Choice Constraints Research Articles

The linear multiple choice knapsack problem

The multiple choice knapsack problem is defined as a knapsack problem with additional mutually exclusive multiple choice constraints. We present an algorithm for solving the linear programming relaxation of the multiple choice knapsack problem. The method is based on systematically perturbing the right-hand side of the knapsack constraint and the application of a dual-simplex based strategy. Computational experience with the method is also presented.

Bioconstitutional Politics: Toward an Interdisciplinary Paradigm

This article integrates theory and data culled from two largely unrelated subdisciplines—biopolitics and constitutional politics—to provide a “bioconstitutional” overview of power relationships among Homo sapiens. That overview features three aspects of constitutional configuration: (1) the biopsychological, evidence of which is drawn chiefly from neuroscience, primatology, biochemistry, and championship chess play; (2) the biosocial, evidence of which is drawn chiefly from gene-culture coevolutionary analysis, anthropology, social psychology, jurisprudence, and political science; (3) the biopolicy aspect, evidence of which is drawn exclusively from the American scene, most particularly Supreme Court decision making involving reproductive choice and governmental constraints on gene-cloning. Constitutionalism is conceived as a thought-action field theory, whose values are not only dynamic and functional, but also both politically influential and subject to political influence. Bioconstitutionalism supplies the requisite life science context for these patterns, and itself presents notable feedback features as humans acquire greater capacity to order their adaptive strategies through biological intervention programs.

On quasiblock discrete programming problems with supplementary constraints

The efficiency of a modified local algorithm for solving 2-quasiblock discrete programming problems with supplementary constraints of multiple choice is studied.

Reliability analysis of a non-redundant repairable multiplexing unit : A. Pattavina, A. Roveri and A. Leccese. IEEE Trans. Reliab.R-34(3), 275 (1985)

In this paper, the problem of determining an optimal file allocation in a distributed database is considered. The solution method is based on the isomorphism between the non-redundant file allocation problem and the “multiple choice constraints” knapsack problem, which is a well-known, classical problem of operations research. An ‘ad hoc’ branch and bound algorithm is then introduced for the redundant file allocation problem. Computational results showing the efficiency of the proposed technique are included.

Linear programming with multiple choice constraints for single chain undiscounted Markov decision problems

This paper develops an efficient LP algorithm for solving single chain undiscounted Markov decision problems. The algorithm imposes, in the framework of the simplex method, the multiple choice constraints that exactly one basic variable be chosen from each Markov state. It is proved that the algorithm converges to an optimal solution in a finite number of steps.

On the convergence of cutting plane algorithms for a class of nonconvex mathematical programs

We discuss the convergence of cutting plane algorithms for a class of nonconvex programs called the Generalized Lattice Point Problems (GLPP). A set of sufficient conditions which guarantee finite convergence are presented. Although these conditions are usually difficult to enforce in a practical implementation, they do illustrate the various factors that must be involved in a convergent rudimentary cutting plane algorithm. A striking example of nonconvergence (in which no subsequence converges to a feasible solution, even when seemingly strong cutting planes are used), is presented to show the effect of neglecting one such factor. We give an application of our analysis to problems with multiple choice constraints and finally discuss a modification of cutting plane algorithms so as to make finite convergence more readily implementable.

The reduced cost branch and bound algorithm for mixed integer programming

A different branch and bound algorithm for mixed integer programming is presented. Unlike standard linear programming based branch and bound algorithms, where a single fractional variable (or Special Ordered Set) is selected for problem separation, the proposed method selects groups of variables for separation on the basis of their reduced cost in an LP relaxation. The proposed method restricts a large portion of the integer variables to zero on one branch. The net effect is that the original integer program is solved by optimizing a series of smaller, more tightly restricted, integer programs. The authors have programmed the algorithm using the Extended Control Language of the IBM MPSX/370-MIP/370 mixed integer programming package. Computational results are presented that demonstrate the efficiency of the method on problems where the 0 1 variables are partitioned into multiple choice constraints containing special ordered sets of variables. While the computational results are limited to this class of problems the algorithm can, in theory, be applied to any mixed integer programming problem.

