Results 11  20
of
148
A New Multiobjective Evolutionary Optimisation Algorithm: The TwoArchive Algorithm
"... Many MultiObjective Evolutionary Algorithms (MOEAs) have been proposed in recent years. However, almost all MOEAs have been evaluated on problems with two to four objectives only. It is unclear how well these MOEAs will perform on problems with a large number of objectives. Our preliminary study [1 ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
(Show Context)
Many MultiObjective Evolutionary Algorithms (MOEAs) have been proposed in recent years. However, almost all MOEAs have been evaluated on problems with two to four objectives only. It is unclear how well these MOEAs will perform on problems with a large number of objectives. Our preliminary study [1] showed that performance of some MOEAs deteriorates significantly as the number of objectives increases. This paper proposes a new MOEA that performs well on problems with a large number of objectives. The new algorithm separates nondominated solutions into two archives, and is thus called the TwoArchive algorithm. The two archives focused on convergence and diversity, respectively, in optimisation. Computational studies have been carried out to evaluate and compare our new algorithm against the best MOEA for problems with a large number of objectives. Our experimental results have shown that the TwoArchive algorithm outperforms existing MOEAs on problems with a large number of objectives. 1
RMMEDA: a regularity modelbased multiobjective estimation of distribution algorithm
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 2007
"... Under mild conditions, it can be induced from the Karush–Kuhn–Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is a piecewise continuous @ IAD manifold, where is the number of objectives. Based on this regularity property, we propose ..."
Abstract

Cited by 19 (3 self)
 Add to MetaCart
Under mild conditions, it can be induced from the Karush–Kuhn–Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is a piecewise continuous @ IAD manifold, where is the number of objectives. Based on this regularity property, we propose a regularity modelbased multiobjective estimation of distribution algorithm (RMMEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a @ IAD piecewise continuous manifold. The local principal component analysis algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A nondominated sortingbased selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RMMEDA outperforms three other stateoftheart algorithms, namely, GDE3, PCXNSGAII, and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RMMEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RMMEDA have also been identified and discussed in this paper.
Towards Estimating Nadir Objective Vector Using Evolutionary Approaches
 Department of Trade & Industry
, 2006
"... Nadir point plays an important role in multiobjective optimization because of its importance in estimating the range of objective values corresponding to desired Paretooptimal solutions and also in using many classical interactive optimization techniques. Since this point corresponds to the worst ..."
Abstract

Cited by 18 (7 self)
 Add to MetaCart
(Show Context)
Nadir point plays an important role in multiobjective optimization because of its importance in estimating the range of objective values corresponding to desired Paretooptimal solutions and also in using many classical interactive optimization techniques. Since this point corresponds to the worst Paretooptimal solution of each objective, the task of estimating the nadir point necessitates information about the whole Pareto optimal frontier and is reported to be a difficult task using classical means. In this paper, for the first time, we have proposed a couple of modifications to an existing evolutionary multiobjective optimization procedure to focus its search towards the extreme objective values frontwise. On up to 20objective optimization problems, both proposed procedures are found to be capable of finding a near nadir point quickly and reliably. Simulation results are interesting and should encourage further studies and applications in estimating the nadir point, a process which should lead to a better interactive procedure of finding and arriving at a desired Paretooptimal solution.
Multiobjective test problems, linkages, and evolutionary methodologies
 in Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation GECCO’06
"... Existing test problems for multiobjective optimization are criticized for not having adequate linkages among variables. In most problems, the Paretooptimal solutions correspond to a fixed value of certain variables and diversityof solutions comes mainlyfrom a random variation of certain other vari ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
(Show Context)
Existing test problems for multiobjective optimization are criticized for not having adequate linkages among variables. In most problems, the Paretooptimal solutions correspond to a fixed value of certain variables and diversityof solutions comes mainlyfrom a random variation of certain other variables. In this paper, we introduce explicit linkages among variables so as to develop difficult two and multiobjective test problems along the lines of ZDT and DTLZ problems. On a number of such test problems, this paper compares the performance of a number of EMO methodologies having (i) variablewise versus vectorwise recombination operators and (ii) spatial versus unidirectional recombination operators. Interesting and useful conclusions on the use of above operators are made from the study.
Investigating and Exploiting the Bias of the Weighted Hypervolume to Articulate User Preferences
"... Optimizing the hypervolume indicator within evolutionary multiobjective optimizers has become popular in the last years. Recently, the indicator has been generalized to the weighted case to incorporate various user preferences into hypervolumebased search algorithms. There are two main open questio ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
(Show Context)
Optimizing the hypervolume indicator within evolutionary multiobjective optimizers has become popular in the last years. Recently, the indicator has been generalized to the weighted case to incorporate various user preferences into hypervolumebased search algorithms. There are two main open questions in this context: (i) how does the specified weight influence the distribution of a fixed number of points that maximize the weighted hypervolume indicator? (ii) how can the user articulate her preferences easily without specifying a certain weight distribution function? In this paper, we tackle both questions. First, we theoretically investigate optimal distributions of μ points that maximize the weighted hypervolume indicator. Second, based on the obtained theoretical results, we propose a new approach to articulate user preferences within biobjective hypervolumebased optimization in terms of specifying a desired density of points on a predefined (imaginary) Pareto front. Within this approach, a new exact algorithm based on dynamic programming is proposed which selects the set of μ points that maximizes the (weighted) hypervolume indicator. Experiments on various test functions show the usefulness of this new preference articulation approach and the agreement between theory and practice.
A software framework based on a conceptual unified model for evolutionary multiobjective optimization: ParadisEOMOEO
, 2010
"... ..."
ApproximationGuided Evolutionary MultiObjective Optimization
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... Multiobjective optimization problems arise frequently in applications but can often only be solved approximately by heuristic approaches. Evolutionary algorithms have been widely used to tackle multiobjective problems. These algorithms use different measures to ensure diversity in the objective sp ..."
Abstract

