A computational study of cuts derived from the Chvatal-Gomory cut for interger programming problems

Orientador: Vinicius Amaral ArmentanoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Em 1958, Gomory propôs uma desigualdade válida ou corte a partir do tableau do método simplex para programação linear, que foi utilizado no primeiro método genérico para resolução de problemas de programação inteira. Em 1960, o corte foi estendido para problemas de programação inteira mista. Em 1973, Chvátal sugeriu um corte derivado da formulação original do problema de programação inteira, e devido à equivalência com o corte de Gomory, este passou a ser chamado de corte de Chvátal-Gomory. A importância do corte de Gomory só foi reconhecida em 1996 dentro do contexto do método branch-and-cut para resolução de problemas de programação inteira e programação inteira mista. Desde então, este corte é utilizado em resolvedores comerciais de otimização. Recentemente, diversos cortes novos derivados do corte de Chvátal-Gomory foram propostos na literatura para programação inteira. Este trabalho trata do desenvolvimento de algoritmos para alguns destes cortes, e implementação computacional em um contexto de branch-and-cut, no ambiente do resolvedor CPLEX. A eficácia dos cortes é testada em instâncias dos problemas da mochila multidimensional, designação generalizada e da biblioteca MIPLIB.Abstract: In 1958, Gomory proposed a valid inequality or cut from the tableau of the simplex method for linear programming, which was used in the first generic method for solving integer programming problems. In 1960, the cut was extended to handle mixed integer programming problems. In 1973, Chvátal suggested a cut that is generated from the original formulation of an integer programming problem, and due to the equivalence with the Gomory cut, it was named Chvátal-Gomory cut. The importance of the Gomory cut was recognized only in 1996 in the context of the branch-and-cut method for solving (mixed) integer programming problems. Today, such a cut is utilized in optimization commercial solvers. Recently, several new cuts derived from the Chvátal-Gomory cut have been proposed in the literature for integer programming. This work deals with the development of algorithms and computational implementations for some of the new proposed cuts, in a context of the branch-and-cut method, by using the CPLEX solver. The efficiency of the cuts is tested on instances of the multi-dimensional knapsack, generalized assignment problems, and instances from the MIPLIB library.MestradoAutomaçãoMestre em Engenharia Elétric

The development of methods for the design and evolution of reconfigurable cellular manufacturing systems.

Doctor of Philosophy in Engineering (Mechanical Engineering)The concept of reconfigurable manufacturing is presently being researched due to the need for production systems that are able to economically respond to changes in markets and the rapid introduction of new products. Cellular Manufacturing Systems (CMS) are a central concept in just-in-time and lean manufacturing. Although CMS are able to provide a strategic operating advantage, machine cell clusters do not remain optimal over an extended period of time. The concept of a Dynamic CMS (DCMS) has received attention in recent years; a DCMS is a system where the layout of machines change in order to improve the responsiveness of CMS to changing production requirements. A deficiency in existing DCMS methods is that reconfiguration plans are generated without the consideration of an initial design of the factory floor space for future change. This research distinguishes Reconfigurable CMS (RCMS) from DCMS, as a system that is designed at the outset for changes to system layout and cell configurations. The concept of a Factory Configuration Template (FCT) is proposed in this research; the FCT is a design of the factory floor space to ensure the feasible implementation of reconfiguration plans generated by mathematical models. A nine step method for FCT design is presented that uses a Simultaneous Fuzzy Clustering Heuristic to develop manufacturing cells and part families. A Tabu Search algorithm was develop to generate the optimal arrangement of machine sites in cells. Three multi-period machine assignment models were developed that determine reconfiguration plans based on changing product demand and the introduction of new products. The models that were developed included two integer linear programs that determine the distribution of machine resources among cells over multiple periods. A quadratic zero-one programming model was developed that distributes machines among available sites in cells to promote unidirectional part flow. The results show that RCMS is able to provide a more economical solution than traditional CMS with the added advantage of improved part flow in the system

Generating general-purpose cutting planes for mixed-integer programs

Franz WesselmannPaderborn, Univ., Diss., 201