Showing papers on "Integer programming published in 1992"
TL;DR: This paper presents a new optimization algorithm capable of optimally solving 100-customer problems of the vehicle routing problem with time windows VRPTW and indicates that this algorithm proved to be successful on a variety of practical sized benchmark VRPTw test problems.
Abstract: The vehicle routing problem with time windows VRPTW is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service. In this paper, we present the development of a new optimization algorithm for its solution. The LP relaxation of the set partitioning formulation of the VRPTW is solved by column generation. Feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming. The LP solution obtained generally provides an excellent lower bound that is used in a branch-and-bound algorithm to solve the integer set partitioning formulation. Our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark VRPTW test problems. The algorithm was capable of optimally solving 100-customer problems. This problem size is six times larger than any reported to date by other published research.
1,085 citations
TL;DR: In this paper, the loss minimum reconfiguration problem in the open loop radial distribution system is formulated as a mixed integer programming problem and a detailed solution methodology by the use of genetic algorithm is outlined.
Abstract: The loss minimum reconfiguration problem in the open loop radial distribution system is basically one of complex combinatorial optimization, since the normal open sectionalizing switches must be determined appropriately. The genetic algorithm was successfully applied to the loss minimum reconfiguration problem. In the proposed algorithm, strings consist of sectionalizing switch status or radial configurations, and the fitness function consists of the total system losses and penalty value of voltage drop and current capacity violations. The loss minimum reconfiguration problem is formulated as a mixed integer programming problem. The essential components of the genetic algorithm are briefly described. A detailed solution methodology by the use of genetic algorithm is outlined. Numerical examples demonstrate the validity and effectiveness of the proposed methodology. >
700 citations
TL;DR: A fundamental analis step in an ad',nced optimizing compiler (as well as many other software tools) is data dependence analysis f o r arrays, which determines whether two references to an array can refer to the same e lement and under what conditions.
Abstract: ndamental analis step in an ad',nced optimizing compiler (as well as many other software tools) is data dependence analysis f o r arrays. This means deciding i f two references to an array can refer to the same e lement and i f so, under what conditions. This information is used to determine allowable program transformations and optimizations. For example, we can determine that in the fo l lowing code fragment , no location o f the array is both read and written. Once we also verify that no location is writ ten more than once, we know that the writes can be done in any order. for i = 1 to 100 do f o r j -i to 100 do A[i, j + 11 = A[100,j]
590 citations
TL;DR: Preliminary numerical results on several test problems are reported which show that the expense of solving the MI need to be enumerated, while in most cases the number of NLP subproblems to be solved remains the same.
423 citations
TL;DR: In this research, a concept of coverage is defined, and methods on how to locate monitoring stations in a network are described, and the best set of stations is one that maximizes the coverage.
Abstract: The Safe Drinking Water Act requires that the water quality in water distribution systems is to be sampled at locations that are representative of the system; but the act does not describe how the sampling should be done. In this research, a concept of coverage is defined, and methods on how to locate monitoring stations in a network are described. The best set of stations is one that maximizes the coverage. The problems were formulated as integer programming problems, and were solved on a PC using an integer programming code. Two examples of their application to real systems are shown.
232 citations
TL;DR: In this paper, the authors consider non-preemptive single machine scheduling problems using time-indexed variables and derive a variety of valid inequalities, and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities.
Abstract: We consider the formulation of non-preemptive single machine scheduling problems using time-indexed variables. This approach leads to very large models, but gives better lower bounds than other mixed integer programming formulations. We derive a variety of valid inequalities, and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities. A cutting plane/branch-and-bound algorithm based on these inequalities has been implemented. Computational experience on small problems with 20/30 jobs and various constraints and objective functions is presented.
225 citations
TL;DR: The fuzzy optimization techniques can be useful during initial stages of the conceptual design of engineering systems where the design goals and design constraints have not been clearly identified or stated, and for decision making problems in ill-structured situations.
