Urniaieva I. Optimization problems of container loading: mathematical models, solution methods and applications

The thesis is devoted to the creation of modern computer technologies (mathematical models, methods, algorithms and programs), focused on solving problems of designing the optimal loading of containers, taking into account the geometric constraints and balance conditions. A system analysis of the problem of optimal loading of containers in different areas of application was carried out The review and analysis of the problems of optimal loading of containers at the level of container terminals as nodes of transport systems are performed. The problems of construction of optimal layouts that arise in the aerospace industry are analyzed, namely: problems of designing the optimal placement of payloads of given shapes and sizes in containers of arbitrary shape, taking into account geometric and mechanical constraints. A review and analysis of mathematical modeling tools and solving problems of optimal loading of containers, in particular, methods of geometric design. The problem of constructing an equilibrium layout in a container of 3D-objects in a container divided by horizontal racks into subcontainers is investigated. A mathematical model is built that takes into account not only the geometric constraints and conditions of the balance, but also the combinatorial features of the problem associated with the need to build a partition of the set of placed objects in subcontainers. A solution strategy is proposed, which includes procedures: generation of split tuples; construction of starting points in the field of acceptable solutions; local optimization. The problem of optimal packing of convex 3D-objects in a container with supporting shelves (racks) is analyzed, taking into account the constraints of placement and balance conditions. The method of phi-functions is used for the analytical description of placement constraints. A general mathematical model of the combinatorial problem of equilibrium layout with special geometric and balance conditions is constructed. A multi-start solution strategy is proposed and involves the use of a valid starting point and a local optimization algorithm. In particular, in the case of packing cylinders, the problem is reduced to the problem of packing circles. The multicriteria problem of optimization of placement of 3D-objects in the container taking into account constraints of placement (non-intersection, inclusion, distance) and balance (equilibrium, inertia and stability) is formulated - the multi-criteria balance layout problem (MBLP). The method of phi-function was used for analytical description of placement constraints. A mathematical model of the problem in the form of a multicriteria optimization problem is constructed. Variants of the MBLP problem are presented depending on the forms of objective functions, forms of objects and containers, combinations of constraints. The problem of packing (layout) for a set of groups of convex objects is investigated, which is motivated by the problems of container loading, which arise in logistics problems. The load is considered for a rectangular container of a given size under the condition of non-intersection (continuously broadcast and rotating) of objects in the group. New tools of mathematical modeling of groups that do not intersect and are placed inside the container are proposed. A new mathematical model for optimal placement of groups is constructed, which is formulated as a nonlinear continuous optimization problem. A new algorithm for finding feasible starting solutions to speed up and improve the local optimization procedure has been developed. The problem of analysis and modeling of the railway terminal operation during container reloading operations is analyzed. The problem of optimizing the assignment of trains on railway tracks during cargo handling at the railway terminal is investigated. The mathematical model and method of solving the problem are presented. An approach is proposed to increase the efficiency of container handling operations at the railway terminal. According to the approach, the placement of containers on railway platforms and in the storage area at the railway terminal is optimized. A mathematical model in the form of a combinatorial optimization problem is constructed; the properties of the model are analyzed. The use of the algorithms of the solution of problems of loading of containers in the subsystem "Planning of actions and preparation of decisions" of the Regional information and analytical subsystem on emergencies RIASE is recommended. The proposed methods and algorithms for solving the problems of optimal loading of containers can be used to increase the efficiency of transport companies.