Cited by 14 (6 self)
 Add to MetaCart
(Show Context)
Multiobjective optimization problems arise frequently in applications but can often only be solved approximately by heuristic approaches. Evolutionary algorithms have been widely used to tackle multiobjective problems. These algorithms use different measures to ensure diversity in the objective space but are not guided by a formal notion of approximation. We present a new framework of an evolutionary algorithm for multiobjective optimization that allows to work with a formal notion of approximation. Our experimental results show that our approach outperforms stateoftheart evolutionary algorithms in terms of the quality of the approximation that is obtained in particular for problems with many objectives.
RMMEDA: A Regularity Model Based Multiobjective Estimation of Distribution Algorithm
, 2008
"... Under mild conditions, it can be induced from the KarushKuhnTucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is (m − 1)D piecewise continuous, where m is the number of objectives. Based on this regularity property, we propose a Regul ..."
Abstract

Cited by 14 (8 self)
 Add to MetaCart
Under mild conditions, it can be induced from the KarushKuhnTucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is (m − 1)D piecewise continuous, where m is the number of objectives. Based on this regularity property, we propose a Regularity Model based Multiobjective Estimation of Distribution Algorithm (RMMEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a (m−1)D piecewise continuous manifold. The Local Principal Component Analysis algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A nondominated sorting based selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RMMEDA outperforms three other stateoftheart algorithms, namely, GDE3, PCXNSGAII and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RMMEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RMMEDA have also been identified and discussed in this paper.
HCS: A new local search strategy for memetic multiobjective evolutionary algorithms
 IEEE Trans. Evolutionary Computation
"... Abstract — In this paper, we propose and investigate a new local search strategy for multiobjective memetic algorithms. More precisely, we suggest a novel iterative search procedure, known as the Hill Climber with Sidestep (HCS), which is designed for the treatment of multiobjective optimization pro ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
Abstract — In this paper, we propose and investigate a new local search strategy for multiobjective memetic algorithms. More precisely, we suggest a novel iterative search procedure, known as the Hill Climber with Sidestep (HCS), which is designed for the treatment of multiobjective optimization problems, and show further two possible ways to integrate the HCS into a given evolutionary strategy leading to new memetic (or hybrid) algorithms. The pecularity of the HCS is that it is intended to be capable both moving toward and along the (local) Pareto set depending on the distance of the current iterate toward this set. The local search procedure utilizes the geometry of the directional cones of such optimization problems and works with or without gradient information. Finally, we present some numerical results on some wellknown benchmark problems, indicating the strength of the local search strategy as a standalone algorithm as well as its benefit when used within a MOEA. For the latter we use the state of the art algorithms Nondominated Sorting Genetic AlgorithmII and Strength Pareto Evolutionary Algorithm 2 as base MOEAs. Index Terms — Continuation, hill climber, memetic strategy, multiobjective optimization.
Borg: An AutoAdaptive ManyObjective Evolutionary Computing Framework
"... This study introduces the Borg multiobjective evolutionary algorithm (MOEA) for manyobjective, multimodal optimization. The Borg MOEA combines ǫdominance, a measure of convergence speed named ǫprogress, randomized restarts and autoadaptive multioperator recombination into a unified optimization ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
(Show Context)
This study introduces the Borg multiobjective evolutionary algorithm (MOEA) for manyobjective, multimodal optimization. The Borg MOEA combines ǫdominance, a measure of convergence speed named ǫprogress, randomized restarts and autoadaptive multioperator recombination into a unified optimization framework. A comparative study on 33 instances of 18 test problems from the DTLZ,WFG, and CEC 2009 test suites demonstrates Borg meets or exceeds 6 stateoftheart MOEAs on the majority of the tested problems. Performance for each test problem is evaluated using a 1000 point Latin hypercube sampling of each algorithm’s feasible parameterization space. The statistical performance of every sampledMOEA parameterization is evaluated using 50 replicate random seed trials. The Borg MOEA is not a single algorithm; instead it represents a class of algorithms whose operators are adaptively selected based on the problem. The adaptive discovery of key operators is of particular importance for benchmarking how variation operators enhance search for complex manyobjective problems.