NeatWork is an advanced optimization and simulation tool for the design of purely gravity-driven water distribution systems aiming at delivering clean water to poor rural communities. The exclusion of any adjustable devices, such as pumps and valves, for controlling pressures and flows is motivated by two main reasons: firstly, the system should be as simple … Read more
We consider a novel method entitled constraints reduction programming which aims to reduce the constraints in an optimization model. This method is derived from various applications of management or decision making, and has potential ability to handle a wider range of applications. Due to the high combinatorial complexity of underlying model, it is difficult to … Read more
We address the multi container loading problem of a company that has to serve its customers by first putting the products on pallets and then loading the pallets into trucks. We approach the problem by developing and solving integer linear models. To be useful in practice, our models consider three types of constraints: geometric constraints, … Read more
This study looks at the application of mathematical concepts of entropy and Fibonacci sequence in creating optimal dimensional relations of classification character. The paper is devoted to optimization of some numerical relations and integers as unified threshold characteristics of classification type, aimed for example at systemic optimizing the measuring information of various processes. The paper … Read more
We describe the fundamentals of algorithms for minimizing a smooth nonlinear function, and extensions of these methods to the sum of a smooth function and a convex nonsmooth function. Such objective functions are ubiquitous in data analysis applications, as we illustrate using several examples. We discuss methods that make use of gradient (first-order) information about … Read more
We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. In particular, the proposed method enables … Read more
A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of functions describing the algorithmic steps. The optimization variables are the parameters – within this family of algorithms- that encode algorithm design: … Read more
Abstract—In this article, we introduce new techniques to solve the nonlinear regression problem and the nonlinear classification problem. Our benchmarks suggest that our method for regression is significantly more effective when compared to classical methods and our method for classification is competitive. Our list of classical methods includes least squares, random forests, decision trees, boosted … Read more
Assume we are given a system of ordinary differential equations x 0 = f(x, p) depending on a parameter p ∈ R pe . In this dissertation we consider the problem of locating a parameter p and an initial condition ξ that give rise to a heteroclinic orbit. In the case that such p and … Read more
This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities … Read more