Scheduling as a Constraint Satisfaction Problem (Using the Example of Open-Pit Minе Production Scheduling Problem)

The research described in the work is aimed at developing methods for Scheduling. The fundamental disadvantage of the existing methods of Mixed-Integer Linear Programming in application to the problems under consideration is the fact that they are too demanding on the amount of RAM. The difficulty of applying local search procedures to such high-dimensional problems is to develop an effective way to find an acceptable initial approximation and determine the neighboring state transition function, which would allow achieving the optimum fast enough. In the Operations Research Theory, adding additional conditions to a problem can lead to a fundamental change in the problem-solving scheme. The methods proposed in the study are implemented within the framework of the Constraint Programming Paradigm which makes it possible to represent the subject domain dependencies saving RAM, as well as to provide the ability to step-by-step take into account heterogeneous problem conditions without essentially changing the scheme of finding solutions. A significant part of the research deals with methods of logical inference on constraints to reduce the search space and speed up the computational process. The approach to scheduling is illustrated by the Open-Pit Mine Production Scheduling Problem, which was first proposed to be solved as a Constraint Satisfaction Problem. In order to find the first feasible solution, a «greedy» search method is proposed, the result of which can be improved using the developed hybrid method. Both methods rely on original procedures of inference on constraints. The proposed approach has proven its efficiency for block models with sizes of tens and hundreds of thousands of blocks.

constraint satisfaction problem, constraint programming, constraint propagation, local search, mixed-integer optimization, open pit mine production scheduling