9 research outputs found
Insertion Heuristics for Central Cycle Problems
A central cycle problem requires a cycle that is
reasonably short and keeps a the maximum distance
from any node not on the cycle to its nearest
node on the cycle reasonably low. The objective
may be to minimise maximumdistance or cycle
length and the solution may have further constraints.
Most classes of central cycle problems
are NP-hard. This paper investigates insertion
heuristics for central cycle problems, drawing on
insertion heuristics for p-centres [7] and travelling
salesman tours [21]. It shows that a modified
farthest insertion heuristic has reasonable worstcase
bounds for a particular class of problem.
It then compares the performance of two farthest
insertion heuristics against each other and
against bounds (where available) obtained by integer
programming on a range of problems from
TSPLIB [20]. It shows that a simple farthest insertion
heuristic is fast, performs well in practice
and so is likely to be useful for a general problems
or as the basis for more complex heuristics
for specific problems
Solving the conditional and unconditional p-center problem with modified harmony search: A real case study
AbstractIn this paper, we solve the well-known conditional and unconditional p-center problem using a modified harmony search algorithm. This music inspired algorithm is a simple meta-heuristic that was proposed recently for solving combinatorial and large-scale engineering and optimization problems. This algorithm is applicable to both discrete and continuous search spaces. We have tested the present algorithm on ORLIB and TSP test problems and compared the results of the classic harmony search approach to those of the modified harmony search method. We also present some results for other meta-heuristic algorithms including the variable neighborhood search, the Tabu search, and the scatter search. Finally, we utilize this location model to locate bicycle stations in the historic city of Isfahan in Iran
Hybrid Meta-heuristics with VNS and Exact Methods: Application to Large Unconditional and Conditional Vertex p-Centre Problems
Large-scale unconditional and conditional vertex p-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with p varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex p-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems
Exact solution approaches for the discrete -neighbor -center problem
The discrete -neighbor -center problem (d--CP) is an
emerging variant of the classical -center problem which recently got
attention in literature. In this problem, we are given a discrete set of points
and we need to locate facilities on these points in such a way that the
maximum distance between each point where no facility is located and its
-closest facility is minimized. The only existing algorithms in
literature for solving the d--CP are approximation algorithms and
two recently proposed heuristics.
In this work, we present two integer programming formulations for the
d--CP, together with lifting of inequalities, valid inequalities,
inequalities that do not change the optimal objective function value and
variable fixing procedures. We provide theoretical results on the strength of
the formulations and convergence results for the lower bounds obtained after
applying the lifting procedures or the variable fixing procedures in an
iterative fashion. Based on our formulations and theoretical results, we
develop branch-and-cut (B&C) algorithms, which are further enhanced with a
starting heuristic and a primal heuristic.
We evaluate the effectiveness of our B&C algorithms using instances from
literature. Our algorithms are able to solve 116 out of 194 instances from
literature to proven optimality, with a runtime of under a minute for most of
them. By doing so, we also provide improved solution values for 116 instances
Robustness in facility location
Facility location concerns the placement of facilities, for various objectives, by use of mathematical models and solution procedures. Almost all facility location models that can be found in literature are based on minimizing costs or maximizing cover, to cover as much demand as possible. These models are quite efficient for finding an optimal location for a new facility for a particular data set, which is considered to be constant and known in advance.
In a real world situation, input data like demand and travelling costs are not fixed, nor known in
advance. This uncertainty and uncontrollability can lead to unacceptable losses or even bankruptcy. A way of dealing with these factors is robustness modelling. A robust facility location model aims to locate a facility that stays within predefined limits for all expectable circumstances as good as possible. The deviation robustness concept is used as basis to develop a new competitive deviation robustness model. The competition is modelled with a Huff based model, which calculates the market share of the new facility. Robustness in this model is defined as the ability of a facility location to capture a
minimum market share, despite variations in demand.
