Zhihua Cui

General framework of Artificial Physics Optimization Algorithm

This paper presents a general framework of physics-inspired method named Artificial Physics Optimization (APO) Algorithm, a population-based, stochastic for multidimensional search and optimization. APO invokes a gravitational metaphor in which the force of gravity may be attractive or repulsive, the aggregate effect of which is to move particles toward local and global optima. APOs particles (solutions to the optimization problem) are treated as physical individuals, each individual has a mass, position and velocity. The mass of each individual corresponds to a user-defined function of the value of an objective function to be optimized. Responding to virtual forces, APOs individuals move toward other particles with larger “masses” (better fitnesses) and away from lower mass particles (worse fitnesses). Each individual attracts all others whose mass is lower, and repels all others whose mass is greater. The individual with the greatest mass (“best” individual) attracts all other individuals, and it is neither attracted to nor repelled by all the others. The attraction-repulsion rule causes APOs population to search regions of the decision space with better fitnesses. Experimental simulations show that APO is tested against several benchmark functions with better results.

A new stochastic algorithm to direct orbits of chaotic systems

In this paper, a new stochastic optimisation algorithm is introduced to simulate the plant growing process. It employs the photosynthesis operator and phototropism operator to mimic photosynthesis and phototropism phenomena. For the plant growing process, photosynthesis is a basic mechanism to provide the energy from sunshine, while phototropism is an important character to guide the growing direction. In our algorithm, each individual is called a branch, and the sampled points are regarded as the branch growing trajectory. Phototropism operator is designed to introduce the fitness function value, as well as to decide the growing direction. To test the performance, it is used to solve the directing orbits of chaotic systems, simulation results show this new algorithm increases the performance significantly when compared with other four optimisation algorithms.

Nearest neighbor interaction PSO based on small-world model

Particle swarm optimization with passive congregation (PSOPC) is a novel variant of particle swarm optimization (PSO) by simulating the animal congregation phenomenon. Although it is superior to the standard version in some cases, however, due to the randomly selected neighbor particle, the performance of PSOPC is not always stable. Therefore, in this paper, a new variant -- nearest neighbor interaction particle swarm optimization based on small world model (NNISW) is designed to solve this problem. In NNISW, the additional congregation item is associated with the best particle, nor the random ones, and the small world topology structure is introduced also to simulate the true swarm behavior. After compared with other seven famous benchmarks in high-dimensional cases, the performance of this new variant is superior to other three variants of PSO.

Particle swarm optimization using lévy probability distribution

Velocity threshold is an important parameter to affect the performance of particle swarm optimization. In this paper, a novel velocity threshold automation strategy is proposed by incorporated with Levy probability distribution. Different from Gaussian and Cauchy distribution, it has an infinite second moment and is likely to generate an offspring that is far away from its parent. Therefore, this method employs a larger capability of the global exploration by providing a large velocity scale for each particle. Simulation results show the proposed strategy is effective and efficient.

Self-adaptive PID-Controlled Particle Swarm Optimization

As a new version of particle swarm optimization (PSO), PID-controlled PSO introduces the concept of controller into the algorithm structure. However, with the introduction of PID controller, three additional parameters are incorporated into the algorithm. Thus, how to provide a proper selection of these parameters is an important problem to affect the algorithm efficiency. In this paper, the relationships among these parameters are conducted by the stability theory. Further, a self-adaptive parameter selection strategy is proposed. Simulation results show the proposed strategy is effective.

A hybrid social emotional optimization algorithm with Metropolis rule

Social emotional optimization algorithm (SEOA) is a novel swarm intelligent population-based optimization algorithm by simulating the human social behaviors. However, its diversity is decreased increased when solving high-dimensional multi-modal optimization problems. Therefore, in this paper, a new hybrid SEOA with Metropolis rule is introduced to enhance the exploration capability. To test the performance, five famous benchmarks are selected, and compared with the standard version with different dimensions. Simulation results show this hybrid algorithm can increase the global search capability significantly.

Solving redundancy optimisation problem with social emotional optimisation algorithm

Social emotional optimisation algorithm (SEOA) is a new swarm intelligent technique to stimulate human behaviours. However, up to date, there are few applications. Therefore, in this paper, SEOA is successfully applied to the redundancy optimisation problem. The objective of the redundancy allocation problem is to select from available components and to determine an optimal design configuration to maximise system reliability. BP neural network is trained to calculate the objective fitness, while SEOA is applied to check the best choice of feasibility of solution. One example is used to illustrate the effectiveness of SEOA.

Stochastic Dynamic Step Length Particle Swarm Optimization

Stochastic particle swarm optimization is a novel variant of particle swarm optimization that convergent to the global optimum with probability one. However, the local search capability is not always well in some cases, therefore, in this paper, a technique, dynamic step length, is incorporated into the structure of stochastic particle swarm optimization aiming to further improve the performance. In this modification, each particle will adjust its velocity according to its performance. In other words, if it finds a better region, it will make a local search, otherwise, a global search pattern is given. By the way, to combining the advantages between the standard version (with better exploitation capability) and the stochastic version (with better exploration capability), the first half period is used with the standard version incorporated with dynamic step length, while in later generations, the stochastic version with dynamic step length is used to escape from a local optimum. Simulation results show this strategy may provide well balance between exploration and exploitation capabilities, and improve the performance significantly.

Particle Swarm Optimization with Dynamic Step Length

Particle swarm optimization (PSO) is a robust swarm intelligent technique inspired from birds flocking and fish schooling. Though many effective improvements have been proposed, however, the premature convergence is still its main problem. Because each particles movement is a continuous process and can be modelled with differential equation groups, a new variant, particle swarm optimization with dynamic step length (PSO-DSL), with additional control coefficient- step length, is introduced. Then the absolute stability theory is introduced to analyze the stability character of the standard PSO, the theoretical result indicates the PSO with constant step length can not always be stable, this may be one of the reason for premature convergence. Simulation results show the PSO-DSL is effective.

Self-learning Particle Swarm Optimization Based on Environmental Feedback

Particle swarm optimization (PSO) simulates the behaviors of birds ocking and poundsh schooling. However, its biological background does not concern the environmental affection. Inspired by the interaction between environment and individuals, a new version - self-learning particle swarm optimization based on environmental feedback (SL-PSO), is proposed, in which two self-learning strategies are designed so that each particle adjusts its moving direction according to the feedback information from the environment. Furthermore, a mutation operator is introduced to avoid premature convergence phenomenon. Simulation results show the proposed algorithm is effective and efpoundcient.