Optimizing and Reoptimizing: tackling static and dynamic combinatorial problems

As suggested by the title, in this thesis both static and dynamic problems of Operations Research will be addressed by either designing new procedures or adapting well-known algorithmic schemes. Specifically, the first part of the thesis is devoted to the discussion of three variants of the widely studied Shortest Path Problem, one of which is defined on dynamic graphs. Namely, first the Reoptimization of Shortest Paths in case of multiple and generic cost changes is dealt with an exact algorithm whose performance is compared with Dijkstra's label setting procedure in order to detect which approach has to be preferred. Secondly, the k-Color Shortest Path Problem is tackled. It is a recent problem, defined on an edge-constrained graph, for which a Dynamic Programming algorithm is proposed here; its performance is compared with the state of the art solution approach, namely a Branch & Bound procedure. Finally, the Resource Constrained Clustered Shortest Path Tree Problem is presented. It is a newly defined problem for which both a mathematical model and a Branch & Price procedure are detailed here. Moreover, the performance of this solution approach is compared with that of CPLEX solver. Furthermore, in the first part of the thesis, also the Path Planning in Urban Air Mobility, is discussed by considering both the definition of the Free-Space Maps and the computation of the trajectories. For the former purpose, three different but correlated discretization methods are described; as for the latter, a two steps resolution, offline and online, of the resulting shortest path problems is performed. In addition, it is checked whether the reoptimization algorithm can be used in the online step. In the second part of this thesis, the recently studied Additive Manufacturing Machine Scheduling Problem with not identical machines is presented. Specifically, a Reinforcement Learning Iterated Local Search meta-heuristic featuring a Q-learning Variable Neighbourhood Search is described to solve this problem and its performance is compared with the one of CPLEX solver. It is worthwhile mentioning that, for each of the proposed approaches, a thorough experimentation is performed and each Chapter is equipped with a detailed analysis of the results in order to appraise the performance of the method and to detect its limits

Advanced network connectivity features and zonal requirements in covering location problems

Real-world facility planning problems often require to tackle simultaneously network connectivity and zonal requirements, in order to guarantee an equitable provision of services and an efficient flow of goods, people and information among the facilities. Nonetheless, such challenges have not been addressed jointly so far. In this paper we explore the introduction of advanced network connectivity features and spatial-related requirements within Covering Location Problems. We adopt a broad modelling perspective, accounting for structural and economic aspects of connectivity features, while allowing the choice for one or more facilities to serve the facility networks as depots, and containing the maximal distance between any active facility and such depot(s). A novel class of Multi-objective Covering Location problems are proposed, utilising Mixed Integer Linear Programming as a modelling tool. Aiming at obtaining efficiently the arising Pareto Sets and providing actionable decision-making support throughout real planning processes, we adapt to our problem the robust variant of the AUGMEnted ɛ -CONstraint method (AUGMECON-R). Furthermore, we exploit the mathematical properties of the proposed problems to design tailored Matheuristic algorithms which boost the scalability of the solution method, with particular reference to the case of multiple depots. By conducting a comprehensive computational study on benchmark instances, we provide a thorough proof of concept for the novel problems, highlighting the challenging nature of the advanced connectivity features and the scalability of the proposed Matheuristics. From a managerial standpoint, the suitability of the proposed work in responding effectively to the motivating needs is showcased

A simple method for generating full length cDNA from low abundance partial genomic clones

BACKGROUND: PCR amplification of target molecules involves sequence specific primers that flank the region to be amplified. While this technique is generally routine, its applicability may not be sufficient to generate a desired target molecule from two separate regions involving intron /exon boundaries. For these situations, the generation of full-length complementary DNAs from two partial genomic clones becomes necessary for the family of low abundance genes. RESULTS: The first approach we used for the isolation of full-length cDNA from two known genomic clones of Hox genes was based on fusion PCR. Here we describe a simple and efficient method of amplification for homeobox D13 (HOXD13) full length cDNA from two partial genomic clones. Specific 5' and 3' untranslated region (UTR) primer pairs and website program (primer3_www.cgv0.2) were key steps involved in this process. CONCLUSIONS: We have devised a simple, rapid and easy method for generating cDNA clone from genomic sequences. The full length HOXD13 clone (1.1 kb) generated with this technique was confirmed by sequence analysis. This simple approach can be utilized to generate full-length cDNA clones from available partial genomic sequences

Shortest path reoptimization vs resolution from scratch: a computational comparison

The Shortest Path Problem (SPP) is among the most studied problems in Operations Research, for its theoretical aspects but also because it appears as sub-problem in many combinatorial optimization problems, e.g. Vehicle Routing and Maximum Flow-Minimum Cost problems. Given a sequence of SPPs, suppose that two subsequent instances solely differ by a slight change in the graph structure: that is the set of nodes, the set of arcs or both have changed; then, the goal of the reoptimization consists in solving the (Formula presented.) SPP of the sequence by reusing valuable information gathered in the solution of the (Formula presented.) one. We focused on the most general scenario, i.e. multiple changes for any subset of arcs, for which, only the description of a dual-primal approach has been proposed so far [S. Pallottino and M.G. Scutell‘a, A new algorithm for reoptimizing shortest paths when the arc costs change, Oper. Res. Lett. 31 (2003), pp. 149-160.]. We implemented this framework exploiting efficient data structures, i.e. the Multi Level Bucket. In addition, we compare the performance of our proposal with the well-known Dijkstra's algorithm, applied for solving each modified problem from scratch. In this way, we draw the line–in terms of cost, topology, and size–among the instances where the reoptimization approach is efficient from those that should be solved from scratch

An environmental accounting of water resources production system in the Samoggia creek area using emergy method

3nonenoneFugaro L.; Marchettini N.; Principi I.;Fugaro, L.; Marchettini, Nadia; Principi, I

On the shortest path problems with edge constraints

The goal of this work is to provide a brief classification of some Shortest Path Problem (SPP) variants that include edge constraints and that find applications in several different contexts, including optical networks, transportation and logistics. One of the most broad and notable classes of edge-constrained SPPs is given by Resource Constrained Shortest Path Problems (RCSPPs). In RCSPPs, in addition to the customary directed graph G=(V, A) and edge-distance function, a L-dimensional vector of resources R is defined. Essentially, each resource is related to relevant link attributes that need to be accounted for in the planning of the path. Accordingly, a path P∗ is optimal whenever it is minimal w.r.t. the distance function, and satisfies the restrictions enforced on the resources Other variants can involve colors assigned to the nodes and/or the edges of the graph and/or reload costs. These kinds of problems have relevant applications in network reliability. Particularly interesting is the so-called k-Color SPP, where a color is assigned to each edge and the minimum path from a given source node s to a target node t must not cross more than k differently colored edges. As for the use of reload cost, a reload cost r(b, c) is assigned to each pair of colors (b, c) and represents the amount to be paid if in a path P an arc of color c is traversed after an arc of color b