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41
A Parallel Genetic Algorithm for the Set Partitioning Problem
, 1994
"... In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problema difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed stea ..."
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Cited by 81 (2 self)
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In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problema difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed steadystate genetic algorithm in conjunction with a specialized local search heuristic for solving the set partitioning problem. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steadystate genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty realworld set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, highquality integer feasible solutions were found for problems with 36,699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints.
Computational Study of a Family of MixedInteger Quadratic Programming Problems
 Mathematical programming
, 1995
"... . We present computational experience with a branchandcut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in financial applications. The algorithm solves the largest reallife problems in a few minutes of run ..."
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Cited by 71 (6 self)
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. We present computational experience with a branchandcut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in financial applications. The algorithm solves the largest reallife problems in a few minutes of runtime. 1 Introduction. We are interested in optimization problems QMIP of the form: min x T Qx + c T x s.t. Ax b (1) jsupp(x)j K (2) 0 x j u j ; all j (3) where x is an nvector, Q is a symmetric positivesemidefinite matrix, supp(x) = fj : x j ? 0g and K is a positive integer. Problems of this type are of interest in portfolio optimization. Briefly, variables in the problem correspond to commodities to be bought, the objective is a measure of "risk", the constraints (1) prescribe levels of "performance", and constraint (2) specifies that not too many 1 different types of commodities can be chosen. All data is derived from statistical information. A good deal of previous work ha...
A Computational Study of Search Strategies for Mixed Integer Programming
 INFORMS Journal on Computing
, 1997
"... The branch and bound procedure for solving mixed integer programming (MIP) problems using linear programming relaxations has been used with great success for decades. Over the years, a variety of researchers have studied ways of making the basic algorithm more effective. Breakthroughs in the fiel ..."
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Cited by 63 (7 self)
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The branch and bound procedure for solving mixed integer programming (MIP) problems using linear programming relaxations has been used with great success for decades. Over the years, a variety of researchers have studied ways of making the basic algorithm more effective. Breakthroughs in the fields of computer hardware, computer software, and mathematics have led to increasing success at solving larger and larger MIP instances. The goal of this paper is to survey many of the results regarding branch and bound search strategies and evaluate them again in light of the other advances that have taken place over the years. In addition, novel search strategies are presented and shown to often perform better than those currently used in practice. October 1997 The effectiveness of the branch and bound procedure for solving mixed integer programming (MIP) problems using linear programming relaxations is well documented. After the introduction of this procedure in the 1960's [26] [10]...
Progress in linear programmingbased algorithms for integer programming: An exposition
 INFORMS JOURNAL ON COMPUTING
, 2000
"... This paper is about modeling and solving mixed integer programming (MIP) problems. In the last decade, the use of mixed integer programming models has increased dramatically. Fifteen years ago, mainframe computers were required to solve problems with a hundred integer variables. Now it is possible t ..."
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Cited by 30 (0 self)
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This paper is about modeling and solving mixed integer programming (MIP) problems. In the last decade, the use of mixed integer programming models has increased dramatically. Fifteen years ago, mainframe computers were required to solve problems with a hundred integer variables. Now it is possible to solve problems with thousands of integer variables on a personal computer and obtain provably good approximate solutions to problems such as set partitioning with millions of binary variables. These advances have been made possible by developments in modeling, algorithms, software, and hardware. This paper focuses on effective modeling, preprocessing, and the methodologies of branchandcut and branchandprice, which are the techniques that make it possible to treat problems with either a very large number of constraints or a very large number of variables. We show how these techniques are useful
Application of a Hybrid Genetic Algorithm to Airline Crew Scheduling
 Computers & Operations Research
, 1996
"... This paper discusses the development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steadystate genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of forty realworld problems. It found the ..."
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This paper discusses the development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steadystate genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of forty realworld problems. It found the optimal solution for half the problems, and good solutions for nine others. The results were compared to those obtained with branchandcut and branchand bound algorithms. The branchandcut algorithm was significantly more successful than the hybrid algorithm, and the branchandbound algorithm slightly better. 1 Introduction Genetic algorithms (GAs) are search algorithms that were developed by John Holland [17]. They are based on an analogy with natural selection and population genetics. One common application of GAs is for finding approximate solutions to difficult optimization problems. In this paper we describe the application of a hybrid GA (a genetic algorithm combined with a local s...
Algorithms and software for convex mixed integer nonlinear programs
, 2009
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 28 (4 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
FATCOP 2.0: Advanced Features in an Opportunistic Mixed Integer Programming Solver
"... We describe FATCOP 2.0, a new parallel mixed integer program solver that works in an opportunistic computing environment provided by the Condor resource management system. We outline changes to the search strategy of FATCOP 1.0 that are necessary to improve resource utilization, together with new te ..."
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Cited by 27 (10 self)
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We describe FATCOP 2.0, a new parallel mixed integer program solver that works in an opportunistic computing environment provided by the Condor resource management system. We outline changes to the search strategy of FATCOP 1.0 that are necessary to improve resource utilization, together with new techniques to exploit heterogeneous resources. We detail several advanced features in the code that are necessary for successful solution of a variety of mixed integer test problems, along with the different usage schemes that are pertinent to our particular computing environment. Computational results demonstrating the effects of the changes are provided and used to generate effective default strategies for the FATCOP solver.
FATCOP: A fault tolerant CondorPVM mixed integer program solver. Mathematical Programming
, 1999
"... Abstract. We describe FATCOP, a new parallel mixed integer program solver written in PVM. The implementation uses the Condor resource management system to provide a virtual machine composed of otherwise idle computers. The solver differs from previous parallel branchandbound codes by implementing ..."
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Cited by 25 (4 self)
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Abstract. We describe FATCOP, a new parallel mixed integer program solver written in PVM. The implementation uses the Condor resource management system to provide a virtual machine composed of otherwise idle computers. The solver differs from previous parallel branchandbound codes by implementing a general purpose parallel mixed integer programming algorithm in an opportunistic multiple processor environment, as opposed to a conventional dedicated environment. It shows how to make effective use of resources as they become available while ensuring the program tolerates resource retreat. The solver performs well on test problems arising from real applications and is particularly useful for solving long running hard mixed integer programming problems.
A problemspecific faulttolerance mechanism for asynchronous, distributed systems
 In Proceedings of the International Conference on Parallel Processing 2000
, 2000
"... The idle computers on a local area, campus area, or even wide area network represent a significant computational resource—one that is, however, also unreliable, heterogeneous, and opportunistic. We describe an algorithm that allows branchandboundproblems to be solved in such environments. In desig ..."
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Cited by 19 (0 self)
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The idle computers on a local area, campus area, or even wide area network represent a significant computational resource—one that is, however, also unreliable, heterogeneous, and opportunistic. We describe an algorithm that allows branchandboundproblems to be solved in such environments. In designing this algorithm, we faced two challenges: (1) scalability, to effectively exploit the variably sized pools of resources available, and (2) fault tolerance, to ensure the reliability of services. We achieve scalability through a fully decentralized algorithm, in which the dynamically available resources are managed through a membership protocol. We guarantee fault tolerance in the sense that the loss of up to all but one resource will not affect the quality of the solution. For propagating information reliably, we use epidemic communication for both the membership protocol and the faulttolerance mechanism. We have developed a simulation framework that allows us to evaluate design alternatives. Results obtained in this framework suggest that our techniques can execute scalably and reliably. 1.