A New Algorithm for Solving a Special Matching Problem with a General Form Value Function under Constraints

• Published in: Automation and remote control Vol. 80; no. 1; pp. 81 - 92
• Main Authors: Uzhegov, D. V., Anan’ev, A. A., Lomovitskii, P. V., Khlyupin, A. N.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2019; Springer Nature B.V
• Subjects: Algorithms; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Computer-Aided Engineering (CAD; Control; Control in Technical Systems; Graph theory; Matching; Mathematics; Mathematics and Statistics; Mechanical Engineering; Mechatronics; Operations research; Permutations; Robotics; Shortest-path problems; Systems Theory; Well drilling; shortest path in a graph; quadratic assignment problem; invalid matchings; Dijkstra’s algorithm
• ISSN: 0005-1179; 1608-3032
• DOI: 10.1134/S0005117919010077

We consider the assignment problem with a special structure with a general form value function and constraints prohibiting certain matchings. In this case, the matching cost may be undefined until some permutation is found. We formulate the problem in terms of graph theory and reduce it to finding a minimal cost path in a graph with nonlocal edge weights. The proposed method for solving the problem is a modification of the Dijkstra’s shortest path algorithm in a weighted directed graph. This research is motivated by well drilling applications. We also show the analysis of our numerical experiments.