706 research outputs found
R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection
short paperInternational audienceAn indicator-based evolutionary multiobjective optimization algorithm (EMOA) is introduced which incorporates the contribution to the unary R2-indicator as the secondary selection criterion. First experiments indicate that the R2-EMOA accurately approximates the Pareto front of the considered continuous multiobjective optimization problems. Furthermore, decision makers' preferences can be included by adjusting the weight vector distributions of the indicator which results in a focused search behavior
Preference Articulation by Means of the R2 Indicator
International audienceIn multi-objective optimization, set-based performance indicators have become the state of the art for assessing the quality of Pareto front approximations. As a consequence, they are also more and more used within the design of multi-objective optimization algorithms. The R2 and the Hypervolume (HV) indicator represent two popular examples. In order to understand the behavior and the approximations preferred by these indicators and algorithms, a comprehensive knowledge of the indicator's properties is required. Whereas this knowledge is available for the HV, we presented a first approach in this direction for the R2 indicator just recently. In this paper, we build upon this knowledge and enhance the considerations with respect to the integration of preferences into the R2 indicator. More specifically, we analyze the effect of the reference point, the domain of the weights, and the distribution of weight vectors on the optimization of μ solutions with respect to the R2 indicator. By means of theoretical findings and empirical evidence, we show the potentials of these three possibilities using the optimal distribution of μ solutions for exemplary setups
Magnetic phase diagram of the Hubbard model with next-nearest-neighbour hopping
We calculate the magnetic phase diagram of the Hubbard model for a Bethe
lattice with nearest neighbour (NN) hopping and next nearest neighbour
(NNN) hopping in the limit of infinite coordination. We use the amplitude
of the NNN hopping to tune the density of states (DOS) of the
non-interacting system from a situation with particle-hole symmetry to an
asymmetric one with van-Hove singularities at the lower ()
respectively upper () band edge for large enough . For
this strongly asymmetric situation we find rather extended parameter regions
with ferromagnetic states and regions with antiferromagnetic states.Comment: 13 pages, 7 figure
Bringing Order to Special Cases of Klee's Measure Problem
Klee's Measure Problem (KMP) asks for the volume of the union of n
axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm
has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known
for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP
(where all boxes are cubes of equal side length), Hypervolume (where all boxes
share a vertex), and k-Grounded (where the projection onto the first k
dimensions is a Hypervolume instance).
In this paper we bring some order to these special cases by providing
reductions among them. In addition to the trivial inclusions, we establish
Hypervolume as the easiest of these special cases, and show that the runtimes
of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we
show that any algorithm for one of the special cases with runtime T(n,d)
implies an algorithm for the general case with runtime T(n,2d), yielding the
first non-trivial relation between KMP and its special cases. This allows to
transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)}
algorithm exists for any of the special cases under reasonable complexity
theoretic assumptions. Furthermore, assuming that there is no improved
algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 -
eps})) this reduction shows that there is no algorithm with runtime
O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same
assumption we show a tight lower bound for a recent algorithm for 2-Grounded
[Yildiz,Suri'12].Comment: 17 page
A Study of Archiving Strategies in Multi-Objective PSO for Molecular Docking
Molecular docking is a complex optimization problem aimed at predicting the position of a ligand molecule in the active site of a receptor with the lowest binding energy. This problem can be formulated as a bi-objective optimization problem by minimizing the binding energy and the Root Mean Square Deviation (RMSD) difference in the coordinates of ligands. In this context, the SMPSO multi-objective swarm-intelligence algorithm has shown a remarkable performance. SMPSO is characterized by having an external archive used to store the non-dominated solutions and also as the basis of the leader selection strategy. In this paper, we analyze several SMPSO variants based on different archiving strategies in the scope of a benchmark of molecular docking instances. Our study reveals that the SMPSOhv, which uses an hypervolume contribution based archive, shows the overall best performance.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
Dominance Based Crossover Operator for Evolutionary Multi-objective Algorithms
