Evidences have manifested that unidirectional ring neural networks lack the ability to generate desired chaos. This paper formulates a novel memristor regulation (MR) approach to constructing a no-equilibrium bi-memristor unidirectional ring neural network (BMURNN), in which two distinct memristors are incorporated into a unidirectional ring neural network derived from the Hopfield neural network, with enhanced chaotic complexity, whereas one serving as a memristive synapse and the other as an emitter of electromagnetic radiation. Numerical simulations reveal that any desired number of multi-scroll hidden chaotic attractors can be generated from the BMURNN via the non-ideal multi-piecewise nonlinear memristor, while the time-controlled multi-scroll attractor growth is output from the periodic function memristor, demonstrating that the memristors can enhance the chaos complexity of the original unidirectional ring neural network. Additionally, diverse coexisting hidden attractors, that is, hidden heterogeneous/homogeneous multistability evoked by the memory attributes of memristors, can be dynamically regulated by varying the initial conditions. Finally, a digital circuit is designed and implemented based on CH32 to validate the numerical simulations and theoretical analyses, and a new pseudorandom number generator is devised to explore the BMURNN for practical applications. Performance analyses demonstrate its superiority and high randomness, providing further proof for the effectiveness of the proposed MR method.

Ant Colony Optimization (ACO) has witnessed great success in tackling the Traveling Salesman Problem (TSP). In ACO, ants involved in the pheromone update play pivotal roles in its optimization effectiveness. Along this road, this paper designs an ant selection mechanism along with a non-linear weight method for ACO to update the pheromone effectively, leading to a novel ACO, called NLW-ACO. Particularly, NLW-ACO leverages the fitness values of ants to assign each ant a selection probability. Then, it adaptively chooses ants for pheromone update. Subsequently, a nonlinear weight is assigned to each selected ant based on its fitness value to update the pheromone matrix. Resultantly, better ants have higher selection probabilities and larger weights to take part in the pheromone update. This leads to that NLW-ACO compromises search convergence and search diversity appropriately to seek for the optimum. Experiments have been carried out on 10 TSP instances of diverse scales. The experimental findings substantiate that NLW-ACO significantly outperforms the 5 typical ACO methods, especially on large-scale TSP problems.

Leading exemplars play significant roles in updating particles to seek optimal solutions for Particle Swarm Optimization (PSO). Along this road, this paper devises an Individual-level Dominant Exemplar Selection (IDES) framework for PSO, giving rise to a new PSO variant named IDESPSO. Specifically, instead of using their own personally best positions and the globally best position of the entire swarm to update particles, IDES first randomly chooses two different exemplars for each particle from all personally best positions. Then, it compares the two selected exemplars with the personally best position of this particle. Based on the comparison results, different updating strategies are utilized to update different particles. This method notably enriches the variety among the chosen leading exemplars, thereby substantially bolstering the updating diversity of particles. Under IDES, this paper further develops seven selection strategies to help IDESPSO pick up promising exemplars for particles to evolve. Specifically, the seven selection schemes are the roulette wheel selection, the tournament selection, and five hybridizations of two basic models. A series of experiments have been undertaken on the universally used CEC2014 problem suite to compare IDESPSO with the seven selection schemes and two classic PSOs. The empirical results show that IDESPSO paired with anyone of the seven selection methods, markedly outperforms the two classical PSO variants, highlighting its significant performance.

A phase-shifting chaotic oscillator is constructed by memristive coupling. The introduced memristor revises the frequency response as the core of the frequency selection network in the oscillator. A controlled memristor is derived to maintain a stable amplification. Thus, the oscillator has two independent offset boosting voltages, and the voltages of two capacitors can be effectively controlled by cancellation. More conveniently, the simultaneous and proportional change of the op-amp supply voltage and the memristor in the oscillator also rescales the capacitors’ voltages in the same proportion. Finally, a memristor-equivalent circuit with the feedback from AD633 for division operation greatly reduces the cost of components. The hardware experiment confirms the theoretical analysis and numerical simulations.

In high dimensional environment, the interaction among particles significantly affects their movements in searching the vast solution space and thus plays a vital role in assisting particle swarm optimization (PSO) to attain good performance. To this end, this paper designs a random contrastive interaction (RCI) strategy for PSO, resulting in RCI-PSO, to tackle large-scale optimization problems (LSOPs) effectively and efficiently. Unlike existing interaction mechanisms for low-dimensional problems, RCI randomly chooses several different peers from the current swarm to construct a random interaction topology for each particle. Then, it lets the particle interact with the selected peers based on their current evolutionary information instead of their historical evolutionary information. Within the topology, RCI only propagates the evolutionary information of two contrastive dominators with the largest difference in fitness to direct the evolution of the particle. Therefore, particles with no more than two dominators in their topologies are not updated. Furthermore, a dynamic topology size adjustment scheme is devised to gradually enlarge the interaction topology. In this way, the swarm gradually switches from exploring the immense search space dispersedly to exploiting the found optimal regions intensively as the evolution continues. With these two strategies, RCI-PSO expectedly compromises search diversity and search convergence well at the swarm level and the particle level. At last, extensive experiments executed on two public LSOP suites verify that RCI-PSO performs competitively with or even much better than totally 40 state-of-theart large-scale approaches and preserves a good capability and scalability in tackling complex LSOPs.

