Optimizing scheduling is an effective way to improve the profit of refineries; it usually requires accurate models to describe the complex and nonlinear refining processes. However, conventional nonlinear models will result in a complex mixed integer nonlinear programming (MINLP) problem for scheduling. This paper presents a piecewise linear (PWL) modeling approach, which can describe global no...

The redundancy allocation problem involves the selection of components and the appropriate levels of redundancy to maximize reliability or minimize cost of a series-parallel system given design constraints. Different optimization approaches have been previously applied to the problem including dynamic programming, integer programming, and mixed integer and nonlinear programming. However these a...

Abstract: A mixed integer programming based approach for optimal control of a class of nonlinear systems with typical non-smooth and even discontinuous components is presented. Firstly, a model denoted as General Linear System Model (GLSM), which can be used to describe accurately a wide range of nonlinear systems with typical nonlinear components, is established. Secondly, based on GLSM, mixed...

In the present paper, we focus on multi-level nonlinear integer programming problems (MLNLIPPs) in which there exist decision makers (DMs) with integer decision variables at all levels. Various approaches for multi-level programming problems could exist according to situations which the DMs are placed in. Assuming the cooperative relationship among the DMs at all levels, in this paper, an inter...

The combinatorial nature of integer programming is inevitable even after taking specific model structure into consideration. This is the root problem in implementing large-scale nonlinear integer programming models regardless of which algorithm one chooses to use. Consequently, we suggest that the size of origin-destination be moderate. In the case of large origin-destination problems, more inf...

This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The method is compared to alternative approaches proposed in the literature and appears to be efficient.

Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...

This paper considers two-level integer programming problems involving random fuzzy variables with cooperative behavior of the decision makers. Considering the probabilities that the decision makers’ objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile criteria to optimize the target variables under the con...

The Fortran subroutine MISQP solves mixed-integer nonlinear programming problems by a modified sequential quadratic programming (SQP) method. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when inor decrementing an integer value, successive quadratic approximations are applied. The algorithm is sta...

The Fortran subroutine MISQP solves mixed-integer nonlinear programming problems by a modified sequential quadratic programming (SQP) method. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when inor decrementing an integer value, successive quadratic approximations are applied. The algorithm is sta...