Vector Method Based On The Constraints To Maintain Quasi-state Physics Constrained Optimization Algorithm

There are many constraint optimization problems which are difficult to optimize in the production, combining intelligence evolutionary algorithm with the traditional constraint processing method become the effective method to solve this kind of problem. APO algorithm is a new proposed heuristic algorithm. VM-APO algorithm introduces vector model based on the artificial physics optimization algorithm, enhance the diversity of population, and the individual move to the area in which the optimal value of objective function under the regular action of gravitation and repulsion. The VM-APO algorithm which is not affected by the characteristics of constrained function itself has good global search capability, and the theory of the algorithm is simple. It's suited to combine the VM-APO algorithm with traditional constraint processing method to solve the constraint optimization problems.A new method which is combined the VM-APO algorithm with constraint-preserving method is adopted to solve the constrained optimization problem in this text. Constraint-preserving method which is a kind of traditional constraint processing method requires all individual in the feasible region at all times, so it requires that the individuals must be feasible solutions in the initial case. First random method and VM-APO algorithm are used respectively to produce all feasible individuals. Simulation experiment shows that VM-APO algorithm is better than random method when the initial feasible solutions to produce. Then shrinkage coefficient is introduced aiming at cross-border individual, which is shrinked back to the problem space without changing the direction of speed. The violation degree function is used to determine whether every individual is in the feasible region or not, and the Gold Cutting Method, the Dichotomy Method and Fibonacci method are used respectively to pull the unfeasible individuals back to the feasible region. Finally the VM -APO algorithm is adopted to search the optimal value of objective function. The Simulation results show that the search performance and stability of VM-APO-GDM algorithm is the best and the most stable, this is followed by VM-APO-FM and VM-APO-DM algorithm. When the VM-APO algorithm with mixed multidimensional search is used to solve constraint optimization problems, the process of pulling infeasible individual back to the feasible region is turned into solving optimal value problem of the violation degree function in terms of contraction matrixη. Contrasting multi-dimensional search method with one-dimension search method on searching feasible individual in hypersurface, the probability of former is greater than the latter, and the diversity of population is increased. The simulation results indicate that the VM-APO-MDCPM algorithm is better than VM-APO-ODCPM algorithm in search performance and stability.