Different from existing studies where low-dimensional optimizers are utilized to optimize the path of an unmanned aerial vehicle (UAV), this paper attempts to employ large-scale swarm optimizers to solve the path planning problem of UAV, such that the path can be subtler and smoother. To this end, a variation encoding scheme is devised to encode particles. Specifically, each dimension of a particle is encoded by a triad consisting of the relative movements of UAV along the three coordinate axes. With this encoding scheme, a large number of anchor points can be optimized to form the path and repetitive anchor points can be avoided. Subsequently, this paper embeds this encoding scheme into four representative and well-performed large-scale swarm optimizers, namely the stochastic dominant learning swarm optimizer (SDLSO), the level-based learning swarm optimizer (LLSO), the competitive swarm optimizer (CSO), and the social learning particle swarm optimizer (SL-PSO), to optimize the path of UAV. Experiments have been conducted on 16 scenes with 4 different numbers of peaks in the landscapes. Experimental results have demonstrated that the devised encoding scheme is effective to cooperate with the four large-scale swarm optimizers to solve the path planning problem of UAV and SDLSO achieves the best performance.

Ant Colony Optimization (ACO) has shown very promising performance in solving Traveling Salesman Problem (TSP). However, most existing ACO algorithms utilize either the absolutely best ants or all ants to update the pheromone matrix. This leads to either serious diversity loss or slow convergence. To alleviate these predicaments, this paper designs a random pairwise competition based ant selection for pheromone updating. Specifically, a number of ants are randomly selected from the ant colony and then are randomly paired together. Subsequently the better one in each pair is selected to update the pheromone matrix. In this way, a good balance between search diversity and search convergence is potentially maintained. Integrating this selection strategy along with a local search scheme into the ACO framework, a new ACO algorithm called random pairwise competition based ACO (RPCACO) is developed. Experiments conducted on 8 TSP instances from the TSPLIB benchmark set demonstrate that RPCACO is more effective and efficient than the five classical ACO algorithms in solving TSP.

Multiple traveling salesmen problem (MTSP) is an extension of traditional traveling salesman problem (TSP). It involves both the city assignment optimization and the route optimization of each salesman. Genetic algorithms (GA) have been widely used to solve MTSP thanks to its easiness in implementation and good global search ability. To help GA effectively solve MTSP, researchers have developed various encoding schemes. However, there is no systematic and comparative study on the effectiveness of these encoding strategies. To fill this gap, this paper conducts investigations to compare four popular encoding strategies for MTSP, namely the one-chromosome encoding, the two-chromosome encoding, the two-part-chromosome encoding and the multi-chromosome encoding. Experimental results on different MTSP instances with different numbers of cities and salesmen show that the multi-chromosome encoding is far better than the other encoding strategies.

Mutation plays a crucial role in assisting differential evolution (DE) to effectively solve optimization problems. The key to mutation lies in the selection of parent individuals participating in the mutation. Along this road, this paper devises a binomial distribution-assisted individual selection strategy for DE. Specifically, this paper takes advantage of the probability distribution function of the binomial distribution to assign weights to individuals based on their fitness rankings. In this way, the selection of individuals focuses more on medium better individuals instead of the top best ones. Therefore, high mutation diversity can be preserved and thus it is likely that falling into local regions can be effectively avoided. Embedding this selection strategy into DE, a novel DE variant called binomial distribution assisted DE (BDDE) is developed. Experiments conducted on the CEC2017 benchmark suite have verified the effectiveness of BDDE in solving optimization problems. Particularly, BDDE gains much better performance against the well-known and representative mutation strategies.

Expensive optimization problems (EOPs) are becoming more and more ubiquitous nowadays. To effectively solve such problems, surrogate-assisted evolutionary algorithms (SAEAs) have been developed. Specifically, a SAEA usually maintains a surrogate model to simulate the real objective function of an EOP. Such a surrogate model is trained based on real-evaluated solutions. Then, it is utilized to evaluate the fitness of individuals in the EA instead of the real expensive fitness evaluation. Though many SAEAs have been designed, they mainly concentrate on dealing with low-dimensional EOPs with fewer than 300 dimensions. Their performance on large-scale EOPs with more than 300 dimensions is unknown. To fill this gap, this paper conducts a comparative study on two types of state-of-the-art SAEAs with a total of four algorithms on four classical EOPs. To make comprehensive comparisons, we range the dimension size from 50 to 1000. As far as we know, this is the first time to assess SAEAs on EOPs with such a wide range of dimension sizes and such high dimensionality. The comparison results show that the optimization performance of the compared four SAEAs on high-dimensional EOPs with more than 500 dimensions is not as satisfactory as their performance on low-dimensional EOPs because of their slow convergence. Therefore, research on large-scale SAEAs for high-dimensional EOPs still deserves intensive attention.

