Multi - Criteria And Multi - Constrained Horizontal Nonlinear Programming Theory And Its Application

Many specific problems, met during the process of scientific research, development planning, production design, and management decision and so on, can be summarized as optimization problems. In real life, these optimization problems often involve multiple objectives, which restrict each other, even contradict each other, and are often difficult to simultaneously achieve optimal. In addition, when making economic decisions, the decision-makers are often faced with fluctuations of the level of economic activity; in the group decision-making, different decision-makers always have different preferences on resource efficiency levels, both of these determines that the optimization problems must consider several discrete levels of resource efficiency. Considering these two aspects, the multi-criteria and multiple constraint-level programming has been formed. Theory and applications of multi-criteria and multiple constraint-level linear programming has been fully studied. To deal with the widespread nonlinear phenomena in the real world, this paper formulated the model and theory of multi-criteria and multiple constraint-level nonlinear programming and testified its correctness and validity with several numerical and practical cases. This paper has not only pioneering significance in theory but also provide effective scientific guidance for production practice. The main work and research results are summarized as follows:1. A novel model of multi-criteria and multiple constraint level nonlinear programming is formulated to accommodate the complex system of oilfield development.From the reality of oilfield development planning, this paper develop a new model of multi-criteria and multiple constraint level nonlinear programming in accord with the law of oilfield development by the use of oil field development planning, mathematical modeling, multi-criteria multiple constraint level linear programming and nonlinear programming theory and method. This model conforms to the oilfield development system with the properties of nonlinear, time-varying and uncertainty, and its resulting scheme can not only feedback integrated information about development programming to decision makers, but also provide a contingency plan for the possible changes of the resource constraint level, which overcome the deficiency of the existing models of oilfield production allocation planning.2. A creative theory of multi-criteria and multiple constraint level nonlinear programming is set up.From the model in1, this paper establishes a set of general theory and method of multi-criteria and multiple constraint level nonlinear programming:studies the extend-relationship among the original multi-criteria nonlinear programming, multi-criteria multiple constraint-level linear programming and the new model; defines its solution and investigates several properties of the solution set; provides a necessary and sufficient optimality conditions for a particular model.3. Three special models of multi-criteria and multiple constraint level nonlinear 4. programming are studied.Based on the general theory and method of multi-criteria and multiple constraint level nonlinear programming, three special models:the model both of which the objective function and constraint function are convex functions, the model with linear constraint and convex objective function and the model contains a special nonlinear relationship in constraints, are respectively discussed. For each model, corresponding solving process and programmatic implementation by MATLAB are provided, verifies the validity of these models and the algorithms by numerical experiments and the practical case in oilfield development.