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Zusammenfassung:
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In this dissertation, three NP-hard optimization problems are studied and va-
rious computational intelligence methods are considered for solving them, with a
special emphasis on the possibilities of applying fuzzy logic in order to improve the
performances of proposed methods. In addition, it is shown how fuzzy logic can be
incorporated into a model to make it more adequate to real world applications. The
first problem considered is the Risk-Constrained Cash-in-Transit Vehicle Routing
Problem (RCTVRP) that represents a special case of the vehicle routing problem
(VRP). Similar to the classical VRP, the aim is to determine the collection routes
from one depot to a number of customers in order to minimize the overall travel
distance (or cost). Additionally, the safety aspect of the routed risk constraints
are introduced in the case of RCTVRP. The RCTVRP concerns the issue of secu-
rity during the transportation of cash or valuable goods (e.g. in the cash-in-transit
industry).
The other two problems studied in this dissertation belong to the class of loca-
tion problems: the Load Balancing Problem (LOBA) and the Max-Min Diversity
Problem (MMDP). The goal of the LOBA problem is to locate a fixed number of
facilities, such that the difference between the maximum and minimum number of
customers served by each facility is balanced. The LOBA model is useful in cases
where customers naturally choose the closest facility. The MMDP consists of se-
lecting a subset of a fixed number of elements from a given set in such a way that
the diversity among the selected elements is maximized. This problem also arises
in real world situations encompassing a variety of fields, particularly the social and
biological sciences.
In order to solve the RCTVRP, a fuzzy GRASP (Greedy Randomized Adaptive
Search Procedure) is hybridized with Path Reliking (PR) methodology. Carefully
adjusted fuzzy modification incorporated into the proposed GRASP for the RC-
TVRP improved its performance. Moreover, in this dissertation a new PR structure
is implemented and can be used for other vehicle routing problems. To improve
the algorithm’s time complexity, a new data structure for the RCTVRP is incor-
porated. The proposed fuzzy GRASP with PR hybrid shows better computational
performance compared to its non-fuzzy version. Furthermore, computational results
on publicly available data sets indicate that the proposed algorithm outperforms all
existing methods from the literature for solving the RCTVRP.
For solving the LOBA problem two efficient hybrid metaheuristic methods are
proposed: a combination of reduced and standard variable neighborhood search met-
hods (RVNS-VNS) and hybridization of evolutionary algorithm and VNS approach
(EA-VNS). The proposed hybrid methods are first benchmarked and compared to
all the other methods on existing test instances for the LOBA problem with up to
100 customers and potential suppliers. In order to test the effectiveness of the pro-
posed methods, we modify several large-scale instances from the literature with up
to 402 customers and potential suppliers. Exhaustive computational experiments
show that the proposed hybrid methods quickly reach all known optimal solutions
while providing solutions on large-scale problem instances in short CPU times. Re-
garding solution quality and running times, we conclude that the proposed EA-VNS
approach outperforms other considered methods for solving the LOBA problem.
EA approach is also proposed for solving the MMDP. Computational experi-
ments on a smaller benchmark data set showed that the classic EA quickly reached
all optimal solutions obtained previously by an exact solver. However, some of the
larger instances of MMDP were challenging for classic EA. Although researchers
have established the most commonly used parameter setting for EA that has good
performance for most of the problems, it is still challenging to choose the adequate
values for the parameters of the algorithm. One approach to overcome this is chan-
ging parameter values during the algorithm run. As part of this dissertation this
problem was addressed by extending the evolutionary algorithm by adding a fuzzy
rule formulated from EA experts’ knowledge and experience. The implemented
fuzzy rule changes the mutation parameter during the algorithm run. The results
on tested instances indicate that the proposed fuzzy approach is more suitable for
solving the MMDP than classic EA.
For all three problems addressed whereas the smaller instances that CPLEX was
able to solve, obtained optimal solutions were used for comparison with proposed
methods and all of the proposed methods obtained these optimal solutions.
Moreover, in this dissertation it has been shown that fuzzy logic is a successful
tool in modeling the RCTVRP. In this problem the risk constraints are set by
using a risk threshold T on each route and thus, the routes with risk larger than
T are forbidden. However, in this dissertation the aim is to take into account the
probability of being robbed along each route instead of just allowing solutions with
routes that satisfy the risk constraints. A new fuzzy model for the RCTVRP is
developed which takes into account the value of the risk index of each route and the
solutions with lower values of risk indexes on their routes are considered superior. In
order to achieve that fuzzy numbers are used in the improved model. Moreover, two
mixed integer program formulations of new fuzzy model are developed and presented
in this dissertation. The introduced fuzzy model is compared with the model from
the literature using an adequate example and the advantages of the newly proposed
fuzzy RCTVRP is demonstrated. Computational experiments are performed and
the comparison of the two models given in the paper show that the newly presented
approach leads to safer routes. |