Showing papers on "Integer programming published in 1997"

A Branch-and-Price Algorithm for the Generalized Assignment Problem

Abstract: The generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents. A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem.

A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem

Abstract: We consider a variant of the classical symmetric Traveling Salesman Problem in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster This NP-hard problem is known in the literature as the symmetric Generalized Traveling Salesman Problem (GTSP), and finds practical applications in routing, scheduling and location-routing In a companion paper (Fischetti et al [Fischetti, M, J J Salazar, P Toth 1995 The symmetric generalized traveling salesman polytope Networks 26 113–123]) we modeled GTSP as an integer linear program, and studied the facial structure of two polytopes associated with the problem Here we propose exact and heuristic separation procedures for some classes of facet-defining inequalities, which are used within a branch-and-cut algorithm for the exact solution of GTSP Heuristic procedures are also described Extensive computational results for instances taken from the literature and involving up to 442 nodes are reported

Computing Maximum Task Execution Times — A Graph-BasedApproach

Abstract: The knowledge of program execution times is crucial for the development and the verification of real-time software. Therefore, there is a need for methods and tools to predict the timing behavior of pieces of program code and entire programs. This paper presents a novel method for the analysis of program execution times. The computation of MAximum eXecution Times (MAXTs) is mapped onto a graph-theoretical problem that is a generalization of the computation of a maximum cost circulation in a directed graph. Programs are represented by T-graphs, timing graphs, which are similar to flow graphs. These graphs reflect the structure and the timing behavior of the code. Relative capacity constraints, a generalization of capacity constraints that bound the flow in the edges, express user-supplied information about infeasible paths. To compute MAXTs, T-graphs are searched for those execution paths which correspond to a maximum cost circulation. The search problem is transformed into an integer linear programming problem. The solution of the linear programming problem yields the MAXT. The special merits of the presented method are threefold: It uses a concise notation to characterize the static structure of a program and its possible execution paths. Furthermore, the notation allows for a description of the feasible paths through the program code that characterizes the behavior of the code sufficiently to compute the exact maximum execution time of the program – not just a bound thereof. Finally, linear program solving does not only yield maximum execution times, but also produces detailed information about the execution time and the number of executions of every single program construct in the worst case. This knowledge is valuable for a more comprehensive analysis of the timing of a program.

A Minimal Algorithm for the 0-1 Knapsack Problem

Abstract: Several types of large-sized 0-1 Knapsack Problems (KP) may be easily solved, but in such cases most of the computational effort is used for sorting and reduction. In order to avoid this problem it has been proposed to solve the so-called core of the problem: a Knapsack Problem defined on a small subset of the variables. The exact core cannot, however, be identified before KP is solved to optimality, thus, previous algorithms had to rely on approximate core sizes. In this paper we present an algorithm for KP where the enumerated core size is minimal, and the computational effort for sorting and reduction also is limited according to a hierarchy. The algorithm is based on a dynamic programming approach, where the core size is extended by need, and the sorting and reduction is performed in a similar “lazy” way. Computational experiments are presented for several commonly occurring types of data instances. Experience from these tests indicate that the presented approach outperforms any known algorithm for KP...

A Genetic Algorithm for the Multiple-Choice Integer Program

Abstract: We present a genetic algorithm for the multiple-choice integer program that finds an optimal solution with probability one though it is typically used as a heuristic. General constraints are relaxed by a nonlinear penalty function for which the corresponding dual problem has weak and strong duality. The relaxed problem is attacked by a genetic algorithm with solution representation special to the multiple-choice structure. Nontraditional reproduction, crossover and mutation operations are employed. Extensive computational tests for dual degenerate problem instances show that suboptimal solutions can be obtained with the genetic algorithm within running times that are shorter than those of the OSL optimization routine.

