Search results for "Graph theory"
showing 10 items of 784 documents
Variable Fixing for Two-Arc Sequences in Branch-Price-and-Cut Algorithms on Path-Based Models
2020
Variable fixing by reduced costs is a popular technique for accelerating the solution process of mixed-integer linear programs. For vehicle-routing problems solved by branch-price-and-cut algorithms, it is possible to fix to zero the variables associated with all routes containing at least one arc from a subset of arcs determined according to the dual solution of a linear relaxation. This is equivalent to removing these arcs from the network used to generate the routes. In this paper, we extend this technique to routes containing sequences of two arcs. Such sequences or their arcs cannot be removed directly from the network because routes traversing only one arc of a sequence might still b…
A more efficient cutting planes approach for the green vehicle routing problem with capacitated alternative fuel stations
2021
AbstractThe Green Vehicle Routing Problem with Capacitated Alternative Fuel Stations assumes that, at each station, the number of vehicles simultaneously refueling cannot exceed the number of available pumps. The state-of-the-art solution method, based on the generation of all feasible non-dominated paths, performs well only with up to 2 pumps. In fact, it needs cloning the paths between every pair of pumps. To overcome this issue, in this paper, we propose new path-based MILP models without cloning paths, for both the scenario with private stations (i.e., owned by the fleet manager) and that with public stations. Then, a more efficient cutting plane approach is designed for addressing both…
Cimo: An efficient 2-phases calculator of multimodal itineraries for real trans-territories based on a dynamic programming
2015
In this work we propose an exact solution for calculating multimodal itinerary. This solution is named Cimo (Calculateur d'Itineraires Multimodaux Ordonnes). Cimo is an exact optimal itineraries' calculator wherein itineraries are sorted, multimodal, and trans-territorial. The solution is based on a dynamic programming algorithm "cut", "price" and "share". This solution is multi-objectives and multi-constraints. Several versions of this algorithm are proposed following a methodological approach that enables evaluation of efficiency and complexity's gain : through theoretical calculus and benchmarks. In the first version of realistic problem, we propose a solution with itineraries calculated…
Branch-and-price-and-cut for a service network design and hub location problem
2015
In the context of combined road-rail freight transport, we study the integrated tactical planning of hub locations and the design of a frequency service network. We consider a number of real-world constraints such as multiple transshipments of requests at hubs, transport time limits for requests, request splitting, and outsourcing possibilities. To our knowledge, the combination of problem features we deal with has not been described before. We present a path-based model and solve it with a branch-and-price-and-cut algorithm. Computational experiments show that large realistic instances from a major German rail freight company can be solved close to optimality within one hour on a standard …
Miscellaneous Graph Preliminaries
2020
Summary This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library [2] to the best of the author’s knowledge. Most of them regard graph theory as formalized in the GLIB series (cf. [8]) and most of them are preliminaries needed in [7] or other forthcoming articles.
What do we mean by diversity? : the path towards quantification
2018
The concept of biological diversity has evolved from a simple count of species to more sophisticated measures that are sensitive to relative abundances and even to evolutionary divergence times between species. In the course of this evolution, diversity measures have often been borrowed from other disciplines. Biological reasoning about diversity often implicitly assumed that measures of diversity had certain mathematical properties, but most of biologys traditional diversity measures did not actually possess these properties, a situation which often led to mathematically and biologically invalid inferences. Biologists now usually transform the traditional measures to the «effective number …
Characterization of the consistent completion of analytic hierarchy process comparison matrices using graph theory
2019
Decision-making is frequently affected by uncertainty and/or incomplete information, which turn decision-making into a complex task. It is often the case that some of the actors involved in decision-making are not sufficiently familiar with all of the issues to make the appropriate decisions. In this paper, we are concerned about missing information. Specifically, we deal with the problem of consistently completing an analytic hierarchy process comparison matrix and make use of graph theory to characterize such a completion. The characterization includes the degree of freedom of the set of solutions and a linear manifold and, in particular, characterizes the uniqueness of the solution, a re…
Synthesis and solution properties of star-shaped poly(tert-butyl acrylate)
2000
A series of star polymers consisting of poly(tert-butyl acrylate) arms and an ethyleneglycol dimethacrylate (EGDMA) microgel core were synthesized using anionic polymerization. The effect of various parameters (precursor length, ratio [[EGDMA]/[Initiator], reaction time, and overall concentrations) on the average number of arms was investigated. Molecular weights were determined using GPC coupled with an online viscometer and MALLS. The exponents for the relation between intrinsic viscosity or radius of gyration and molecular weight, respectively, are extremely low, indicating that the dimensions of the star polymers only slightly increase with the number of arms. After a certain number of …
Adaptive memory programing for the robust capacitated international sourcing problem
2008
The International Sourcing Problem consists of selecting a subset from an available set of potential suppliers internationally located. The selected suppliers must meet the demand for items from a set of plants, which are also located worldwide. Since the costs are affected by macroeconomic conditions in the countries where the supplier and the plant are located, the formulation considers the uncertainty associated with changes in these conditions. We formulate the robust capacitated international sourcing problem by means of a scenario-optimization approach. When dealing with uncertainty, one of the most common approaches in the literature is to formulate the problem via a set of possible …
Scatter Search and Path Relinking: Foundations and Advanced Designs
2004
Scatter Search and its generalized form Path Relinking, are evolutionary methods that have been successfully applied to hard optimization problems. Unlike genetic algorithms, they operate on a small set of solutions and employ diversification strategies of the form proposed in Tabu Search, which give precedence to strategic learning based on adaptive memory, with limited recourse to randomization. The fundamental concepts and principles were first proposed in the 1970s as an extension of formulations, dating back to the 1960s, for combining decision rules and problem constraints. (The constraint combination approaches, known as surrogate constraint methods, now independently provide an impo…