. Combining PNM with a genetic algorithm, a novel genetic algorithm, called PNGACD, is putting forward to enhance the GAs efficiency, in which a priori edge recognition of PNM is integrated into the phase of initialization. Moreover, experiments in six real-world networks are used to evaluate the efficiency of the proposed method. Results show that there is a remarkable improvement in term of the robustness and accuracy, which demonstrates that PNGACD has a better performance, compared with the existing algorithms.

An Enhanced Markov Clustering Algorithm Based on Physarum

Community mining is a vital problem for complex network analysis. Markov chains based algorithms are known as its easy-to-implement and have provided promising solutions for community mining. Existing Markov clustering algorithms have been optimized from the aspects of parallelization and penalty strategy. However, the dynamic process for enlarging the inhomogeneity attracts little attention. As the key mechanism of Markov chains based algorithms, such process affects the qualities of divisions and computational cost directly. This paper proposes a hybrid algorithm based on Physarum, a kind of slime. The new algorithm enhances the dynamic process of Markov clustering algorithm by embedding the Physarum-inspired feedback system. Specifically, flows between vertexes can enhance the corresponding transition probability in Markov clustering algorithms, and vice versa. Some networks with known and unknown community structures are used to estimate the performance of our proposed algorithms. Extensive experiments show that the proposed algorithm has higher NMI, Q values and lower computational cost than that of the typical algorithms.