Abstract: A multiobjective reliability apportionment problem for a series system with time-dependent reliability is presented. The resulting mathematical programming formulation determines the optimal level of component reliability and the number of redundant components at each stage. The problem is a multiobjective, nonlinear, mixed-integer mathematical programming problem, subject to several design constraints. Sequential unconstrained minimization techniques in conjunction with heuristic algorithms are used to find an optimum solution. A generalization of the problem in view of inherent vagueness in the objective and the constraint functions results in an ill-structured reliability apportionment problem. This multiobjective fuzzy optimization problem is solved using nonlinear programming. The computational procedure is illustrated through a numerical example. The fuzzy optimization techniques can be useful during initial stages of the conceptual design of engineering systems where the design goals and design constraints have not been clearly identified or stated, and for decision making problems in ill-structured situations. >
224 citations
Dissertation•
01 Feb 1992
TL;DR: In this paper, the authors formulated and studied several integer programming models to assign ground-holding delays optimally in a general network of airports, so that the total (ground plus airborne) delay cost of all flights is minimized.
Abstract: Motivated by the important problem of congestion costs (they were estimated to be $2 billion in 1991) in air transportation and observing that ground delays are more preferable than airborne delays, we have formulated and studied several integer programming models to assign ground-holding delays optimally in a general network of airports, so that the total (ground plus airborne) delay cost of all flights is minimized. All previous research on this problem has been restricted to the single-airport case, which neglects "down-the-road" effects due to transmission of delays between successive flights performed by the same aircraft. We formulate several models, and then propose a heuristic algorithm which finds a feasible solution to the integer program by rounding the optimal solution of the LP relaxation. Finally, we present extensive computational results with the goal of obtaining qualitative insights on the behavior of the problem under various combinations of the input parameters. We demonstrate that the problem can be solved in reasonable computation times for networks with at least as many as 6 airports and 3,000 flights. Congestion problems are becoming increasingly I ~~ acute in many major European and American airports. For European airlines, the total yearly delay cost due to congestion (including cost to passengers) was estimated to be $5 billion in 1989 (Terrab 1990). For U.S. airlines, the direct delay cost due to congestion is claimed to amount to approximately $2 billion per year. Given the fact that the total profits of the U.S. airline industry rarely exceed $1 billion, congestion problems are a phenomenon of undeniable significance.
210 citations
TL;DR: The method applies to reliability optimization problems for general systems, enabling complex systems such as communication networks to be treated and compared with other approaches to show the efficiency of the method.
Abstract: A method for solving the problem of optimizing both, redundancy (number of redundant components) and component reliability in each stage of a system under multiple constraints is presented. A mixed-integer nonlinear programming formulation and the surrogate dual method are used. The solution of the surrogate dual problem is not always feasible in the original problem, that is, a 'surrogate gap' exists. Two countermeasures to surrogate gaps are considered: (1) modifying the original problem to tighten the constraints, with the modification being continued until the solution of the surrogate dual problem of the modified problem becomes feasible in the original problem, and (2) decreasing component reliabilities in the vertical direction to the tangential plane of the objective function. The method applies to reliability optimization problems for general systems, enabling complex systems such as communication networks to be treated. Some computational results are shown and compared with other approaches; they show the efficiency of the method. >
147 citations
TL;DR: In this paper, an integer-programming formulation for the design of symmetric and balanced laminated plates under biaxial compression is presented, where both maximization of buckling load for a given total thickness and minimization of total thickness subject to a buckling constraint are formulated.
Abstract: Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.
143 citations
TL;DR: In this paper, a Lagrangean relaxation-based heuristic procedure was developed to generate near-optimal solutions to very large-scale capacitated lot-sizing problems with setup times and limited overtime.
Abstract: In this paper, we develop a Lagrangean relaxation-based heuristic procedure to generate near-optimal solutions to very-large-scale capacitated lot-sizing problems CLSP with setup times and limited overtime. Our computational results show that large problems involving several thousand products and several thousand 0/1 integer variables can be solved in a reasonable amount of computer time to within one percent of their optimal solution. The proposed procedure is general enough to be applied directly or with slight modification to real-life production problems.
TL;DR: An optimization approach to the design of products in a concurrent engineering environment is explored which allows for the incorporation of concurrent engineering design attributes in the objective function using a five-step algorithm containing attribute-based utility values.
