The global optimization of mixed integer non-linear programming (MINLP) problems is an active research area in many engineering fields. In this work, Differential Evolution (DE), a hybrid Evolutionary Computation method, is used for the optimization of nonconvex MINLP problems and a comparison is made among the algorithms based on hybrid of Simplex & Simulated Annealing (MSIMPSA), Genetic Algor...

Strong branching is an effective branching technique that can significantly reduce the size of the branch-and-bound tree for solving Mixed Integer Nonlinear Programming (MINLP) problems. The focus of this paper is to demonstrate how to effectively use “discarded” information from strong branching to strengthen relaxations of MINLP problems. Valid inequalities such as branching-based linearizati...

We develop a novel superstructure of algal biorefinery processes for biological carbon sequestration and utilization, encompassing off-gas purification, algae cultivation, harvesting and dewatering, lipid extraction, remnant treatment, biogas utilization, and algal oil upgrading stages. Based on the superstructure, we propose a mixed-integer nonlinear programming (MINLP) model to minimize the u...

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 describes the extensions that were added to the constraint integer programmingframework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinearprograms (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithmbased on a linear outer-approximation, which is computed by convex overand underestimationof nonconvex functio...

We propose a bilevel mixed-integer nonlinear programming (MINLP) model for the optimal investment of biorefinery facilities considering non-cooperative farmers and biofuel consumers. Interactions among the supply chain players are captured through a single-leader-multiple-follower Stackelberg game under the generalized Nash equilibrium assumption. Given a three-echelon superstructure, the lead ...

This paper studies the integration of geological sequestration and microalgae biofixation options for greenhouse gas (GHG) abatement using a supply chain optimisation approach. We propose a multi-scale multi-period mixed-integer nonlinear programming (MINLP) model, which accounts for CO2 transportation pipeline network design, algae processing route and product selection, as well as the seasona...

The traveling salesman problem with neighborhoods extends the traveling salesman problem to the case where each vertex of the tour is allowed to move in a given region. This NP-hard optimization problem has recently received increasing attention in several technical fields such as robotics, unmanned aerial vehicles, or utility management. In this paper, the problem is formulated as a nonconvex ...

This article addresses a general tri-objective two-echelon capacitated vehicle routing problem (2E-CVRP) to minimize the total travel cost, customers waiting times and carbon dioxide emissions simultaneously in distributing perishable products. In distributing perishable products, customers’ satisfaction is very important and is inversely proportional to the customers waiting times. The propose...

This paper aims to compare a two-echelon and a single-echelon distribution system. A mathematical model for the Single-Echelon Capacitated Vehicle Routing Problem (SE-CVRP) is proposed. This SE-CVRP is the counterpart of Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) introduced in the authors’ previous work. The proposed mathematical model is Mixed-Integer Non-Linear Programming (MIN...