this paper uses the l1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (wdsnd) vectorsof a multi-objective mixed integer linear programming (momilp) problem.the proposed method generalizes the proposed approach by tohidi and razavyan[tohidi g., s. razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

This work concerns the topological optimization problem for determining the optimal petroleum refinery configuration. We are interested in further investigating and hopefully advancing the existing optimization approaches and strategies employing logic propositions to conceptual process synthesis problems. In particular, we seek to contribute to this increasingly exciting area of chemical proce...

In this paper, we present a mixed-integer linear programming (MILP) formulation of piecewise, polyhedral relaxation (PPR) multilinear term using its convex-hull representation. Based on the PPR’s solution, also MILP whose solutions are feasible for nonconvex, equations. We then computational results showing effectiveness proposed formulations standard benchmark nonlinear programs (NLPs) with te...

We combine mixed integer linear programming (MILP) and constraint programming (CP) to minimize tardiness in planning and scheduling. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. We consider two objectives: minimizing the number of late tasks, and minimizing total tardiness. Our main theoretical contribution is...

We present a bandwidth allocation scheme offering optimal solutions to the network optimization problem. The bandwidth allocation policy in class-based networks can be defined with the proportionally fair rule expressed by piecewise linear objective functions. This scheme is formulated as a mixed-integer linear programming (MILP) model, preparing a database identifying suitable paths upon each ...

Branch and bound algorithms for Mixed-Integer Linear Programming (MILP) almost universally branch on a single variable to create disjunctions. General linear expressions involving multiple variables are another option for branching disjunctions, but are not used for two main reasons: (i) descendent LPs tend to solve more slowly because of the added constraints, so the overall solution time is i...

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...

In this paper, we propose a vibration damping optimization algorithm to solve a fuzzy mathematical model for the single-item capacitated lot-sizing problem. At first, a fuzzy mathematical model for the single-item capacitated lot-sizing problem is presented. The possibility approach is chosen to convert the fuzzy mathematical model to crisp mathematical model. The obtained crisp model is in the...

Network Function Virtualization (NFV) allows multiple Virtual Networks (VNs) to share the underlying physical infrastructure via VN mapping, thus improving the utilization of physical resources. In this paper, for the first time, we study the multicast service-oriented VN mapping that can support big data applications over Elastic Optical Networks (EONs). We first formulate the problem of minim...