The Theory And Algorithm Of The Three-Dimensional Layout Optimization With Behavioral Constraints

Layout problems, which seek for the reasonable placement of a set of objects into a limitedspace, are categorized as hybrid (discrete and continuous) combinatorial optimization problemswith broad applications.In the same time, it is also the hot point problem in operational andcombinatorial mathematics. This dissertation studies the three-dimensional layout optimiza-tion problems with behavioral constraints, based on the background of optimization design ofapparatus layout in the apparatus vessel of the artificial satellite.The layout problems in the apparatus vessel of the artificial satellite are to study how toarrange the instruments and equipments inside the apparatus vessel of the artificial satellitewhile satisfying all kinds of engineering constraints, so that one or more best targets are to befulfilled.The three-dimensional layout optimization problems are known as NP-hard problems orNP-complete problems in mathematics.Considerable challenges and difficulties exist in the solution of the problems, and the for-mulation of a competent problem-solving process, and solving the combinatorial explosion inmathematics in the same time.Since the three-dimensional layout optimization problems with behavioral constraints havehigh compléxity in terms of modeling and computing, they still need long period researchingprocess to perfectly solve the problems.The main results obtained in this dissertation may be summarized as follows:1. This dissertation studies the three-dimensional layout optimization problems for pack-ing cylindrical graph elements into the cylindrical space. The paper analysis the characteristicsof this sort problems. The three-dimensional layout model(PⅠ) is presented which takes thecapacity function as the objective function. Moreover, the optimization model(PⅡ) is presentedwhich takes the static non-equilibrium quantity as the objective function. The multi-objectiveprogramming model(PⅢ) is presented firstly on three-dimensional layout optimization problemwith behavior constraints.2. The concept of the non-overlapping function is presented so that the feasibility of thethree-dimensional layout problems can be given strict judgement. The presented mathemat-ical models are so flexible that it can conveniently deal with other three-dimensional layoutproblems with behavioral constraints. For the optimization models(PⅡ) and (PⅢ) of packingcylindrical objects into the cylindrical space, the paper studies a number of important properties of objective functions and proves their first-order optimality conditions.3. The three-dimensional hybrid layout optimization models with behavioral constraintsare established for packing cuboidal graph elements and cylindrical graph elements into thecuboidal space. In terms of graph theory and group theory, a global optimization algorithm isconstructed to overcome the difficulty rooted int the on-off nature of the layout problems.4. The optimization algorithm plays a dominant roles in solving three-dimensional prob-lems and is also an important factor in evaluating a research work. For three optimizationmodels of packing cylindrical objects into the cylindrical space, the optimization algorithms forsolving three-dimensional layout problems with behavioral constraints are studied. On MAT-LAB platform, a number of numerical examples are computed by the SUMT method, min-maxmethod and ideal point method in multi-objective programming, respectively. The experimentalresults from the numerical examples of given scale show that the proposed methods are feasiblefor the layout design problems of the apparatus vessel of the artificial satellite. Moreover, theproposed methods are suitable for solving larger-scale and more complicated satellite layoutdesign problems and lay a mathematical foundation for solving the practical problems of thelayout design of the apparatus vessel of the artificial satellite.In a word, this work is expected to extend and apply to the layout problems which havedifferent layout space and other design target with other constraints. Moreover, this work isalso likely to advance the layout design theory of spacecraft and benefit the research and de-velopment of practical methods and techniques for the layout design problems of the apparatusvessel of the artificial satellite. Finally, the main results of this research are likely to be appliedto the other more complicated layout design of other spacecraft.