Design And Performance Analysis Of A Global Optimization Based On Artificial Physics

Optimization problems are ubiquitous in many area of the real world. Many scientific, engineering and application problems can be turned into optimization problems. In order to solve complex optimization problems, many studies have been done to look for efficient and robust intelligent optimization algorithms. Physicomimetics (or Artificial Physics, AP) is a method motivated by natural physical forces. The virtual physical forces drive a multi-robots system to a desired configuration or state. The system acts as the simulation of Newton's Second law. Artificial Physics focus on collections of small entities yield complex behaviors from the simple attractive or repulsive force between entities. AP framework has been applied to the distributed control of swarms of robots, which has become an effective tool to solve distributed complex problems. In this thesis, a novel optimization algorithm is proposed based on AP method, and several aspects of the algorithm, such as its framework establishment, force law design, mass function construction, hybrid algorithm, convergence analysis, parameter selection, swarm robots search for target, are researched to make it more effective.Inspired by Physicomimetics, a relationship of mapping between AP approach and a population-based optimization algorithm is constructed through comparing the similarities and differences of physical individual simulating animals foraging and ideal particle. A framework of artificial physics optimization (APO) algorithm is constructed, in which a swarm of particles (solutions to the optimization problem) are treated as physical individuals looking for a global optimum in the problem space driven by virtual force. Three force laws, such as: negative exponential force law, unimodal force law and linear force law, are designed. To make a deep insight, different versions of APO algorithm with the three force laws are theoretic analyzed and used to solve benchmark functions. Simulation results show that APO algorithm driven by linear force law is more effective and robust, which is fitter for solving complex optimization problems. The mass of each individual corresponds to a user-defined function of the value of an objective to be optimized, which can supply some important information for searching global optima. This thesis proposes the basic requirement and design method of mass function, and classifies mass functions into four different types of curvilinear functions according to their curvilinear styles, such as convex function, linear function and concave function, etc.. Simulation results show the mass functions with concave curve may generally obtain the satisfied solution within the allowed iterations.Drawing lessons from the memory and interaction capability of social animal, an extended artificial physics optimization (EAPO) algorithm is proposed, in which individuals are treated as agents with memory and interaction capability. Simulation results show EAPO converges more quickly than APO and with better diversity. In addition, a vector model of APO (VM-APO) algorithm is constructed in order to effectively utilize the directions of individuals'motion vectors. One-dimensional search method and multi-dimensional search method are combined respectively into VM-APO to improve its local search capability. Simulation results confirm that the two hybrid vector APO algorithms can enhance the local exploitation capability significantly.Convergence is a strong emphasis on the theoretical research of optimization algorithm. The necessary and sufficient conditions for APO convergence are deduced through analyzing APO algorithm based on discrete-time linear system theory. And APO algorithm converge to the vicinity of global optimum with probability one is proved. Two selection strategies of G, such as: the constant G and adaptive G, are designed. Simulation results show that APO with an adaptive G has a better diversity and bigger global convergence probability than that with a constant G.As to the task named target search, APO is used to model and control swarm robots system. Viewed as an individual moving in a closed two-dimensional workspace, each robot is abstracted as one order inertial element, and further, the model of swarm robotic search for target with global sense based on APO is given, in which the virtual force law among robots is constructed through drawing lessons from the attraction-repulsion rule of APO. Due to robot's limited sensing ability in practical applications, time varying sense domain are introduced, and further, the model of swarm robotic search for target with local sense based on APO is proposed. At the same time, the cooperative control strategies and algorithms of the two models are designed. Simulation results under an ideal environment show that APO is feasible and effective when applied to swarm robotic search for target with global sense and local sense.