On the Use of Gray Codes for Solving 0-1 Combinatorial Problems of Optimization in Environmental and Economic Systems

Introduction. The application of binary-reflected (mirror, reflexive) Gray codes for solving combinatorial problems with pseudo-Boolean functions (polynomials from Boolean variables) is considered. A recursive Ehrlich algorithm given generating a sequence lines n-bit codes, in which each subsequent line differs the previous one by only digit (bit). As an example effectiveness use these solution two variables complete enumeration solutions considered, and it shown how can be used to efficiently calculate values objective function constraints. results experimental study are presented, show that practically applied branching schemes, example, branch bound method, when number nodes decision does not exceed 35. Purpose. purpose article developers algorithms programs apply various schemes algorithm, binary (Boolean) at tree small (less than 35). technique. research methodology based on computational experiment 0-1 knapsack problem proposed exhaustive search partial full recalculation constraint problem. During experiment, accuracy “greedy” heuristic time complexity O(n2) was also checked. Results. result found restrictions practical calculations faster average 7 times. "greedy" practice solve large dimension (more 10,000 items), need obtain approximate value limited computing resources. Scientific novelty significance. work lies approach optimization using codes. efficiency constraints shown, its algorithm. Keywords: problems, time.