2,478 research outputs found
Output-sensitive complexity of multiobjective combinatorial optimization
We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output-sensitive, i.e., its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of MOCO problems for which such an efficient algorithm exists as well as problems for which no efficient algorithm exists under mild complexity theoretic assumptions
A Novel Multiobjective Cell Switch-Off Framework for Cellular Networks
Cell Switch-Off (CSO) is recognized as a promising approach to reduce the
energy consumption in next-generation cellular networks. However, CSO poses
serious challenges not only from the resource allocation perspective but also
from the implementation point of view. Indeed, CSO represents a difficult
optimization problem due to its NP-complete nature. Moreover, there are a
number of important practical limitations in the implementation of CSO schemes,
such as the need for minimizing the real-time complexity and the number of
on-off/off-on transitions and CSO-induced handovers. This article introduces a
novel approach to CSO based on multiobjective optimization that makes use of
the statistical description of the service demand (known by operators). In
addition, downlink and uplink coverage criteria are included and a comparative
analysis between different models to characterize intercell interference is
also presented to shed light on their impact on CSO. The framework
distinguishes itself from other proposals in two ways: 1) The number of
on-off/off-on transitions as well as handovers are minimized, and 2) the
computationally-heavy part of the algorithm is executed offline, which makes
its implementation feasible. The results show that the proposed scheme achieves
substantial energy savings in small cell deployments where service demand is
not uniformly distributed, without compromising the Quality-of-Service (QoS) or
requiring heavy real-time processing
Output-sensitive complexity of multiobjective combinatorial optimization with an application to the multiobjective shortest path problem
In this thesis, we are concerned with multiobjective combinatorial optimization
(MOCO) problems. We attempt to fill the gap between theory and practice, which
comes from the lack of a deep complexity theory for MOCO problems. In a first part,
we consider a complexity notion for multiobjective optimization problems which derives
from output-sensitive complexity. The primary goal of such a complexity notion is
to classify problems into easy and hard problems. We show that the multiobjective
minimum cut problem as well as the multiobjective linear programming problem are
easy problems in this complexity theory. We also show that finding extreme points
of nondominated sets is an easy problem under certain assumptions. On the side of
hard problems, there are obvious ones like the multiobjective traveling salesperson
problem. Moreover, we show that the well-known multiobjective shortest path problem
is a hard problem. This is also the case for the multiobjective matching and integer
min-cost flow problem. We also identify a class of problems for which the biobjective
unconstraint combinatorial optimization problem is a barrier for efficient solvability.
In a second part, we are again concerned with the gap between theory and practice.
This time, we approach the multiobjective shortest path (MOSP) problem from the
practical side. For the application in the planning of power transmission lines, we
need to have implementations which can cope with large graphs and a larger number
of objectives. The results from the first part suggest that exact methods might be
incapable of achieving this goal which we also prove empirically. This is why we
decide to study the literature on approximation algorithms for the MOSP problem.
We conclude that they do not scale well with the number of objectives in general
and that there are no practical implementations available. Hence, we develop a novel
approximation algorithm in the second part which leans to the exact approaches
which are well tested in practice. In an extensive computational study, we show
that our implementation of this algorithm performs well even on a larger number
of objectives. We compare our implementation to implementations of the other
existing approximation algorithms and conclude that our implementation is superior
on instances with more than three objectives.Diese Dissertation ist mit der KomplexitÀt von mehrkriteriellen kombinatorischen
Optimierungsproblemen (MOCO) befasst. Hierbei wollen wir die LĂŒcke schlieĂen, die
sich aus dem Fehlen einer umfassenden KomplexitÀtstheorie dieser Probleme ergibt.
In einem ersten Teil beschreiben wir einen KomplexitĂ€tsbegriff fĂŒr mehrkriterielle
Optimierungsprobleme, der sich von ausgabesensitiver KomplexitÀt ableitet. Das
Ziel eines KomplexitÀtsbegriffes ist die Klassifikation von Problemen in einfache und
schwierige Probleme. Wir zeigen, dass die Probleme einen Pareto-optimalen Schnitt
in einem Graphen zu bestimmen, sowie mehrkriterielle lineare Optimierung einfache
Probleme nach dieser KomplexitÀtstheorie sind. Auch das Problem Extrempunkte von
Pareto-Fronten zu bestimmen ist unter bestimmten Bedingungen ein einfaches Problem.
Auf der Seite der schwierigen Probleme können wir ĂŒber die offensichtlichen Probleme
wie das mehrkriterielle Handlungsreisendenproblem hinaus auch zeigen, dass das
bekannte mehrkriterielle KĂŒrzeste-Wege-Problem ein schwieriges Problem darstellt.
