Swarm intelligence and linear programming synergetic method for mixed integer nonlinear programming problems

Abstract

The invention discloses a swarm intelligence and linear programming synergetic method for mixed integer nonlinear programming problems. The method comprises an improved particle swarm algorithm for solving outer problems and a linear programming algorithm for solving inner problems; the algorithms have the global optimization ability of a heuristic algorithm, and have higher convergence speeds andless calculation time when being compared with a pure heuristic algorithm; the algorithms import velocity disturbance probability functions, so that the ability of preventing the algorithms from falling into local optimum is improved, and optimum particles are backed up, so that the problem of low convergence speeds after the velocity disturbance is prevented; the algorithms consider the robustness of solutions and improve fitness functions of particle swarms, so that sharp values in solution spaces are effectively eliminated; and the algorithms further import double-fitness functions and system tolerance, and carry out particle selection according to more reasonable rules. Being used as a universal solution strategy for mixed integer nonlinear programming problems, the swarm intelligenceand linear programming synergetic method can be widely applied in mixed integer nonlinear programming problems, and is high in solution efficiency, reliable in result and good in robustness.

Description

technical field [0001] The invention belongs to the field of system engineering, and in particular relates to a collaborative method of group intelligence and linear programming for mixed integer nonlinear programming problems. Background technique [0002] Mixed Integer Non-Linear Programming (MINLP for short) is a kind of nonlinear programming problem including continuous variables and discrete variables. The application of MINLP covers science, engineering, life and many other fields: planning and scheduling problems of chemical production, unit combination problems in the power market, logistics base layout optimization problems, design, combination and control interaction problems, process combination and control under uncertain conditions. Design application issues, water resource management and sharing issues, etc. [0003] The MINLP problem has been at the forefront of international research for the past few decades. However, due to the complexity of the MINLP prob...

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Problems solved by technology

However, due to the complexity of the MINLP problem, how to effectively solve the algorithm for the MINLP problem has always been a major challenge faced by the scientific and technological circles and the business community, and has not been well solved so far.

Deterministic algorithms for solving MINLP, such as branch and bound method, generalized decomposition method, and extended cut plane method, are feasible for small-scale convex models, but when the objective function presents strong nonlinearity and the optimal variable dimension When the feasible area is very large and the feasible area is non-convex, there are many problems in deterministic algorithms, such as difficulty in guaranteeing the global optimal solution or even inability to solve it; therefore, heuristic algorithms are more and more widely used. Motion shape to solve optimization problems, such as genetic algorithm, ant colony algorithm, particle swarm algorithm, theoretically has the ability of global optimization, but the heuristic algorithm is easy to fall into the local optimum when the feasible region is non-convex, and the When the number is large, the convergence speed is slow and the calculation time is long, which limits their popularization and application.

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