This paper offers a novel approach for computing globally optimal solutions to the pump scheduling problem in drinking water distribution networks. A tight integer linear relaxation of the original non-convex formulation is devised and solved by branch and bound where integer nodes are investigated through non-linear programming to check the satisfaction of the non-convex constraints … Read more
The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions become popular as ways of solving these sort of problems. However, they rely on the steepest descent method for local searches. Here we present an approach that does not … Read more
We study the unequal circle-circle non-overlapping constraints, a form of reverse convex constraints that often arise in optimization models for cutting and packing applications. The feasible region induced by the intersection of circle-circle non-overlapping constraints is highly non-convex, and standard approaches to construct convex relaxations for spatial branch-and-bound global optimization of such models typically yield … Read more
The application of mathematical optimization methods provides the capacity to increase the energy efficiency and to lower the investment costs of technical systems, considerably. We present a system approach for the optimization of the design and operation of pumping systems and exemplify it by applying it to the water supply of high-rise buildings. The underlying … Read more
Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in vectorial form. In this survey we discuss the fundamental problem of mapping graphs to vectors, and its … Read more
The purpose of this paper is to find appropriate solutions to concave quadratic programming using outer approximation algorithm, which is one of the algorithm of global optimization, in the target of the strong of concavity of object function i.e. high of nonlinear risk of portfolio. Firstly, my target model is a mathematical optimization programming to … Read more
We present a model development framework and numerical solution approach to the general problem-class of packing convex objects into optimized convex containers. Specifically, here we discuss the problem of packing ovals (egg-shaped objects, defined here as generalized ellipses) into optimized regular polygons in R”. Our solution strategy is based on the use of embedded Lagrange … Read more
LSP(n), the largest small polygon with n vertices, is defined as the polygon of unit diameter that has maximal area A(n). Finding the configuration LSP(n) and the corresponding A(n) for even values n >= 6 is a long-standing challenge that leads to an interesting class of nonlinear optimization problems. We present numerical solution estimates for … Read more
The Douglas-Rachford algorithm is a classical and a successful method for solving the feasibility problems. Here, we provide a region for global convergence of the algorithm for the feasibility problem involving a disc and a circle in the Euclidean space of dimension two. Citation 1. Borwein, J.M., Sims, B.: The Douglas-Rachford algorithm in the absence … Read more
We show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular … Read more