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MultiObjective Optimization Using Genetic Algorithms: A Tutorial
"... abstract – Multiobjective formulations are a realistic models for many complex engineering optimization problems. Customized genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In many reallife problems, objectives under consid ..."
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abstract – Multiobjective formulations are a realistic models for many complex engineering optimization problems. Customized genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In many reallife problems, objectives under consideration conflict with each other, and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives. A reasonable solution to a multiobjective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. In this paper, an overview and tutorial is presented describing genetic algorithms developed specifically for these problems with multiple objectives. They differ from traditional genetic algorithms by using specialized fitness functions, introducing methods to promote solution diversity, and other approaches. 1.
A multiobjective evolutionary algorithm based on decomposition
 IEEE Transactions on Evolutionary Computation, Accepted
, 2007
"... 1 Decomposition is a basic strategy in traditional multiobjective optimization. However, this strategy has not yet widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a MOP into a number o ..."
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Cited by 44 (14 self)
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1 Decomposition is a basic strategy in traditional multiobjective optimization. However, this strategy has not yet widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a MOP into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and NSGAII. Experimental results show that it outperforms or performs similarly to MOGLS and NSGAII on multiobjective 01 knapsack problems and continuous multiobjective optimization problems. Index Terms multiobjective optimization, decomposition, evolutionary algorithms, memetic algorithms, Pareto optimality, computational complexity. I.
An introduction to Multiobjective Metaheuristics for Scheduling and Timetabling
 Metaheuristic for Multiobjective Optimisation, Lecture Notes in Economics and Mathematical Systems
, 2004
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The Design of Memetic Algorithms for Scheduling and Timetabling Problems
 Recent Advances in Memetic Algorithms, Studies in Fuzziness and Soft Computing
, 2004
"... Summary. There are several characteristics that make scheduling and timetabling problems particularly difficult to solve: they have huge search spaces, they are often highly constrained, they require sophisticated solution representation schemes, and they usually require very timeconsuming fitness ..."
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Cited by 23 (2 self)
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Summary. There are several characteristics that make scheduling and timetabling problems particularly difficult to solve: they have huge search spaces, they are often highly constrained, they require sophisticated solution representation schemes, and they usually require very timeconsuming fitness evaluation routines. There is a considerable number of memetic algorithms that have been proposed in the literature to solve scheduling and timetabling problems. In this chapter, we concentrate on identifying and discussing those strategies that appear to be particularly useful when designing memetic algorithms for this type of problems. For example, the many different ways in which knowledge of the problem domain can be incorporated into memetic algorithms is very helpful to design effective strategies to deal with infeasibility of solutions. Memetic algorithms employ local search, which serves as an effective intensification mechanism that is very useful when using sophisticated representation schemes and timeconsuming fitness evaluation functions. These algorithms also incorporate a population, which gives them an effective explorative ability to sample huge search spaces. Another important aspect that has been investigated when designing memetic algorithms for scheduling and timetabling problems, is how to establish the right balance between the work performed by the genetic search and the work performed by the local search. Recently, researchers have put considerable attention in the design of selfadaptive memetic algorithms. That is, to incorporate memes that adapt themselves according to the problem domain being solved and also to the particular conditions of the search process. This chapter also discusses some recent ideas proposed by researchers that might be useful when designing selfadaptive memetic algorithms. Finally, we give a summary of the issues discussed throughout the chapter and propose some future research directions in the design of memetic algorithms for scheduling and timetabling problems. 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 ..."
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Cited by 19 (3 self)
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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.
Diversityadaptive parallel memetic algorithm for solving large scale combinatorial optimization problems
 SOFT COMPUTING
, 2007
"... Parallel Memetic Algorithms (PMAs) are a class of modern parallel metaheuristics that combine evolutionary algorithms, local search, parallel and distributed computing technologies for global optimization. Recent studies on PMAs for largescale complex combinatorial optimization problems have sho ..."
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Parallel Memetic Algorithms (PMAs) are a class of modern parallel metaheuristics that combine evolutionary algorithms, local search, parallel and distributed computing technologies for global optimization. Recent studies on PMAs for largescale complex combinatorial optimization problems have shown that they converge to high quality solutions significantly faster than canonical GAs and MAs. However, the use of local learning for every individual throughout the PMA search can be a very computationally intensive and inefficient process. This paper presents a study on two diversityadaptive strategies, i.e., 1) diversitybased static adaptive strategy (PMASLS) and 2) diversitybased dynamic adaptive strategy (PMADLS) for controlling the local search frequency in the PMA search. Empirical study on a class of NPhard combinatorial optimization problem, particularly largescale quadratic assignment problems (QAPs) shows that the diversityadaptive PMA converges to competitive solutions at significantly lower computational cost when compared to the canonical MA and PMA. Furthermore, it is found that the diversitybased dynamic adaptation strategy displays better robustness in terms of solution quality across the class of QAP problems considered. Static adaptation strategy on the other hand requires extra effort in selecting suitable parameters to suit the problems in hand.
Dgpf – an adaptable framework for distributed multiobjective search algorithms applied to the genetic programming of sensor networks
 In Proceedings of the Second International Conference on Bioinspired Optimization Methods and their Application, BIOMA 2006
, 2006
"... Abstract: We present DGPF, a framework providing multiobjective, autoadaptive search algorithms with a focus on Genetic Programming. We first introduce a Common Search API, suitable to explore arbitrary problem spaces with different search algorithms. Using our implementation of Genetic Algorithms ..."
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Cited by 15 (10 self)
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Abstract: We present DGPF, a framework providing multiobjective, autoadaptive search algorithms with a focus on Genetic Programming. We first introduce a Common Search API, suitable to explore arbitrary problem spaces with different search algorithms. Using our implementation of Genetic Algorithms as an example, we elaborate on the distribution utilities of the framework which enable local, Master/Slave, PeerToPeer, and P2P/MS hybrid distributed search execution. We also discuss how heterogeneous searches consisting of multiple, cooperative search algorithms can be constructed. Sensor networks are distributed systems of nodes with scarce resources. We demonstrate how Genetic Programming based on our framework can be applied to create algorithms for sensor nodes that use these resources very efficiently.
Stochastic Local Search Algorithms for Multiobjective Combinatorial Optimization: Methods and Analysis
, 2006
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Evolving dispatching rules using genetic programming for solving multiobjective flexible jobshop problems
, 2008
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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 ..."
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Cited by 14 (8 self)
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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.