It is known that a large number of applied optimization problems can’t be exactly solved nowadays, because their computational complexity is related to the NP-hard class. In many cases metaheuristics of various types are used to search for approximate solutions, but the choice of the concrete metaheuristic has open question of the quality of the chosen method. There are several possible solutions to this problem, one of which is the verification of metaheuristic algorithms using examples from known test libraries with known records. Another approach to solving the problem of evaluating the quality of algorithms is to compare the "new" algorithm with other algorithms, the work of which has already been investigated. The construction a generator of random problems with a known optimal solution can solve the problem of obtaining "average" estimates of the accuracy for used algorithm in comparison with other methods. The article considers the construction of generators of random non-waste maps of rec-tangular cutting with restrictions on the rectangles of limited sizes. The existence of sets of such cards forms the basis of test problems for checking the quality of approximate algorithms for searching for optimal solution. Rectangular cutting, which is considered in the article, is also the basis for building cuts using more complex shapes. As the simplest method of generating random rectangular non-waste maps, considered a method that uses guillotine cutting. Also, a more complex algorithm for generating a random rectangular cut is given, whose job is to generate a random dot grid and remove some random points from this grid. Much attention is paid to the implementation of the above methods, since the main purpose of the article is to simplify using of generators in practice. All the above algorithms are already used in the software system for testing evolution-aryfragmentary algorithms for various classes of optimization problems on the graphs
Quadratization and Roof Duality of Markov Logic Networks