Abstract: In this paper an optimization approach to the design of products in a concurrent engineering environment is explored. A five-step algorithm containing attribute-based utility values is utilized which allows for the incorporation of concurrent engineering design attributes in the objective function. Two integer programming models are presented. Model 1 considers module/part interactions; however, it does not consider the interactions among various part options making up a product. Model 2 considers both interactions and also results in groups of part options that can be designed and manufactured together. In each step of the optimization process, the design of a pad assembly of a braking system is considered and explained.
TL;DR: In this paper, an integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented, where the design variables that define the stacking sequence of the laminate are ply-identity zero-one integers.
Abstract: An integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented. The design variables that define the stacking sequence of the laminate are ply-identity zero-one integers. The buckling constraint is linear in terms of the ply-identity design variables, but strains are nonlinear functions of these variables. A linear approximation is developed for the strain constraints so that the problem can be solved by sequential linearization using the branch and bound algorithm. Examples of graphite-epox y plates under biaxial compression are presented. Optimum stacking sequences obtained using the linear approximation are compared with global optimum designs obtained using a genetic search procedure.
TL;DR: It is shown that the new technique proposed in this paper is not only useful in linearizing binary quadratic and cubic integer problems, but also applicable to the case of quadRatic and to a certain class of cubic “mixed-integer” problems.
Abstract: Several techniques of linearization have appeared in the literature. The technique of F. Glover, which seems to be the most efficient, linearizes a binary quadratic integer problem of n variables by introducing n new continuous variables and 4n auxiliary linear constraints. The new technique proposed in this paper is not only useful in linearizing binary quadratic and cubic integer problems, but also applicable to the case of quadratic and to a certain class of cubic “mixed-integer” problems. It is shown that the new technique further reduces the number of auxiliary linear constraints from 4n to n, while keeping the number of new continuous variables at n for the binary quadratic integer problem of n variables. And, it requires, in the case of a certain class of cubic mixed-integer problems having 2n of 0–1 variables, only 3n auxiliary linear constraints and the same number of new continuous variables. The analytical superiority of the new linearization technique has also been observed, in terms of the nu...
TL;DR: A dual adjustment procedure, which exploits the structure of the model, is used to implement the relaxation and makes it possible to efficiently obtain close-to-optimal solutions to problems of realistic size.
Abstract: The problem of determining optimal train connections, frequencies, and blocking and routing plans for freight cars in single-carload general commodity service is modeled as an all-integer linear programming problem. The objective is to minimize train cost, car time cost, and yard classification cost, subject to limits on train size, number of blocks formed by yard, and maximum origin-to-destination trip times. A Lagrangian relaxation technique is used to solve the problem. A dual adjustment procedure, which exploits the structure of the model, is used to implement the relaxation. This procedure makes it possible to efficiently obtain close-to-optimal solutions to problems of realistic size.
TL;DR: In this article, the authors developed several optimal/near-optimal procedures for the Capacitated Lot-Sizing and Scheduling Problem (CLSP) with setup times, limited regular time and limited overtime.
TL;DR: In this paper, the authors show that many nonlinear models for batch design which are based on the assumption of continuous sizes can be reformulated as MILP problems when sizes are restricted to discrete values.
Abstract: The objective of the paper is to show that many nonlinear models for batch design which are based on the assumption of continuous sizes can be reformulated as MILP problems when sizes are restricted to discrete values. Problems considered include multiproduct plants operating with single product and mixed product campaigns, and multipurpose plants with single and multiple production routes. It is shown that, by exploiting the structure of the proposed MILP models, solutions can be obtained with modest computational effort. In addition, as opposed to the use of rounding schemes for continuous models, global optimum solutions are guaranteed
TL;DR: An efficient and interactive two-stage heuristic for the generation of block layouts is presented, which generates a hexagonal and maximum weight planar adjacency subgraph, which incorporates relationships with the outside of the layout in a consistent manner.
TL;DR: In this article, power system engineering applications of linear programming and indicate the potential for its future use are outlined in three areas: generation scheduling, loss minimization through allocation of reactive power supply, and planning of capital investments in generation equipment.
