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Reliability and cost are two most important issues in network design optimization that is extensively applied into various optimization problems such as supply chain network design, telecommunication network design, and transportation engineering. This paper proposes an efficient deterministic optimization approach for solving the problem of designing a reliable network. The problem discussed in this paper considers the minimization of the total cost subject to demand, flow balance, and capacity constraints while simultaneously employing mitigation resources to reduce the risk of network failures. Such a problem is typically formulated as a nonconvex mixed-integer program that cannot be easily solved to obtain a global optimum. The proposed optimization method transforms the original nonconvex program into a mixed-integer linear program by linearization techniques and is thus guaranteed to reach a global optimum. In addition, an extended model of minimizing the total weighted loss subject to resource constraints is discussed and globally solved by the proposed method. Experimental results show that the proposed approach effectively solves the reliable network design problem with the minimal total cost or the minimal total weighted loss under an appropriate allocation of mitigation resources. [ABSTRACT FROM AUTHOR]

The three-dimensional open dimension rectangular packing problem (3D-ODRPP) aims to pack a set of given rectangular boxes into a large rectangular container of minimal volume. This problem is an important issue in the shipping and moving industries. All the boxes can be any rectangular stackable objects with different sizes and may be freely rotated. The 3D-ODRPP is usually formulated as a mixed-integer non-linear programming problem. Most existing packing optimization methods cannot guarantee to find a globally optimal solution or are computationally inefficient. Therefore, this paper proposes an efficient global optimization method that transforms a 3D-ODRPP as a mixed-integer linear program using fewer extra 0–1 variables and constraints compared to existing deterministic approaches. The reformulated model can be solved to obtain a global optimum. Experimental results demonstrate the computational efficiency of the proposed approach in globally solving 3D-ODRPPs drawn from the literature and the practical applications. [ABSTRACT FROM AUTHOR]

The rectangular packing problem aims to seek the best way of placing a given set of rectangular pieces within a large rectangle of minimal area. Such a problem is often constructed as a quadratic mixed-integer program. To find the global optimum of a rectangular packing problem, this study transforms the original problem as a mixed-integer linear programming problem by logarithmic transformations and an efficient piecewise linearization approach that uses a number of binary variables and constraints logarithmic in the number of piecewise line segments. The reformulated problem can be solved to obtain an optimal solution within a tolerable error. Numerical examples demonstrate the computational efficiency of the proposed method in globally solving rectangular packing problems. [ABSTRACT FROM PUBLISHER]