Dies gilt ebenso auch fĂŒr das mehrkriterielle Zuordnungsproblem in allgemeinen
Graphen und das mehrkriterielle Flussproblem mit ganzzahligen Flussvariablen. Wir
finden in dieser Arbeit auĂerdem eine Klasse von Problemen, deren effiziente Lösbarkeit
von der effizienten Lösbarkeit des bikriteriellen unrestringierten kombinatorischen
Optimierungsproblems abhÀngt.
In einem zweiten Teil beschĂ€ftigen wir uns wieder mit der LĂŒcke zwischen Theorie
und Praxis. Diesmal nĂ€hern wir uns dem mehrkriteriellen KĂŒrzeste-Wege-Problem von
der praktischen Seite. FĂŒr eine Anwendung in der Stromtrassenoptimierung ist es nötig
einen Algorithmus zu finden, der sowohl mit groĂen Graphen, als auch mit mehreren
Zielfunktionen umgehen kann. Aus dem ersten Teil können wir ableiten, dass exakte
Methoden dort an ihre Grenzen stoĂen, was wir auch empirisch belegen. Wir studieren
daher Approximationsalgorithmen aus der Literatur und stellen fest, dass sie in der
Anzahl der Zielfunktionen nur schlecht skalieren und auch noch nicht praxiserprobt sind.
Daher entwickeln wir im zweiten Teil einen neuen Approximationsalgorithmus, der sich
stark an die Errungenschaften der praktischen Algorithmen orientiert. Wir zeigen in
einem groĂ angelegten Experiment, dass unsere Implementierung des Algorithmus auch
noch auf einer gröĂeren Anzahl von Zielfunktionen praxistauglich ist. Der Vergleich
mit unseren Implementierungen der existierenden Approximationsalgorithmen zeigt
zudem, dass unsere Implementierung den anderen auf Instanzen mit mehr als drei
Zielfunktionen ĂŒberlegen ist
Grammar-based Representation and Identification of Dynamical Systems
In this paper we propose a novel approach to identify dynamical systems. The
method estimates the model structure and the parameters of the model
simultaneously, automating the critical decisions involved in identification
such as model structure and complexity selection. In order to solve the
combined model structure and model parameter estimation problem, a new
representation of dynamical systems is proposed. The proposed representation is
based on Tree Adjoining Grammar, a formalism that was developed from linguistic
considerations. Using the proposed representation, the identification problem
can be interpreted as a multi-objective optimization problem and we propose a
Evolutionary Algorithm-based approach to solve the problem. A benchmark example
is used to demonstrate the proposed approach. The results were found to be
comparable to that obtained by state-of-the-art non-linear system
identification methods, without making use of knowledge of the system
description.Comment: Submitted to European Control Conference (ECC) 201
Multiobjective scheduling for semiconductor manufacturing plants
Scheduling of semiconductor wafer manufacturing system is identified as a complex problem, involving multiple and conflicting objectives (minimization of facility average utilization, minimization of waiting time and storage, for instance) to simultaneously satisfy. In this study, we propose an efficient approach based on an artificial neural network technique embedded into a multiobjective genetic algorithm for multi-decision scheduling problems in a semiconductor wafer fabrication environment
An outer approximation algorithm for multi-objective mixed-integer linear and non-linear programming
In this paper, we present the first outer approximation algorithm for
multi-objective mixed-integer linear programming problems with any number of
objectives. The algorithm also works for certain classes of non-linear
programming problems. It produces the non-dominated extreme points as well as
the facets of the convex hull of these points. The algorithm relies on an
oracle which solves single-objective weighted-sum problems and we show that the
required number of oracle calls is polynomial in the number of facets of the
convex hull of the non-dominated extreme points in the case of multiobjective
mixed-integer programming (MOMILP). Thus, for MOMILP problems for which the
weighted-sum problem is solvable in polynomial time, the facets can be computed
with incremental-polynomial delay. From a practical perspective, the algorithm
starts from a valid lower bound set for the non-dominated extreme points and
iteratively improves it. Therefore it can be used in multi-objective
branch-and-bound algorithms and still provide a valid bound set at any stage,
even if interrupted before converging. Moreover, the oracle produces Pareto
optimal solutions, which makes the algorithm also attractive from the primal
side in a multi-objective branch-and-bound context. Finally, the oracle can
also be called with any relaxation of the primal problem, and the obtained
points and facets still provide a valid lower bound set. A computational study
on a set of benchmark instances from the literature and new non-linear
multi-objective instances is provided.Comment: 21 page
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