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.

The traveling salesman problem (TSP) is one of the most classical NP-hard problems in the combinatorial optimization, as many practical problems, such as scheduling problems and vehicle-routing cost allocation problems can be abstracted. The introduction of multiobjective in the TSP is a very important research topic, which brings serious challenges to the TSP. Currently, genetic algorithms (GAs) are one of the most effective methods to solve the multiobjective traveling salesman problem (MOTSP). However, GA-based algorithms suffer the premature convergence, the insufficient diversity, and nonuniform distribution of solutions when solving the MOTSP, which further restrict the wide application of GA-based algorithms. In order to overcome these problems, this paper proposes an improved method for GAs based on a novel evolutionary computational model, named the Physarum-inspired computational model (PCM). Based on the prior knowledge of the PCM, the initialization of the population in the proposed method is first optimized to enhance the distribution of solutions. Then, the hill climbing (HC) method is used to improve the diversity of individuals and avert running into the local optimum. Compared to the other MOTSP solving algorithms, a series of experimental results demonstrate that our proposed method achieves a better performance. INDEX TERMS Bi-objective traveling salesman problem, NSGA-II, hill climbing, Physarum.

Designing effective transport networks can be considered as one of the most debated problems in the area of computational intelligence. Some nature-inspired algorithms have shown excellent abilities in the adaptive network construction. In this aspect, a unique creature, called Physarum, has exhibited the computing capacity to optimize protoplasmic networks connecting distributed food sources. This inspires our work to design a Physarum foraging platform for constructing transport networks. Specifically, the traditional Physarum foraging model is adapted to construct transport networks in China. In order to get close to the real scenario, practical data are collected to build the environment of the Physarum foraging model and the structure of real transport networks. Some measurements in the domain of complex networks, such as average path length, network efficiency, topology robustness, and functional robustness, are used for performance comparison. The experimental results demonstrate that Physarum foraging models excel in constructing highly efficient and robust networks, which can be utilized for directing the design of transport networks in the real world. INDEX TERMS Physarum polycephalum, Physarum foraging model, network analysis, transport network design.