Optimal file allocation in a computer network: a solution method based on the knapsack problem

In this paper, the problem of determining an optimal file allocation in a distributed database is considered. The solution method is based on the isomorphism between the non-redundant file allocation problem and the “multiple choice constraints” knapsack problem, which is a well-known, classical problem of operations research. An ‘ad hoc’ branch and bound algorithm is then introduced for the redundant file allocation problem. Computational results showing the efficiency of the proposed technique are included.

Network Relaxations and Lower Bounds for Multiple Choice Problems

AbstractThis paper provides new network relaxations and penalty calculations for 0-1 integer programs with multiple choice constraints. The multiple choice problem, which may be viewed as a 0-1 problem with generalized upper bounding (GUB) restrictions, arises in a variety of applications involving scheduling, location and assignment.The value of network relaxations lies in their speed of solution (roughly two orders of magnitude faster than LP relaxations) and in their numerical accuracy. Nevertheless, LPrelaxations are more restrictive than network relaxations; that is, they provide tighterlower bounds. Hence the practical superiority of network relaxations appears to be chieflyfor ip problems with no more than six or seven non-zeroes per column of the coefficientmatrix. Consequently, it is important to identify new network relaxations with benefits forspecial structures andto derive stronger lower bounds for network relaxations generally, thus extending the range of problems network-based algorithms ca...

Capital budgeting problems in pavement maintenance

This paper models a class of capital budgeting problems in pavement maintenance as nonlinear discontinuous programming problems and presents a solution procedure. The objective of the models developed is to determine if certain road segments should be rehabilitated in the given year (resurfaced, reconstructed or patched), or major maintenance postponed for at least another year. If the road is to be rehabilitated, some variation in funds expended is possible. The marginal return within the allowable interval of variation is estimated to be nonlinear. Two basic models are presented. The first assumes the rehabilitative alternative or design is fixed, and hence the problem has a single linear constraint imposed by the budget. The second is the design selection problem and contains multiple choice constraints in addition to the budget constraint. An illustrative example is included.

The 0–1 knapsack problem with multiple choice constraints

In this paper we consider the 0–1 knapsack problem with multiple choice constraints appended. Such a problem may arise in a capital budgeting context where only one project may be selected from a particular group of projects. Thus the problem is to choose one project from each group such that the budgetary constraint is satisfied and the maximum return is realized. We formulate two branch and bound algorithms which use two different relaxations as the primary bounding relaxations. In addition, theoretical results are given for a simple reduction in the number of variables in the problem.

Inequalities for mixed integer programs with structure

AbstractMixed integer programming problems arising in practice often contain special structures such as imbedded networks and multiple choice constraints. Easily derived inequalities are given that can be used to reduce the range of admissible solutions for such problems.

An attitudinal modal choice model

Explanatory variables in this model of urban residents' mode choice behavior for the home-to-work trip are attitudinal ratings by survey respondents of descriptive attributes of modes perceived to be available to them. The model methodology is presented in three parts: individuals are clustered with respect to homogeneity of their choice constraints; the covariance structure of attitudinal variables is characterized through development of latent factors describing respondents' perceptions of choice alternatives; and logit probabilistic choice models are estimated in terms of subsets of descriptive attribute ratings chosen to represent latent perception factors. Empirical results from application of the model in the Ottawa, Ontario/Hull, Quebec Canadian National Capital Region are extremely encouraging. Goodness-of-fit summaries indicate model performance better than that obtained using conventional logit models based upon perceived time and cost data. Moreover, it is proposed that the attitudinal models provide valuable insights concerning the importance of factors underlying the choice decision structure of the sample population.

Die EINSTEIN‐Gruppe und die Symmetrie‐Gruppen der Gravitationstheorie

AbstractThe transformations x−α = x−α(xβ, gμn̈) in the function space of the gμn̈(xλ) are corresponding to the coordinate transformations xα = xα(xβ) with some non‐covariant conditions on the gμn̈(xλ). Therefore, the transformations in the function space are corresponding to subgroups of the EINSTEIN group. The conditions for the gμn̈ may be given in the space‐ time V4 or on submanifolds (points, curves, surfaces and hypersurfaces) of the V4. – A special case of the last problem is given by the CAUCHY conditions or by the DIRAC constraints for a special choice of the coordinates on a CAUCHY hypersurface x0 = 0. Then, the transformations x−α = x−α(xl, grs, pmn) in the phase space are EINSTEIN transformations preserving the synchronicity for x0 → 0.