Abstract: The authors discuss power system engineering applications of linear programming and indicate the potential for its future use. Applications are outlined in three areas: generation scheduling, loss minimization through allocation of reactive power supply, and planning of capital investments in generation equipment. It is recommended that power system planning models should incorporate financial flows with the linear programming approach to capital budgeting originally formulated in 1963 by H.M. Weingartner. The need for such an approach is illustrated with examples of how capital market conditions can upset the type of engineering economic decision making currently used in planning models. The Lagrangian relaxation method, which can extend computational feasibility for linear and integer programming, is also described. >
TL;DR: An extension of an earlier integer programming model developed by other authors to formulate a general n-job, m-machine job-shop problem involves substantially fewer functional constraints at the expense of an increase in the number of upper bound variables.
Abstract: This paper presents an extension of an earlier integer programming model developed by other authors to formulate a general n-job, m-machine job-shop problem. The new formulation involves substantially fewer functional constraints at the expense of an increase in the number of upper bound variables. This reduction of functional constraints, together with the imposition of upper and lower bounds on the objective value, significantly reduces the computation time for solving the integer model for the job-shop scheduling problem.
TL;DR: In this paper, an integer programming formulation of the problem is given, and an iterative heuristic algorithm is described which makes use of a lower bound derived from the mathematical formulation.
TL;DR: An integer programming (IP) model, which simultaneously schedules and allocates functional units, registers, and buses, is presented for synthesizing cost-constrained globally optimal architectures, which are synthesized in faster CPU times than in previous research.
Abstract: An integer programming (IP) model, which simultaneously schedules and allocates functional units, registers, and buses, is presented for synthesizing cost-constrained globally optimal architectures. This research is important to industry because it provides optimal schedules that minimize interconnect costs and interface to analog and asynchronous processes, since these are seen as key to synthesizing high-performance architectures. A mathematical IP model of the architectural synthesis problem is formulated. A subset of the constraints is transformed into the node-packing problem and integral facets are extracted and generalized. Other constraints are tightened or mapped into the knapsack problem and facets are extracted and generalized. Area-delay cost functions are minimized using branch and bound on the resulting IP model. Globally optimal architectures are synthesized in faster CPU times than in previous research. >
TL;DR: This work proposes two reformulations of the conventional MILP model, one of which is an NLP reformulation which very quickly yields good suboptimal solutions and the other an MILP reformulation for exact solutions which leads to up to an order of magnitude faster computational results for large problems due to its tighter linear programming relaxation.
Abstract: The problem of selecting processes and capacity expansion policies for a chemical complex consisting of continuous chemical processes can be formulated as a multiperiod, mixed integer linear programming (MILP) problem. Based on a variable disaggregation technique which exploits lot sizing substructures, we propose two reformulations of the conventional MILP model. The first one is an NLP reformulation which very quickly yields good suboptimal solutions. The second is an MILP reformulation for exact solutions which leads to up to an order of magnitude faster computational results for large problems due to its tighter linear programming relaxation.
TL;DR: Two approaches incorporating the analytic hierarchy process (AHP) are presented, one of which utilizes AHP in conjunction with integer programming while an alternative approach uses goal programming coupled with the AHP.
Abstract: This paper addresses the media selection problem, a special form of resource allocation problem. After reviewing characteristics of media decisions and existing analytical approaches, two approaches incorporating the analytic hierarchy process (AHP) are presented. The recommended approach utilizes AHP in conjunction with integer programming while an alternative approach uses goal programming coupled with the AHP. Those specific characteristics of AHP that make it particularly well suited to the media selection problem are discussed.
TL;DR: An interactive optimization system for multiperiod exhaust relief planning in the local loop of a public telephone network is described, which decomposes the optimization problem into a single-period dynamic programming problem, and a multiperiod greedy heuristic.
Abstract: We describe an interactive optimization system for multiperiod exhaust relief planning in the local loop of a public telephone network. In exhaust relief planning in the local loop one seeks the minimum cost capacity expansion plan that meets projected demand over a given planning horizon. The problem can be modeled as an integer programming problem. However, due to cost structures and varying transmission technologies, the single-period exhaust relief planning problem is NP-complete. The size of the problem precludes the use of general purpose integer programming. Based on the mathematical structure and complexity of the problem, we decompose the optimization problem into a single-period dynamic programming problem, and a multiperiod greedy heuristic. A software system surrounds the optimization algorithm and provides interactive planning capabilities, before and after creation of the optimized plan. Important aspects of the system are the model assumptions made to keep the problem tractable, and their effect on the standardization of input data and methodology. The system is in use by several hundred outside plant planners in a major U.S. telephone company. An overview of major elements of the package is given as well as a summary of important implementation issues that arose during the first three years of the on-going project.
