Two essential ingredients of modern mixed-integerprogramming solvers are diving heuristics, which simulate a partial depth-first search in a branch-and-bound tree, and conflict analysis, which learns valid constraint...
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Two essential ingredients of modern mixed-integerprogramming solvers are diving heuristics, which simulate a partial depth-first search in a branch-and-bound tree, and conflict analysis, which learns valid constraints from infeasible subproblems. So far, these techniques have mostly been studied independently: primal heuristics for finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. In this paper, we pose the question of whether and how the orthogonal goals of proving infeasibility and generating improving solutions can be pursued in a combined manner such that a state-of-the-art solver can benefit. To do so, we integrate both concepts in two different ways. First, we develop a diving heuristic that simultaneously targets the generation of valid conflict constraints from the Farkas dual and the generation of improving solutions. We show that, in the primal, this is equivalent to the optimistic strategy of diving toward the best bound with respect to the objective function. Second, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classic coefficient diving. In a detailed computational study, both methods are evaluated on the basis of an implementation in the source-open-solver SCIP. The experimental results underline the potential of combining both diving heuristics and conflict analysis. Summary of Contribution. This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed-integer linear programs. It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be combined successfully with diving heuristics that aim at finding primal solutions. For two newly designed diving heuristics, this paper features a thoroughly computational study regarding their impact on the
We consider the discrete single-machine, multi-item lot-sizing and scheduling problem and we propose a Simulated Annealing (SA) approach together with a statistically-principled tuning procedure to solve it. We compar...
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We consider the discrete single-machine, multi-item lot-sizing and scheduling problem and we propose a Simulated Annealing (SA) approach together with a statistically-principled tuning procedure to solve it. We compare our solver with the state-of-the-art methods based on mixed integer programming (MIP), both on publicly-available instances and on a set of new, more challenging ones. In addition, we propose a hybrid SA/MIP method that combines the advantages of the pure methods on the challenging instances. The outcome is that our solver is able to find near-optimal solutions in short time for all instances, including those that are not solved by MIP methods. Instances and solutions are made available on the web for inspection and future comparisons.
We present two new mixed integer programming formulations for the order acceptance and scheduling problem in two machine flow shops. Solving this optimization problem is challenging because two types of decisions must...
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We present two new mixed integer programming formulations for the order acceptance and scheduling problem in two machine flow shops. Solving this optimization problem is challenging because two types of decisions must be made simultaneously: which orders to be accepted for processing and how to schedule them. To speed up the solution procedure, we present several techniques such as preprocessing and valid inequalities. An extensive computational study, using different instances, demonstrates the efficacy of the new formulations in comparison to some previous ones found in the relevant literature. (C) 2015 Elsevier B.V. All rights reserved.
This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows' C-p, as a goodness-of-fit measure, we formulate the subset selection problem as ...
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This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows' C-p, as a goodness-of-fit measure, we formulate the subset selection problem as a mixedinteger quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when the number of candidate explanatory variables is less than 30. Furthermore, when handling datasets consisting of a large number of samples, it finds better-quality solutions faster than stepwise regression methods do. (C) 2014 Elsevier Ltd. All rights reserved.
Soft constraints and penalty functions are commonly used in MPC to ensure that the optimization problem has a feasible solution, and thereby avoid MPC controller failure. On the other hand, soft constraints may allow ...
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Soft constraints and penalty functions are commonly used in MPC to ensure that the optimization problem has a feasible solution, and thereby avoid MPC controller failure. On the other hand, soft constraints may allow for unnecessary violations of the original constraints, i.e., the constraints may be violated even if a valid solution that does not violate any constraints exists. The paper develops procedures for the minimizing (according to some norm) of the Lagrange multipliers associated with a given mp-QP problem, assumed to originate from an MPC problem formulation. To this end the LICQ condition is exploited in order to efficiently formulate the optimization problem, and thereby improve upon existing mixedinteger formulations and enhance the tractability of the problem. The results are used to design penalty functions such that corresponding soft constraints are made exact, that is, the original (hard) constraints are violated only if there exists no solution where all constraints are satisfied. (C) 2013 Elsevier Ltd. All rights reserved.
