Heuristic and metaheuristic methods, which are nondeterministic schemes based on the use of local search methods that search for acceptable solutions in the area of global or local optima, have proven themselves well for solving NP-hard discrete optimization problems. Metaheuritic methods of artificial intelligence provide fast obtaining of solutions close to optimal, but at the same time they cannot guarantee that the fitness function will fall into the global optimum in a predetermined time interval. Therefore, the problem of increasing the speed and quality of suboptimal solutions obtained by various metaheuristic optimization algorithms remains relevant. The chapter discusses the development and analysis of heuristic and metaheuristic methods for solving optimization problems of cutting and packing. New heuristics for the placement of two-dimensional and three-dimensional orthogonal objects designed in relation to a multimethod genetic algorithm are proposed. The effectiveness of application heuristic and metaheuristic algorithms for optimizing the solution of cutting and packing problems has been investigated when solving various sets of standard test problems of optimized placement of rectangles and parallelepipeds.