Enrico Grande's research while affiliated with WWF United Kingdom and other places

Flows over time problems consider finding optimal dynamic flows over a network where capacities and transit times on arcs are given. In this paper we study a multicommodity flow over time problem in which no storage of flow at nodes is allowed and solutions are restricted to loopless flow-paths. We propose an exact algorithm based on a column generation approach for a path-based linear programming model and present the results of a preliminary computational study.

Flows over time problems relate to finding optimal flows over a capacitated network where transit times on network arcs are explicitly considered. In this article, we study the problem of determining a minimum cost origin-destination path where the cost and the travel time of each arc depend on the time taken to travel from the origin to that particular arc along the path. We provide computational complexity results for this problem and an exact solution algorithm based on an enumeration scheme on the corresponding time expanded network. Finally, we show the efficiency of our approach through a number of experimental tests. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

Flows over time problems relate to finding optimal flows over a capacitated network where transit times on network arcs are explicitly considered. In this paper we study the problem of determining a minimum cost source-destination path where the cost of one arc depends on the time taken to travel from s to that particular arc along the path. We provide a computational complexity characterization for this problem and an exact solution algorithm based on an enumeration scheme on the corresponding time expanded network.

The perspective relaxation (PR) is a general approach for constructing tight approximations to mixed-integer nonlinear programs (MINLP) with semicontinuous variables. The PR of a MINLP can be formulated either as a mixed-integer secondorder cone program (MI-SOCP), provided that the original objective function is SOCP-representable, or as a semi-infinite MINLP. In this paper, we show that under some further assumptions (rather restrictive, but satisfied in several practical applications), the PR of a mixed-integer quadratic program (MIQP) can also be reformulated as a piecewise-quadratic program (QP), ultimately yielding a QP relaxation of roughly the same size of the standard continuous relaxation. Furthermore, if the original problem has some exploitable structure, then this structure is typically preserved in the reformulation, thus allowing the construction of specialized approaches for solving the PR. We report on implementing these ideas on two MIQPs with appropriate structure: a sensor placement problem and a quadratic-cost (single-commodity) network design problem.

We address the exact resolution of a MINLP model where resources can be activated in order to satisfy a demand (a partitioning constraint) while minimizing total cost. Cost functions are convex latency functions plus a fixed activation cost. A branch and bound algorithm is devised, featuring three important characteristics. First, the lower bound (therefore each subproblem) can be computed in O(nlog n). Second, to break symmetries resulting in improved efficiency, the branching scheme is n-ary (instead of the "classical" binary). Third, a very affective heuristic is used to compute a good upper bound at the root node of the enumeration tree. All three features lead to a successful comparison against CPLEX MIPQ, which is the fastest among several commercial and open-source solvers: computational results showing this fact are provided.

The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the disc covering problem on a line. The cost of each sensor includes a fixed component f, and a variable component that is a convex function of the diameter of the field-of-view area. When only one type of sensor or, in general, one type of disc, is available, then a simple polynomial algorithm solves the problem. When there are different types of sensors, the problem becomes hard. A branch-and-bound algorithm as well as an efficient heuristic are developed for the special case in which the variable cost component of each sensor is proportional to the square of the measure of the field-of-view area. The heuristic very often obtains the optimal solution as shown in extensive computational testing.Scope and purposeProblems of locating facilities to cover sets of points on networks and planes have been widely studied. This paper focuses on a new covering problem that is motivated by an application where a line segment is to be kept under surveillance using different types of radars. Using reasonable assumptions, some nonlinear covering problems are formulated. Efficient exact algorithms and heuristics are developed and analyzed for “easy” and “hard” cases, respectively.

The Perspective Relaxation (PR) is a general approach for constructing tight approximations to Mixed-Integer NonLinear Problems with semicontinuous variables. The PR of a MINLP can be for-mulated either as a Mixed-Integer Second-Order Cone Program (provided that the original objective function is SOCP-representable), or as a Semi-Infinite MINLP. While these reformulations signifi-cantly improve the lower bound and the running times of the corresponding enumerative approaches, they may spoil some valuable structure of the problem, such as the presence of network constraints. In this paper, we show that under some further assumptions the PR of a Mixed-Integer Quadratic Program can also be reformulated as a piecewise linear-quadratic problem, ultimately yielding a QP relaxation of roughly the same size of the standard continuous relaxation and where the (network) structure of the original problem is safeguarded. We apply this approach to a quadratic-cost single-commodity network design problem, comparing the newly developed algorithm with those based on both the standard continuous relaxation and the two usual variants of PR relaxation.