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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
NILS: a Neutrality-based Iterated Local Search and its application to Flowshop Scheduling
This paper presents a new methodology that exploits specific characteristics
from the fitness landscape. In particular, we are interested in the property of
neutrality, that deals with the fact that the same fitness value is assigned to
numerous solutions from the search space. Many combinatorial optimization
problems share this property, that is generally very inhibiting for local
search algorithms. A neutrality-based iterated local search, that allows
neutral walks to move on the plateaus, is proposed and experimented on a
permutation flowshop scheduling problem with the aim of minimizing the
makespan. Our experiments show that the proposed approach is able to find
improving solutions compared with a classical iterated local search. Moreover,
the tradeoff between the exploitation of neutrality and the exploration of new
parts of the search space is deeply analyzed
Evolutionary algorithm-based analysis of gravitational microlensing lightcurves
A new algorithm developed to perform autonomous fitting of gravitational
microlensing lightcurves is presented. The new algorithm is conceptually
simple, versatile and robust, and parallelises trivially; it combines features
of extant evolutionary algorithms with some novel ones, and fares well on the
problem of fitting binary-lens microlensing lightcurves, as well as on a number
of other difficult optimisation problems. Success rates in excess of 90% are
achieved when fitting synthetic though noisy binary-lens lightcurves, allowing
no more than 20 minutes per fit on a desktop computer; this success rate is
shown to compare very favourably with that of both a conventional (iterated
simplex) algorithm, and a more state-of-the-art, artificial neural
network-based approach. As such, this work provides proof of concept for the
use of an evolutionary algorithm as the basis for real-time, autonomous
modelling of microlensing events. Further work is required to investigate how
the algorithm will fare when faced with more complex and realistic microlensing
modelling problems; it is, however, argued here that the use of parallel
computing platforms, such as inexpensive graphics processing units, should
allow fitting times to be constrained to under an hour, even when dealing with
complicated microlensing models. In any event, it is hoped that this work might
stimulate some interest in evolutionary algorithms, and that the algorithm
described here might prove useful for solving microlensing and/or more general
model-fitting problems.Comment: 14 pages, 3 figures; accepted for publication in MNRA
An efficient genetic algorithm for large-scale planning of robust industrial wireless networks
An industrial indoor environment is harsh for wireless communications
compared to an office environment, because the prevalent metal easily causes
shadowing effects and affects the availability of an industrial wireless local
area network (IWLAN). On the one hand, it is costly, time-consuming, and
ineffective to perform trial-and-error manual deployment of wireless nodes. On
the other hand, the existing wireless planning tools only focus on office
environments such that it is hard to plan IWLANs due to the larger problem size
and the deployed IWLANs are vulnerable to prevalent shadowing effects in harsh
industrial indoor environments. To fill this gap, this paper proposes an
overdimensioning model and a genetic algorithm based over-dimensioning (GAOD)
algorithm for deploying large-scale robust IWLANs. As a progress beyond the
state-of-the-art wireless planning, two full coverage layers are created. The
second coverage layer serves as redundancy in case of shadowing. Meanwhile, the
deployment cost is reduced by minimizing the number of access points (APs); the
hard constraint of minimal inter-AP spatial paration avoids multiple APs
covering the same area to be simultaneously shadowed by the same obstacle. The
computation time and occupied memory are dedicatedly considered in the design
of GAOD for large-scale optimization. A greedy heuristic based
over-dimensioning (GHOD) algorithm and a random OD algorithm are taken as
benchmarks. In two vehicle manufacturers with a small and large indoor
environment, GAOD outperformed GHOD with up to 20% less APs, while GHOD
outputted up to 25% less APs than a random OD algorithm. Furthermore, the
effectiveness of this model and GAOD was experimentally validated with a real
deployment system
On the Neutrality of Flowshop Scheduling Fitness Landscapes
Solving efficiently complex problems using metaheuristics, and in particular
local searches, requires incorporating knowledge about the problem to solve. In
this paper, the permutation flowshop problem is studied. It is well known that
in such problems, several solutions may have the same fitness value. As this
neutrality property is an important one, it should be taken into account during
the design of optimization methods. Then in the context of the permutation
flowshop, a deep landscape analysis focused on the neutrality property is
driven and propositions on the way to use this neutrality to guide efficiently
the search are given.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
Self-adaptation of Genetic Operators Through Genetic Programming Techniques
Here we propose an evolutionary algorithm that self modifies its operators at
the same time that candidate solutions are evolved. This tackles convergence
and lack of diversity issues, leading to better solutions. Operators are
represented as trees and are evolved using genetic programming (GP) techniques.
The proposed approach is tested with real benchmark functions and an analysis
of operator evolution is provided.Comment: Presented in GECCO 201
An efficient genetic algorithm for large-scale transmit power control of dense and robust wireless networks in harsh industrial environments
The industrial wireless local area network (IWLAN) is increasingly dense, due to not only the penetration of wireless applications to shop floors and warehouses, but also the rising need of redundancy for robust wireless coverage. Instead of simply powering on all access points (APs), there is an unavoidable need to dynamically control the transmit power of APs on a large scale, in order to minimize interference and adapt the coverage to the latest shadowing effects of dominant obstacles in an industrial indoor environment. To fulfill this need, this paper formulates a transmit power control (TPC) model that enables both powering on/off APs and transmit power calibration of each AP that is powered on. This TPC model uses an empirical one-slope path loss model considering three-dimensional obstacle shadowing effects, to enable accurate yet simple coverage prediction. An efficient genetic algorithm (GA), named GATPC, is designed to solve this TPC model even on a large scale. To this end, it leverages repair mechanism-based population initialization, crossover and mutation, parallelism as well as dedicated speedup measures. The GATPC was experimentally validated in a small-scale IWLAN that is deployed a real industrial indoor environment. It was further numerically demonstrated and benchmarked on both small- and large-scales, regarding the effectiveness and the scalability of TPC. Moreover, sensitivity analysis was performed to reveal the produced interference and the qualification rate of GATPC in function of varying target coverage percentage as well as number and placement direction of dominant obstacles. (C) 2018 Elsevier B.V. All rights reserved
Algorithms for the minimum sum coloring problem: a review
The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex
coloring problem which has a number of AI related applications. Due to its
theoretical and practical relevance, MSCP attracts increasing attention. The
only existing review on the problem dates back to 2004 and mainly covers the
history of MSCP and theoretical developments on specific graphs. In recent
years, the field has witnessed significant progresses on approximation
algorithms and practical solution algorithms. The purpose of this review is to
provide a comprehensive inspection of the most recent and representative MSCP
algorithms. To be informative, we identify the general framework followed by
practical solution algorithms and the key ingredients that make them
successful. By classifying the main search strategies and putting forward the
critical elements of the reviewed methods, we wish to encourage future
development of more powerful methods and motivate new applications
Ant colony optimisation and local search for bin-packing and cutting stock problems
The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO
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