The pollution routing problem (PRP) aims to determine a set of routes and speed over each leg of the routes simultaneously to minimize the total operational and environmental costs. A common approach to solve the PRP exactly is through speed discretization, i.e., assuming that speed over each arc is chosen from a prescribed set of … Read more
Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, … Read more
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an $\ell_0$-norm penalty. Exactly enforcing the $\ell_0$-norm penalty is computationally intractable for larger scale problems, so different sparsity-inducing penalty … Read more
Non-convex quadratic programming with box constraints is a fundamental problem in the global optimization literature, being one of the simplest NP-hard nonlinear programs. We present a new heuristic for this problem, which enables one to obtain solutions of excellent quality in reasonable computing times. The heuristic consists of four phases: binarisation, convexification, branch-and-bound, and local … Read more
The pooling problem is a folklore NP-hard global optimization problem that finds applications in industries such as petrochemical refining, wastewater treatment, and mining. This paper assimilates the vast literature on this problem that is dispersed over different areas and gives unifying arguments and new insights on prevalent techniques. We also present new ideas for computing … Read more
This paper focuses on transportation network protection to hedge against extreme events such as earthquakes. Traditional two-stage stochastic programming has been widely adopted to obtain solutions under a risk-neutral preference through the use of expectations in the recourse function. In reality, decision makers hold different risk preferences. We develop a mean-risk two-stage stochastic programming model … Read more
We propose an equilibrium model that allows to analyze the long-run impact of the regulatory environment on transmission line expansion by the regulator and investment in generation capacity by private firms in liberalized electricity markets. The model incorporates investment decisions of the transmission operator and private firms in expectation of an energy-only market and cost-based … Read more
When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to complicated mixed-integer nonlinear and nonconvex optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several … Read more
With the fast-growing demand in the electricity market of the last decades, attention has been focused on alternative and flexible sources of energy such as hydro valleys. Managing the hydroelectricity produced by the plants in hydro valleys is called the hydro unit commitment problem. This problem consists in finding the optimal power production schedule of … Read more
We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations over the 0-1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained binary polynomial optimization problem. We define an equivalent … Read more