The analytic hierarchy process is combined with multi-objective mixed integer programming to determine the optimal allocation of a limited number of aircraft among a group of airlift users with varying levels of prior...
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The analytic hierarchy process is combined with multi-objective mixed integer programming to determine the optimal allocation of a limited number of aircraft among a group of airlift users with varying levels of priority and length of usage. Canadian Forces airlift planners typically encounter such a capacity planning problem. The solution to this problem requires the constrained assignment of n variable length missions (tasks) integrating hundreds of airlift requests from several users with many priorities to m airframes (parallel machines).
Cutting plane methods are an important component in solving the mixed integer programming (MIP). By carefully studying the coefficient strengthening method, which is originally a presolving method, we are able to gene...
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Cutting plane methods are an important component in solving the mixed integer programming (MIP). By carefully studying the coefficient strengthening method, which is originally a presolving method, we are able to generalize this method to generate a family of valid inequalities called generalized coefficient strengthening (GCS) inequalities. The invariant property of the GCS inequalities is established under bound substitutions. Furthermore, we develop a separation algorithm for finding the violated GCS inequalities for a general mixedinteger set. The separation algorithm is proved to have the polynomial time complexity. Extensive numerical experiments are made on standard MIP test sets, which demonstrate the usefulness of the resulting GCS separator.
This paper presents a three-stage mixed integer programming approach for optimizing the skill mix and training schedule for aircraft maintenance workers. When all workers are trained for all skills, cheaper workforce ...
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This paper presents a three-stage mixed integer programming approach for optimizing the skill mix and training schedule for aircraft maintenance workers. When all workers are trained for all skills, cheaper workforce schedules are possible. However, the training that is required to acquire all those skills can become very expensive. In the first and second stage, we therefore make a trade-off between the training costs and the resulting cheaper workforce schedule. As we assume that workers are unavailable to work during their training, the resulting schedules are only applicable in practice if the required training can be performed without endangering the current maintenance operations. In the third stage, we therefore want to find an optimal and feasible training schedule in order to obtain the desired skill mix with minimal costs. A computational experiment based on real-life data of an aircraft maintenance company not only demonstrates that our models succeed in finding good solutions within reasonable computation times, but also illustrates how the explicit incorporation of skills training in the scheduling process can lead to significant cost savings. (C) 2017 Elsevier B.V. All rights reserved.
A number of alternative sources of electrical power are investigated for a rapidly developing country, Transkei. The alternatives comprise various hydroelectric projects and associated reservoirs, or purchase of elect...
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A number of alternative sources of electrical power are investigated for a rapidly developing country, Transkei. The alternatives comprise various hydroelectric projects and associated reservoirs, or purchase of electricity from the South African Electricity Supply Corporation (ESCOM). Each project is optimal at a different size, and being in the same river basin, the Mzimvubu basin, they are interdependent. mixed integer programming is used to select which source should be implemented at successive points in time. The ESCOM supply is regarded as a linear variable and the various hydroprojects handled as integers in order to conserve their integrity after project optimization. The effect of different inflation rates of hydro and coal-fired ESCOM power is found to affect the sequencing. With equal inflation, large storage is recommended for hydro, and with lower thermal cost inflation, minimal storage is preferred. The resulting optimal plan may be linked into a national economic master plan by using the decomposition principle.
This paper presents a solver, the PIMAGc, for optimization of constrained mixed integer programming problems based on the Compact Genetic Algorithm (cGA). As the cGA, the PIMAGc works with binary representation of var...
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This paper presents a solver, the PIMAGc, for optimization of constrained mixed integer programming problems based on the Compact Genetic Algorithm (cGA). As the cGA, the PIMAGc works with binary representation of variables. As comparison criteria and to measure the algorithm's performance, the PIMAGc was compared with the MI-LXPM, an appropriate algorithm for solving mixed integer programming problems. By using an appropriate number of problems, it was found that the PIMAGc outperformed the MI-LXPM with a greater success rate and a smaller number of evaluations on the majority of the problems, with equal performance on the others.
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