Logical analysis of numerical data

Abstract: “Logical analysis of data” (LAD) is a methodology developed since the late eighties, aimed at discovering hidden structural information in data sets. LAD was originally developed for analyzing binary data by using the theory of partially defined Boolean functions. An extension of LAD for the analysis of numerical data sets is achieved through the process of “binarization” consisting in the replacement of each numerical variable by binary “indicator” variables, each showing whether the value of the original variable is above or below a certain level. Binarization was successfully applied to the analysis of a variety of real life data sets. This paper develops the theoretical foundations of the binarization process studying the combinatorial optimization problems related to the minimization of the number of binary variables. To provide an algorithmic framework for the practical solution of such problems, we construct compact linear integer programming formulations of them. We develop polynomial time algorithms for some of these minimization problems, and prove NP-hardness of others.

The Covering Tour Problem

Abstract: The Covering Tour Problem (CTP) is defined on a graph G = (V ∪ W, E), where W is a set of vertices that must be covered The CTP consists of determining a minimum length Hamiltonian cycle on a subset of V such that every vertex of W is within a prespecified distance from the cycle The problem is first formulated as an integer linear program, polyhedral properties of several classes of constraints are investigated, and an exact branch-and-cut algorithm is developed A heuristic is also described Extensive computational results are presented

An Exact Algorithm for the Vehicle Routing Problem with Backhauls

Abstract: The Vehicle Routing Problem with Backhauls is an extension of the capacitated Vehicle Routing Problem where the customers' set is partitioned into two subsets. The first is the set of Linehaul, or Delivery, customers, while the second is the set of Backhaul, or Pickup, customers. The problem is known to be NP-hard in the strong sense and finds many practical applications in distribution planning. In this paper we consider, in a unified framework, both the symmetric and the asymmetric versions of the vehicle routing problem with backhauls, for which we present a new integer linear programming model and a Lagrangian lower bound which is strengthened in a cutting plane fashion. The Lagrangian lower bound is then combined, according to-the additive approach, with a lower bound obtained by dropping the capacity constraints, thus obtaining an effective overall bounding procedure. A branch-and-bound algorithm, reduction procedures and dominance criteria are also described. Computational tests on symmetric and as...

An Algorithm for Hardware/Software Partitioning Using Mixed Integer Linear Programming

Abstract: One of the key problems in hardware/software codesign is hardware/software partitioning This paper describes a new approach to hardware/software partitioning using integer programming (IP) The advantage of using IP is that optimal results are calculated for a chosen objective function The partitioning approach works fully automatic and supports multi-processor systems, interfacing and hardware sharing In contrast to other approaches where special estimators are used, we use compilation and synthesis tools for cost estimation The increased time for calculating values for the cost metrics is compensated by an improved quality of the values Therefore, fewer iteration steps for partitioning are needed The paper presents an algorithm using integer programming for solving the hardware/software partitioning problem leading to promising results

A multiparametric programming approach for linear process engineering problems under uncertainty

Abstract: In this paper, a parametric programming approach is proposed for the analysis of linear process engineering problems under uncertainty. A novel branch and bound algorithm is presented for the solut...

Links between linear bilevel and mixed 0-1 programming problems

Abstract: We study links between the linear bilevel and linear mixed 0–1 programming problems. A new reformulation of the linear mixed 0–1 programming problem into a linear bilevel programming one, which does not require the introduction of a large finite constant, is presented. We show that solving a linear mixed 0–1 problem by a classical branch-and-bound algorithm is equivalent in a strong sense to solving its bilevel reformulation by a bilevel branch-and-bound algorithm. The mixed 0–1 algorithm is embedded in the bilevel algorithm through the aforementioned reformulation; i.e., when applied to any mixed 0–1 instance and its bilevel reformulation, they generate sequences of subproblems which are identical via the reformulation.

Static and dynamic channel assignment using neural networks

Abstract: We examine the problem of assigning calls in a cellular mobile network to channels in the frequency domain. Such assignments must be made so that interference between calls is minimized, while demands for channels are satisfied. A new nonlinear integer programming representation of the static channel assignment (SCA) problem is formulated. We then propose two different neural networks for solving this problem. The first is an improved Hopfield (1982) neural network which resolves the issues of infeasibility and poor solution quality which have plagued the reputation of the Hopfield network. The second approach is a new self-organizing neural network which is able to solve the SCA problem and many other practical optimization problems due to its generalizing ability. A variety of test problems are used to compare the performance of the neural techniques against more traditional heuristic approaches. Finally, extensions to the dynamic channel assignment problem are considered.

