A Procedure for Computing theKBest Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem

1972 ◽  
Vol 18 (7) ◽  
pp. 401-405 ◽  
Author(s):  
Eugene L. Lawler
Keyword(s):  
Shortest Path ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Shortest Path Problem ◽  
Discrete Optimization Problems

scholarly journals Network Models for Multiobjective Discrete Optimization

2021 ◽  
Author(s):  
David Bergman ◽  
Merve Bodur ◽  
Carlos Cardonha ◽  
Andre A. Cire
Keyword(s):  
Shortest Path ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Pareto Frontier ◽  
Network Models ◽  
Set Covering ◽  
Objective Functions ◽  
Nondominated Solutions ◽  
Discrete Optimization Problems

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

A Continuous Strategy to Solve a Class of Discrete Optimization Problems

2010 ◽  
Vol 36 ◽  
pp. 279-286 ◽  
Author(s):  
Roberto Quirino do Nascimento ◽  
Edson Figueiredo Lima ◽  
Rubia Mara de Oliveira Santos
Keyword(s):  
Discrete Optimization ◽  
Optimization Problems ◽  
Discrete Optimization Problems

scholarly journals Подход к решению задачи оптимизации логистики агрохолдинга

2013 ◽  
pp. 139-144
Author(s):  
Е. В. Скакалина
Keyword(s):  
Information Technology ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Implementation Process ◽  
Optimal Solutions ◽  
New Class ◽  
Modern Computer ◽  
Foreign Countries ◽  
Intensive Development ◽  
Discrete Optimization Problems

У роботі наведено короткий аналіз використання інформаційних технологій в аграрному напрямі. Вказу-ється на можливість удосконалення управління проце-сом реалізації логістики великих агрохолдингів за раху-нок використання ефективного методу побудови оп-тимальних рішень для узагальнень задачі про призна-чення. Представлений новий клас дискретних оптимі-заційних задач. Звертається увага на інтенсивний роз-виток логістики у зарубіжних країнах на основі викори-стання сучасних комп'ютерних технологій. The paper presents a brief analysis of the use of information technology in the agricultural area. The possibility of improvement of management of logistics implementation process of large agricultural holdings through the use of an effective method of optimal solutions constructing for generalizations of the assignment problem is shown. A new class of discrete optimization problems is presented. The attention is drawn to the intensive development of logistics in foreign countries on the basis of use of modern computer technologies.

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