A test case is developed by which algorithms can be tested on their ability to solve robust facility location models. Four stochastic optimization algorithms are considered from which Simulated Annealing turned out to be the most appropriate. The test case is slightly modified for a competitive market situation. With the Simulated Annealing algorithm, the developed competitive deviation model is solved, for three considered norms of deviation.
At the end, also a grid search is performed to illustrate the landscape of the objective function of the competitive deviation model. The model appears to be multimodal and seems to be challenging for further research
Exact solution methodologies for the p-center problem under single and multiple allocation strategies
Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent Univ., 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical references leaves 89-95.The p-center problem is a relatively well known facility location problem that
involves locating p identical facilities on a network to minimize the maximum
distance between demand nodes and their closest facilities. The focus of the
problem is on the minimization of the worst case service time. This sort of
objective is more meaningful than total cost objectives for problems with a time
sensitive service structure. A majority of applications arises in emergency service
locations such as determining optimal locations of ambulances, fire stations and
police stations where the human life is at stake. There is also an increased
interest in p-center location and related location covering problems in the contexts
of terror fighting, natural disasters and human-caused disasters. The p-center
problem is NP-hard even if the network is planar with unit vertex weights, unit
edge lengths and with the maximum vertex degree of 3. If the locations of the
facilities are restricted to the vertices of the network, the problem is called the
vertex restricted p-center problem; if the facilities can be placed anywhere on the
network, it is called the absolute p-center problem. The p-center problem with
capacity restrictions on the facilities is referred to as the capacitated p-center
problem and in this problem, the demand nodes can be assigned to facilities with
single or multiple allocation strategies. In this thesis, the capacitated p-center
problem under the multiple allocation strategy is studied for the first time in the
literature.
The main focus of this thesis is a modelling and algorithmic perspective in
the exact solution of absolute, vertex restricted and capacitated p-center problems.
The existing literature is enhanced by the development of mathematical
formulations that can solve typical dimensions through the use of off the-shelf commercial solvers. By using the structural properties of the proposed formulations,
exact algorithms are developed. In order to increase the efficiency of the
proposed formulations and algorithms in solving higher dimensional problems,
new lower and upper bounds are provided and these bounds are utilized during
the experimental studies. The dimensions of problems solved in this thesis are
the highest reported in the literature.Çalık, HaticePh.D
Not available
The p-center problem is a relatively well known facility location problem thatinvolves locating p identical facilities on a network to minimize the maximumdistance between demand nodes and their closest facilities. The focus of theproblem is on the minimization of the worst case service time. This sort ofobjective is more meaningful than total cost objectives for problems with a timesensitive service structure. A majority of applications arises in emergency servicelocations such as determining optimal locations of ambulances, fire stations andpolice stations where the human life is at stake. There is also an increasedinterest in p-center location and related location covering problems in the contextsof terror fighting, natural disasters and human-caused disasters. The p-centerproblem is NP-hard even if the network is planar with unit vertex weights, unitedge lengths and with the maximum vertex degree of 3. If the locations of thefacilities are restricted to the vertices of the network, the problem is called thevertex restricted p-center problem; if the facilities can be placed anywhere on thenetwork, it is called the absolute p-center problem. The p-center problem withcapacity restrictions on the facilities is referred to as the capacitated p-centerproblem and in this problem, the demand nodes can be assigned to facilities withsingle or multiple allocation strategies. In this thesis, the capacitated p-centerproblem under the multiple allocation strategy is studied for the first time in theliterature.The main focus of this thesis is a modelling and algorithmic perspective inthe exact solution of absolute, vertex restricted and capacitated p-center problems.The existing literature is enhanced by the development of mathematicalformulations that can solve typical dimensions through the use of off the-shelfcommercial solvers. By using the structural properties of the proposed formulations,exact algorithms are developed. In order to increase the effciency of theproposed formulations and algorithms in solving higher dimensional problems,new lower and upper bounds are provided and these bounds are utilized duringthe experimental studies. The dimensions of problems solved in this thesis arethe highest reported in the literature.Not availabl