192 research outputs found
Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem
In the minimum common string partition (MCSP) problem two related input
strings are given. "Related" refers to the property that both strings consist
of the same set of letters appearing the same number of times in each of the
two strings. The MCSP seeks a minimum cardinality partitioning of one string
into non-overlapping substrings that is also a valid partitioning for the
second string. This problem has applications in bioinformatics e.g. in
analyzing related DNA or protein sequences. For strings with lengths less than
about 1000 letters, a previously published integer linear programming (ILP)
formulation yields, when solved with a state-of-the-art solver such as CPLEX,
satisfactory results. In this work, we propose a new, alternative ILP model
that is compared to the former one. While a polyhedral study shows the linear
programming relaxations of the two models to be equally strong, a comprehensive
experimental comparison using real-world as well as artificially created
benchmark instances indicates substantial computational advantages of the new
formulation.Comment: arXiv admin note: text overlap with arXiv:1405.5646 This paper
version replaces the one submitted on January 10, 2015, due to detected error
in the calculation of the variables involved in the ILP model
Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques
We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further, we show how to use odd-hole inequalities and additional inequalities to strengthen the formulation. Label variables can be added dynamically to the model in the pricing step. Primal heuristics are incorporated into the framework to speed up the overall solution process. After a polyhedral comparison of the involved formulations, comprehensive computational experiments are presented in order to compare and evaluate the underlying formulations and the particular algorithmic building blocks of the overall branch-and-cut- (and-price) framework
Signed double Roman domination on cubic graphs
The signed double Roman domination problem is a combinatorial optimization
problem on a graph asking to assign a label from to each
vertex feasibly, such that the total sum of assigned labels is minimized. Here
feasibility is given whenever (i) vertices labeled have at least one
neighbor with label in ; (ii) each vertex labeled has one
-labeled neighbor or at least two -labeled neighbors; and (iii) the sum
of labels over the closed neighborhood of any vertex is positive. The
cumulative weight of an optimal labeling is called signed double Roman
domination number (SDRDN). In this work, we first consider the problem on
general cubic graphs of order for which we present a sharp
lower bound for the SDRDN by means of the discharging method. Moreover, we
derive a new best upper bound. Observing that we are often able to minimize the
SDRDN over the class of cubic graphs of a fixed order, we then study in this
context generalized Petersen graphs for independent interest, for which we
propose a constraint programming guided proof. We then use these insights to
determine the SDRDNs of subcubic grid graphs, among other results
Semi-Automated Location Planning for Urban Bike-Sharing Systems
Bike-sharing has developed into an established part of many urban transportation systems. However, new bikesharing
systems (BSS) are still built and existing ones are extended. Particularly for large BSS, location planning
is complex since factors determining potential usage are manifold. We propose a semi-automatic approach for
creating or extending real-world sized BSS during general planning. Our approach optimizes locations such that
the number of trips is maximized for a given budget respecting construction as well as operation costs. The
approach consists of four steps: (1) collecting and preprocessing required data, (2) estimating a demand model,
(3) calculating optimized locations considering estimated redistribution costs, and (4) presenting the solution to
the planner in a visualization and planning front end. The full approach was implemented and evaluated positively
with BSS and planning experts
Metaheuristics for solving a multimodal home-healthcare scheduling problem
Abstract We present a general framework for solving a real-world multimodal home-healthcare scheduling (MHS) problem from a major Austrian home-healthcare provider. The goal of MHS is to assign home-care staff to customers and determine efficient multimodal tours while considering staff and customer satisfaction. Our approach is designed to be as problem-independent as possible, such that the resulting methods can be easily adapted to MHS setups of other home-healthcare providers. We chose a two-stage approach: in the first stage, we generate initial solutions either via constraint programming techniques or by a random procedure. During the second stage, the initial solutions are (iteratively) improved by applying one of four metaheuristics: variable neighborhood search, a memetic algorithm, scatter search and a simulated annealing hyper-heuristic. An extensive computational comparison shows that the approach is capable of solving real-world instances in reasonable time and produces valid solutions within only a few seconds
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