Aggregate Homotopy Interior-point Method For Multiobjective Programming

Multi-objective optimization problem is an important branch of Optimization theory problem, with a wide range of applications and distinctive practical background, such as many areas of traffic management, socio-economic, engineering, military defense, and management engineering. Multi-objective optimization methods have also become an important tool for decision-making in these areas. As multi-objective optimization problem involving multiple constraints limit these constraints and do not tend to be independent, they are coupled by the decision variables, in a mutual conflict and competing state. The complexity of this competition and the resulting multi-objective optimization make it become very complicated and difficult. Solving multi-objective optimization problem is generally based on this study aggregate homotopy method.Aggregate homotopy method more research is to use the same method in single-objective optimization and multi-objective optimization problem though it is to promote single-objective optimization problem. However, it is essentially different from the single objective optimization problems. Firstly, the problem of a large number of multi-objective inequality constraints is changed into inequality constraints with only a multi-objective optimization problem, making the complex problem a corresponding simple question and a large problem miniaturization. Second, because the inequality constraint functions are non-smooth after conversion and gradient optimization theory is no longer applicable, we use aggregation functions smooth approximation, based on the traditional differential to transform the non-smooth multi-objective optimization problem into a smooth multi-objective optimization problem. The research results have been mainly aimed at situations with only inequality constraints, we study a more general case, that is using the objective that equality and inequality constrained optimization problem to overcome the non-convex feasible region constraints limit, to an appropriate method of generalized weak cone condition, in this condition for solving numerical example illustrates the method is effective and feasible. Second, it further improves the aggregate constraint homotopy method, introduces twice continuously differentiable mapping and expands the selection of the initial point of the feasible region and Conditions. Cohesion improved homotopy method to achieve a multi-objective optimization with inequality constraints solving problems.This paper is divided into five chapters:the first chapter introduces the history and the research results of homotopy interior point method and cohesion methods; Chapter II is about prior knowledge associated with this article; Chapter III talks about equality and inequality constraints Aggregate Homotopy method under normal cone condition generalized weak multi-objective optimization problem; Chapter IV is about improving the cohesion constraint homotopy method and using the improved cohesion solving multi-objective optimization problem with inequality constraints homotopy method, which proved the existence of a path, bounded and accessibility; The fifth chapter is the summary.