Fleet deployment optimization for liner shipping: an integer programming model

Abstract: Extending and improving an earlier work of the second author, an Integer Programming (IP) model is developed to minimize the operating and lay-up costs for a fleet of liner ships operating on various routes. The IP model determines the optimal deployment of an existing fleet, given route, service, charter, and compatibility constraints. Two examples are worked with extensive actual data provided by Flota Mercante Grancolombiana (FMG). The optimal deployment is solved for their existing ship and service requirements and results and conclusions are given.

Mathematical Programming for Industrial Engineers

Abstract: Linear programming integer programming graph theory and networks dynamic programming nonlinear programming multiobjective programming stochastic programming heuristic methods.

An architectural co-synthesis algorithm for distributed, embedded computing systems

Abstract: Many embedded computers are distributed systems, composed of several heterogeneous processors and communication links of varying speeds and topologies. This paper describes a new, heuristic algorithm which simultaneously synthesizes the hardware and software architectures of a distributed system to meet a performance goal and minimize cost. The hardware architecture of the synthesized system consists of a network of processors of multiple types and arbitrary communication topology; the software architecture consists of an allocation of processes to processors and a schedule for the processes. Most previous work in co-synthesis targets an architectural template, whereas this algorithm can synthesize a distributed system of arbitrary topology. The algorithm works from a technology database which describes the available processors, communication links, I/O devices, and implementations of processes on processors. Previous work had proposed solving this problem by integer linear programming (ILP); our algorithm is much faster than ILP and produces high-quality results.

A study of integer programming formulations for scheduling problems

Abstract: With the advances of powerful computer capacity and efficient integer programming software, mathematical programming-based scheduling research is beginning to receive more and more attention from researchers. Although it is not an efficient solution method, mathematical programming formulation is a natural way to attack scheduling problems. The purpose of this paper is to present a study of five existing integer programming formulations for job-shop, flow-shop and permutation flow-shop scheduling problems, and a comparison of their model sizes for each particular setting. The results show that Manners model is not only the best formulation for both job-shop and flow-shop problems, but is also the best for the permutation flow-shop problem.

Scheduling techniques for variable voltage low power designs

Abstract: This paper presents an integer linear programming (ILP) model and a heuristic for the variable voltage scheduling problem. We present the variable voltage scheduling techniques that consider in turn timing constraints alone, resource constraints alone, and timing and resource constraints together for design space exploration. Experimental results show that our heuristic produces results competitive with those of the ILP method in a fraction of the run-time. The results also show that a wide range of design alternatives can be generated using our design space exploration method. Using different cost/delay combinations, power consumption in a single design can differ by as much as a factor of 6 when using mixed 3.3V and 5V supply voltages.

Mixed-Integer Nonlinear Programming: A Survey of Algorithms and Applications

Abstract: This paper presents an overview of mixed-integer nonlinear programming techniques by first providing a unified treatment of the Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The extension of these methods is also considered for logic based representations. Finally, an overview of the applications in many areas in process engineering is presented.

An annotated bibliography for post-solution analysis in mixed integer programming and combinatorial optimization

Abstract: This annotated bibliography focuses on what has been published since the 1977 Geoffrion-Nauss survey, and it is in BibTEX format, so it can be searched on the World Wide Web. In addition to postoptimal sensitivity analysis, this survey includes debugging a run, such as when the integer program is unbounded, anomalous or infeasible.

System-level synthesis of low-power hard real-time systems

Abstract: We present a system-level approach for power optimization undera set of user specified costs and timing constraints of hard real-timedesigns. The approach optimizes all three degrees of freedom forpower minimization, namely switching activity, effective capacityand voltage supply.We first define two key associated optimization problems, processorallocation and task assignment, and establish their computationalcomplexity. Efficient algorithms are developed for bothsystem design problems. The statistical analysis of comprehensiveexperimental results and their comparison with the developed conservativeand optimistic sharp lower bounds, clearly indicates thequality of the proposed optimization techniques.