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Performance Assessment of Multiobjective Optimizers: An Analysis and Review
 IEEE Transactions on Evolutionary Computation
, 2002
"... An important issue in multiobjective optimization is the quantitative comparison of the performance of di#erent algorithms. In the case of multiobjective evolutionary algorithms, the outcome is usually an approximation of the Paretooptimal front, which is denoted as an approximation set, and the ..."
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Cited by 144 (5 self)
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An important issue in multiobjective optimization is the quantitative comparison of the performance of di#erent algorithms. In the case of multiobjective evolutionary algorithms, the outcome is usually an approximation of the Paretooptimal front, which is denoted as an approximation set, and therefore the question arises of how to evaluate the quality of approximation sets. Most popular are methods that assign each approximation set a vector of real numbers that reflect different aspects of the quality. Sometimes, pairs of approximation sets are considered too. In this study, we provide a rigorous analysis of the limitations underlying this type of quality assessment.
Combining convergence and diversity in evolutionary multiobjective optimization
 Evolutionary Computation
, 2002
"... Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Paretooptimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms c ..."
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Cited by 144 (15 self)
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Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Paretooptimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Paretooptimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Paretooptimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept ofdominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modi�cations to the baseline algorithm are also suggested. The concept ofdominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.
A Tutorial on Evolutionary Multiobjective Optimization
 In Metaheuristics for Multiobjective Optimisation
, 2003
"... Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. ..."
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Cited by 64 (0 self)
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Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. Meanwhil e evol utionary mul tiobjective optimization has become establ ished as a separate subdiscipl ine combining the fiel ds of evol utionary computation and cl assical mul tipl e criteria decision ma ing. This paper gives an overview of evol tionary mu l iobjective optimization with the focus on methods and theory. On the one hand, basic principl es of mu l iobjective optimization and evol tionary alA#xv hms are presented, and various al gorithmic concepts such as fitness assignment, diversity preservation, and el itism are discussed. On the other hand, the tutorial incl udes some recent theoretical resul ts on the performance of mu l iobjective evol tionaryalvDfifl hms and addresses the question of how to simpl ify the exchange of methods and appl ications by means of a standardized interface. 1
Minmax and minmax regret versions of combinatorial optimization problems: A survey
 European Journal of Operational Research
"... Minmax and minmax regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the minmax and minmax regret versions of some combinatorial optimization problems: shortest path, spannin ..."
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Cited by 18 (1 self)
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Minmax and minmax regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the minmax and minmax regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min st cut, knapsack. Since most of these problems are NPhard, we also investigate the approximability of these problems. Furthermore, we present algorithms to solve these problems to optimality.
Archiving with Guaranteed Convergence and Diversity in MultiObjective Optimization
 In Proceedings of the Genetic and Evolutionary Computation Conference
, 2002
"... Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Paretooptimal solutions in a single simulation run. However, none of the multiobjective evolutionary algorithm ..."
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Cited by 18 (4 self)
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Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Paretooptimal solutions in a single simulation run. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Paretooptimal solutions with a wide diversity among the solutions. In this paper we discuss why a number of earlier MOEAs do not have such properties. A new archiving strategy is proposed that maintains a subset of the generated solutions. It guarantees convergence and diversity according to welldefined criteria, i.e. #dominance and #Pareto optimality.
On the Convergence and DiversityPreservation Properties of MultiObjective Evolutionary Algorithms
, 2001
"... Over the past few years, the research on evolutionary algorithms ..."
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Cited by 16 (4 self)
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Over the past few years, the research on evolutionary algorithms
Approximation of minmax and minmax regret versions of some combinatorial optimization problems.
, 2006
"... ..."
Solving efficiently the 0–1 multiobjective knapsack problem
 Computers & Operations Research
"... ∗ corresponding author In this paper, we present an approach, based on dynamic programming, for solving the 01 multiobjective knapsack problem. The main idea of the approach relies on the use of several complementary dominance relations to discard partial solutions that cannot lead to new nondomi ..."
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∗ corresponding author In this paper, we present an approach, based on dynamic programming, for solving the 01 multiobjective knapsack problem. The main idea of the approach relies on the use of several complementary dominance relations to discard partial solutions that cannot lead to new nondominated criterion vectors. This way, we obtain an efficient method that outperforms the existing methods both in terms of CPU time and size of solved instances. Extensive numerical experiments on various types of instances are reported. A comparison with other exact methods is also performed. In addition, for the first time to our knowledge, we present experiments in the threeobjective case.
P.I.: Evolution of hyperheuristics for the biobjective 0/1 knapsack problem by multiobjective genetic programming
 In: GECCO 2008, ACM
"... The 0/1 knapsack problem is one of the most exhaustively studied NPhard combinatorial optimization problems. Many different approaches have been taken to obtain an approximate solution to the problem in polynomial time. Here we consider the biobjective 0/1 knapsack problem. The contribution of th ..."
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The 0/1 knapsack problem is one of the most exhaustively studied NPhard combinatorial optimization problems. Many different approaches have been taken to obtain an approximate solution to the problem in polynomial time. Here we consider the biobjective 0/1 knapsack problem. The contribution of this paper is to show that a genetic programming system can evolve a set of heuristics that can give solutions on the Pareto front for multiobjective combinatorial problems. The genetic programming (GP) system outlined here evolves a heuristic which decides whether or not to add an item to the knapsack in such a way that the final solution is one of the Pareto optimal solutions. Moreover, the Pareto front obtained from the GP system is comparable to the front obtained from other humandesigned heuristics. We discuss the issue of the diversity of the obtained Pareto front and the application of stronglytyped GP as a means of obtaining better diversity.