Multiple traveling salesmen problem with visiting constraints (VCMTSP) is a general version of the classical multiple traveling salesmen problem (MTSP), where each city can be only accessed by a number of salesmen. To cope with this new problem, we adapt the genetic algorithm (GA) for MTSP by using a dual-chromosome representation scheme with one chromosome denoting the visiting sequence of cities and the other representing the assignment of cities to salesmen. To further promote the effectiveness of GA in solving VCMTSP, we modify three popular crossover operators, namely the cycle crossover (CX), the order crossover (OX), and the partially mapped crossover (PMX). Similar to the execution for traditional TSP, the three crossover operators are all executed on the city sequence chromosome, while the adaption of them lies in the modification of the salesman assignment in the second chromosome. To this end, a correction mechanism according to the accessibility matrix is conducted to make the generated solutions after crossover feasible. Extensive experiments conducted on totally 16 VCMTSP instances generated from the benchmark TSPLIB set demonstrate that the adapted GA could effectively cope with VCMTSP, and the GA with the modified PMX achieves the best overall performance.

The scaling factor (F) in the mutation operation and the crossover rate (CR) in the crossover operation are considerably critical in assisting differential evolution (DE) to attain good optimization performance. As a result, DE is very sensitive to these two parameters. To address this predicament, many adaptive parameter control methods have been proposed for these two parameters. However, there are no comprehensive comparisons among these adaptive parameter methods. To make up for this defect, this paper mainly investigates the effectiveness of six widely utilized adaptive strategies, namely the ones in JADE, IDE, jDE, SinDE, FDSADE, and RDE. For fairness, this paper selects the binomial crossover and the mutation “DE/current-to-pbest/1” to accompany the six adaptive parameter strategies. Experimental results on the commonly adopted CEC2014 benchmark suite have demonstrated that the adaptive parameter control methods in IDE and JADE help DE achieve the best overall performance. With these investigations, it is envisaged that this paper provides a fundamental guideline for new learners and those looking for an appropriate adaptive parameter technique for their newly created DE algorithms.

This paper proposes a ranking weight based roulette wheel selection (RWRWS) method for a promising particle swarm optimizer, called comprehensive learning particle swarm optimizer (CLPSO), to further improve its optimization performance. Specifically, the proposed RWRWS adopts a non-linear weight function to enhance the selection probabilities of promising personal best positions during the exemplar construction. In this way, it is expected that the construction efficiency of generating a promising leading exemplar for each particle could be improved and thus the optimization performance of CLPSO is expectedly elevated. To validate the feasibility and effectiveness of RWRWS, we carry out extensive experiments on a widely acknowledged benchmark problem set by comparing it with other three selection methods, namely the fitness-based roulette wheel selection (FRWS), the ranking based roulette wheel selection (RRWS), and the tournament selection (TS). Experimental results demonstrate that RWRWS helps CLPSO attain the best overall performance among the four selection methods.

This paper proposes an adaptive version of an existing promising large-scale optimizer named level-based learning swarm optimizer (LLSO). Though such an optimizer has shown promising performance in dealing with large-scale optimization, it is much sensitive to its two introduced parameters. To alleviate this dilemma, this paper devises two simple yet effective adaptive adjustment strategies for the two parameters, leading to an adaptive LLSO(ALLSO). Specifically, this paper first defines a novel aggregation indicator based on the difference between the global best fitness and the averaged fitness of the swarm, to roughly evaluate the evolution state of the swarm. Then, based on this indicator, two adaptive adjustment strategies are devised to dynamically determine the values of the two parameters during the evolution. With these two strategies, the swarm is expected to maintain a potentially good balance between intensification and diversification. Extensive experiments conducted on two widely used large- scale benchmark sets demonstrate that the two adaptive strategies effectively improve the performance of LLSO.

For loosely coupled wireless power transfer systems, strongly magnetic coupling is becoming a viable scheme to realize power transfer over medium distances. The method using DC-DC circuit is regarded as the most promising way to realize impedance matching for such systems. However, due to the nonlinear nature of rectifying circuit, it is difficult to track the optimal load accurately and the robust stability can not be guaranteed. Based on the above considerations, one tracking operator-based optimal load control method is proposed in this paper. The proposed control system can track the optimal load with high accuracy even when the output load varies, the tracking performance and stability can be verified. Moreover, the robust stability is considered using operator theory. Finally, simulation results are presented to confirm the effectiveness of the proposed control scheme.