In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates - but contradictory conclusions have been reported. This paper introduces a particular mating restriction for Evolutionary Multi-objective Algorithms, based on the Pareto dominance relation: the partner of a non-dominated individual will be preferably chosen among the individuals of the population that it dominates. Coupled with the BLX crossover operator, two different ways of generating offspring are proposed. This recombination scheme is validated within the well-known NSGA-II framework on three bi-objective benchmark problems and one real-world bi-objective constrained optimization problem. An acceleration of the progress of the population toward the Pareto set is observed on all problems
On the Effect of Connectedness for Biobjective Multiple and Long Path Problems
Recently, the property of connectedness has been claimed to give a strong
motivation on the design of local search techniques for multiobjective
combinatorial optimization (MOCO). Indeed, when connectedness holds, a basic
Pareto local search, initialized with at least one non-dominated solution,
allows to identify the efficient set exhaustively. However, this becomes
quickly infeasible in practice as the number of efficient solutions typically
grows exponentially with the instance size. As a consequence, we generally have
to deal with a limited-size approximation, where a good sample set has to be
found. In this paper, we propose the biobjective multiple and long path
problems to show experimentally that, on the first problems, even if the
efficient set is connected, a local search may be outperformed by a simple
evolutionary algorithm in the sampling of the efficient set. At the opposite,
on the second problems, a local search algorithm may successfully approximate a
disconnected efficient set. Then, we argue that connectedness is not the single
property to study for the design of local search heuristics for MOCO. This work
opens new discussions on a proper definition of the multiobjective fitness
landscape.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives
The properties of local optimal solutions in multi-objective combinatorial
optimization problems are crucial for the effectiveness of local search
algorithms, particularly when these algorithms are based on Pareto dominance.
Such local search algorithms typically return a set of mutually nondominated
Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper
investigates two aspects of PLO-sets by means of experiments with Pareto local
search (PLS). First, we examine the impact of several problem characteristics
on the properties of PLO-sets for multi-objective NK-landscapes with correlated
objectives. In particular, we report that either increasing the number of
objectives or decreasing the correlation between objectives leads to an
exponential increment on the size of PLO-sets, whereas the variable correlation
has only a minor effect. Second, we study the running time and the quality
reached when using bounding archiving methods to limit the size of the archive
handled by PLS, and thus, the maximum size of the PLO-set found. We argue that
there is a clear relationship between the running time of PLS and the
difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
Pareto optimality in multilayer network growth
We model the formation of multi-layer transportation networks as a multi-objective optimization process, where service providers compete for passengers, and the creation of routes is determined by a multi-objective cost function encoding a trade-off between efficiency and competition. The resulting model reproduces well real-world systems as diverse as airplane, train and bus networks, thus suggesting that such systems are indeed compatible with the proposed local optimization
mechanisms. In the specific case of airline transportation systems, we show that the networks of routes operated by each company are placed very close to the theoretical Pareto front in the efficiency-competition plane, and that most of the largest carriers of a continent belong to the corresponding Pareto front. Our results shed light on the fundamental role played by multi-objective
optimization principles in shaping the structure of large-scale multilayer transportation systems, and provide novel insights to service providers on the strategies for the smart selection of novel routes
Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives
The properties of local optimal solutions in multi-objective combinatorial
optimization problems are crucial for the effectiveness of local search
algorithms, particularly when these algorithms are based on Pareto dominance.
Such local search algorithms typically return a set of mutually nondominated
Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper
investigates two aspects of PLO-sets by means of experiments with Pareto local
search (PLS). First, we examine the impact of several problem characteristics
on the properties of PLO-sets for multi-objective NK-landscapes with correlated
objectives. In particular, we report that either increasing the number of
objectives or decreasing the correlation between objectives leads to an
exponential increment on the size of PLO-sets, whereas the variable correlation
has only a minor effect. Second, we study the running time and the quality
reached when using bounding archiving methods to limit the size of the archive
handled by PLS, and thus, the maximum size of the PLO-set found. We argue that
there is a clear relationship between the running time of PLS and the
difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
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