This paper addresses the relaxations in alternative models for disjunctions, big-M and convex hull model, in order to develop guidelines and insights when formulating Mixed-Integer Non-Linear Programming (MINLP), Generalized Disjunctive Programming (GDP), or hybrid models. Characterization and properties are presented for various types of disjunctions. An interesting result is presented for imp...

This article presents the formulation and the solution of a class of Mixed-integer Nonlinear Programming (MINLP) problems, applied to optimal synthesis of process systems in a modular simulator environment. The proposed algorithm makes use of module, reduces the work of calculation on model equations, makes the size of MINLP smaller. The algorithm consists of solving alternate sequences of MILP...

Simultaneous synthesis and design of reaction–separation–recycle processes using rigorous models is highly desirable to improve process efficiency. However, it often leads a large-scale challenging optimization problem. In this work, we propose computationally efficient framework for the The reactor separator networks are modeled generalized disjunctive programming, which reformulated into nonc...

The problem regarding the optimal siting and sizing of photovoltaic (PV) generation units in electrical distribution networks with monopolar direct current (DC) operation technology was addressed this research by proposing a two-stage convex optimization (TSCO) approach. In first stage, exact mixed-integer nonlinear programming (MINLP) formulation relaxed via linear programming, defining nodes ...

Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by many researchers. Considering the quantity discount in purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In this paper, stochastic dynamic...

We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a minimal set of variables that need to be fixed in order to linearize each constraint, a so-called cover. Subsequently, these variables are fixed to values obtained from a r...

The general problem in topology optimization is correctly formulated as a doublemin mixed integer nonlinear programming (MINLP) problem based on the minimum total potential energy principle. It is proved that for linear elastic structures, the alternative iteration leads to a Knapsack problem, which is considered to be NP-hard in computer science. However, by using canonical duality theory (CDT...

this paper presents a formulation of unit commitment for thermal units integrated with wind and solar energy systems and electrical vehicles with emphasizing on mixed integer nonlinear programming (minlp). the renewable energy resources are included in this model due to their low electricity cost and positive effect on environment. as well as, coordinated charging strategy of electrical vehicle...

this paper addresses a reliable facility location problem with considering facility capacity constraints. in reliable facility location problem some facilities may become unavailable from time to time. if a facility fails, its clients should refer to other facilities by paying the cost of retransfer to these facilities. hence, the fail of facilities leads to disruptions in facility location dec...