TL;DR: An outer-approximation-based decomposition method for solving multiperiod multiproduct batch plant problems operating with single product campaigns and its results are compared with existing general solution methods.
Abstract: We address the development of an efficient optimization method for convex nonlinear and mixed-integer nonlinear multiperiod design optimization problems. An outer-approximation-based decomposition method for solving these problems is proposed. The method is applied to multiperiod multiproduct batch plant problems operating with single product campaigns. Multiperiod models are presented for the design and future capacity expansions of such plants. Numerical results are compared with existing general solution methods such as MINOS and SQP for the nonlinear programming case and DICOPT++ for the mixed-integer nonlinear programming case
TL;DR: It is shown how the resolution method of theorem proving can be extended to obtain a procedure for solving a fundamental problem of integer programming, that of finding all valid cuts of a set of linear inequalities in 0-1 variables.
Abstract: We show how the resolution method of theorem proving can be extended to obtain a procedure for solving a fundamental problem of integer programming, that of finding all valid cuts of a set of linear inequalities in 0-1 variables. Resolution generalizes to two cutting plane operations that, when applied repeatedly, generate all strongest possible or “prime” cuts (analogous to prime implications in logic). Every valid cut is then dominated by at least one of the prime cuts. The algorithm is practical when restricted to classes of inequalities within which one can easily tell when one inequality dominates another. We specialize the algorithm to several such classes, including inequalities representing logical clauses, for which it reduces to classical resolution.
03 Jan 1992
TL;DR: This paper deals with a special class of nonlinear discrete design optimization problems which involve nonlinear separable objective functions and bilinear constraints and identifies two special cases for which advantage can be taken of the discrete nature of the design variables to reformulate these problems as MILP models which can be solved to global optimality.
Abstract: This paper deals with a special class of nonlinear discrete design optimization problems which involve nonlinear separable objective functions and bilinear constraints. These constraints involve products of design and state variables in which the former are restricted to take discrete values Two special cases are identified for which advantage can be taken of the discrete nature of the design variables to reformulate these problems as MILP models which can be solved to global optimality. The computational expense can be reduced with SOS 1 sets and a simple solution strategy that is proposed. The application of the MILP reformulations is applied to multiproduct batch plant problems in chemical engineering and 1 Engineering Design Research Center, Carnegie Mellon University, Pittsburgh, PA 15213. The authors gratefully acknowledge financial support from the Engineering Design Research Center. University Ubraritt Carnegie Msiion y | Pittsburgh PA l to structural design problems in civil engineering. Numerical results and comparisons with other methods are also presented.
10 May 1992
TL;DR: A heuristic algorithm based on Lagrangian optimization and using an operational rate-distortion framework that, with much-reduced computing complexity, approaches the optimally achievable SNR is provided.
Abstract: The description of the buffer-constrained quantization problem is formalized. For a given set of admissible quantizers for coding a discrete nonstationary signal sequence in a buffer-constrained environment, and for any global distortion minimization criterion that is additive over the individual elements of the sequence, the optimal solution and slightly suboptimal but much faster approximations are formulated. The problem is first defined as one of constrained, discrete optimization, and its equivalence to some problems in integer programming is established. Dynamic programming using the Viterbi algorithm is shown to provide a way of computing the optimal solution. A heuristic algorithm based on Lagrangian optimization and using an operational rate-distortion framework that, with much-reduced computing complexity, approaches the optimally achievable SNR is provided. >
01 Jul 1992
TL;DR: An ILP model for minimizing multiplexer and wiring areas has been mathematically formulated and optimally solved and handles chaining, multi-cycle operations, pipelined modules, conditional branches and trades off wiring area with resource area.
Abstract: The authors present an integer linear program (ILP) formulation for the allocation and binding problem in high-level synthesis. Given a behavioral specification and a time-step schedule of operations, the formulation minimizes wiring and multiplexer areas. An ILP model for minimizing multiplexer and wiring areas has been mathematically formulated and optimally solved. The model handles chaining, multi-cycle operations, pipelined modules, conditional branches and trades off wiring area with resource area. >