We consider problems of choosing an n-vector x, whose entries must be integers, to optimize a linear objective subject to m linear constraints. For example, the "selection problem" is to choose some subset f...
详细信息
We consider problems of choosing an n-vector x, whose entries must be integers, to optimize a linear objective subject to m linear constraints. For example, the "selection problem" is to choose some subset from among n discrete alternatives so that requirements are satisfied at least cost. Such problems are known to be NP-hard. In this paper, we exploit the concept of bandwidth to explain in a novel way why integer linear programming is difficult. The main contribution is a heuristic based on these ideas. It requires computational effort exponential in m but nearly linear in n, and may be run to any desired prespecified accuracy.
A new flexible mixed-integer formulation is presented in this paper for solving the single-stage ac-transmission expansion planning problem. This new formulation handles exactly the discrete nature of equipment additi...
详细信息
A new flexible mixed-integer formulation is presented in this paper for solving the single-stage ac-transmission expansion planning problem. This new formulation handles exactly the discrete nature of equipment additions without resorting to linearized incremental approaches, but still uses integer linear programming. The interconnection of a disconnected system is handled directly without resorting to an initial connected system. The optimal configuration at the end of the planning step under consideration minimizes an annually amortized cost function including the investment cost for equipment additions and the operating cost in terms of real-power transmission losses. Using a new efficient linear load-flow model, this new formulation is characterized by a complete decoupling between real and reactive equations. Examples have been incorporated to illustrate the potentials of this new optimum planning formulation.
A method is proposed to estimate confidence intervals for the solution of integer linear programming (ILP) problems where the technological coefficients matrix and the resource vector are made up of random variables w...
详细信息
In practical reliability optimization models, finding an optimal solution to the model is not the only requirement. One may also be interested in solutions that are close to optimum, or one may want to know what happe...
详细信息
In practical reliability optimization models, finding an optimal solution to the model is not the only requirement. One may also be interested in solutions that are close to optimum, or one may want to know what happens if a change is made in the model. This paper presents new reliability optimization models which can be formulated as parametric nonlinearintegerprogramming problems. Solution methods are illustrated with examples and flow charts.
A generalized discrete location problem on a finite set is defined. An implicit enumeration method and two approximative ones for this problem are presented. Application to a special class of mixed 0-1 integerlinear ...
详细信息
Few studies have been done on techniques to solve multiple objective nonlinearinteger problems. This paper formulates an algorithm for nonlinearinteger goal programming using a branch-and-bound method and Hwang &...
详细信息
Few studies have been done on techniques to solve multiple objective nonlinearinteger problems. This paper formulates an algorithm for nonlinearinteger goal programming using a branch-and-bound method and Hwang & Masud's nonlinear goal programming method. The application of this algorithm is demonstrated by solving reliability problems with single and multiple objectives. The single objective nonlinearinteger problem is solved by the nonlinearinteger goal programming taking the constraints at priority level one and the objective at priority level two. One interesting feature in this algorithm is that the problem is solved by traditional nonlinear search techniques, such as Hooke and Jeeves pattern search, that are originally intended for solving the ``unconstrained'' problem. However, there is no way to guarantee finding the global optimum for a given problem. This means that the investigator must usually be satisfied with a local optimum or a set of local optima.
Given (i) a set of maintenance jobs to be processed over a fixed time horizon, (ii) the breakdown of each job into finite time intervals in which the skills required are known, and (iii) the pool of available manpower...
详细信息
Given (i) a set of maintenance jobs to be processed over a fixed time horizon, (ii) the breakdown of each job into finite time intervals in which the skills required are known, and (iii) the pool of available manpower for each skill type over the horizon, we formulate and solve the problem of scheduling personnel and jobs to minimize personnel idle time, by integerprogramming.
暂无评论