Theoretical Study Of Fractional-Order Ant Colony Algorithm

The "New Generation Artificial Intelligence Development Plan" issued by the State Council lists swarm intelligence as a key research direction and takes the active perception and discovery of swarm intelligence as a key technology.Taking the ant colony algorithm,which has been widely studied in the swarm intelligence algorithm,as an example,ants are non-agent or micro-agent,and can only greedily select the next node according to the pheromone concentration of the adjacent path,so the decision-making performance is poor.In this paper,a single ant in the Ant Colony Optimization(ACO)can only use the pheromone concentration information on the adjacent edge to get greedy decision-making when selecting the next node,and the performance is poor.To model the probability transfer function of ants,the Fractional-Order Ant Colony Algorithm(FACA)is proposed.The ants of FACA can see the future status of multiple branches after making different decisions——the future transfer sequence of the ACO.The ant in FACA synthesizes the transfer probability function of the future transfer sequence and makes a better decision than the traditional ant colony at the current node.The main structure of this paper is "Proposing the framework of the FACA →finding the shortcomings of the FACA in specific applications→Imitating the current optimal algorithm to improve the FACA→ Getting the improved algorithm of FACA under specific application ".The main research contents are as follows:(1)Construct the Fractional-Order Ant Colony Algorithm(FACA)framework.The nonlocality and long-term memory of fractional calculus are used to model the transition probability function of the future node of the ant,so that the ant can make better decisions at the current node in the fractional probability transition function.Simulation results prove that FACA has faster convergence speed and higher optimization performance than Ant Colony System(ACS)and Max-Min Ant Colony System(MMAS)in TSPLIB data set,which proves the effectiveness of FACA algorithm framework.(2)Use graph probability model to prove the convergence of fractional order ant colony algorithm.The FACA can find the global optimal solution with a probability close to 1when the parameters are reasonable and the number of iterations is large enough.After the FACA obtains the global optimal solution,the upper limit of iterative steps required for system convergence is given.When the upper limit of steps is reached,the pheromone concentration in the FACA will no longer change.(3)Follow the Parallel Cooperative hybrid method based on Ant Colony Optimization and the 3-Opt algorithm(PACO-3Opt)to optimize and improve the FACA.First,improve FACA into the Parallel Fractional-Order Ant Colony Algorithm(PFACA)and then combine PFACA with local search algorithm 3-Opt to obtain the Fractional-Order Parallel Ant Colony Algorithm based on the local search algorithm 3-Opt optimization(PFACA-3Opt).The simulation experiment proves that in the TSPLIB data set,the optimization performance of PFACA is slightly better than that of FACA,and the convergence speed and optimization ability of PFACA-3Opt are significantly ahead of PFACA and FACA.The optimization performance of PFACA-3Opt is slightly better than that of the PACO-3Opt.(4)FACA is applied to continuous function optimization.First,the domain of definition of the continuous function is discretized in segments,so that the continuous domain optimization problem is transformed into a discrete combination optimization suitable for FACA optimization,and the continuous domain fractional-order ant colony(CFACA)is obtained.Then the CFACA algorithm and the GA algorithm are fused to make use of the advantages of each other to make up for their own shortcomings,so the Hybrid genetic algorithm and ant colony algorithm applied to continuous function optimization(GACFACA)is proposed.On the classic function optimization benchmark test set,GACFACA has higher optimization performance than CFACA,and can almost find the global optimum.But in the ultra-complex function optimization competition of CEC2021,GA-CFACA is not as good as the improved algorithm of Differential evolutionary(DE).(5)In order to solve the problem of the long execution time of the FACA algorithm,the equivalent circuit of the serial fractional-order memristor is used to calculate the fractional-order probability transfer function in FACA,then the Fractional-order ant colony algorithm based on the fractional-order memristor optimization(FMAC)is proposed.In this paper,according to the topology diagram of the fractional order probability transfer function,an n-level low-pass capacitive serial fractional-order memristor equivalent circuit is constructed.Simulation experiments prove that FMAC and FACA are almost the same in convergence speed and optimization ability,and the running time of FMAC is shorter than that of FACA.