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An analysis on recombination in multiobjective evolutionary optimization
 In Proceedings of the 13th ACM Annual Conference on Genetic and Evolutionary Computation (GECCO’11
, 2011
"... Evolutionary algorithms (EAs) are increasingly popular approaches to multiobjective optimization. One of their significant advantages is that they can directly optimize the Pareto front by evolving a population of solutions, where the recombination (also called crossover) operators are usually emp ..."
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Evolutionary algorithms (EAs) are increasingly popular approaches to multiobjective optimization. One of their significant advantages is that they can directly optimize the Pareto front by evolving a population of solutions, where the recombination (also called crossover) operators are usually employed to reproduce new and potentially better solutions by mixing up solutions in the population. Recombination in multiobjective evolutionary algorithms is, however, mostly applied heuristically. In this paper, we investigate how from a theoretical viewpoint a recombination operator will affect a multiobjective EA. First, we employ artificial benchmark problems: the Weighted LPTNO problem (a generalization of the wellstudied LOTZ problem), and the wellstudied COCZ problem, for studying the effect of recombination. Our analysis discloses that recombination may accelerate the filling of the Pareto front by recombining diverse solutions and thus help solve multiobjective optimization. Because of this, for these two problems, we find that a multiobjective EA with recombination enabled achieves a better expected running time than any known EAs with recombination disabled. We further examine the effect of recombination on solving the multiobjective minimum spanning tree problem, which is an NPHard problem. Following our finding on the artificial problems, our analysis shows that recombination also helps accelerate filling the Pareto front and thus helps find approximate solutions faster.
Multiobjective EA approach for improved quality of solutions for spanning tree problem
 in: Proc. Internat. Conf. Evolutionary MultiCriterion Optimization (EMO), Lecture Notes in Computer Science
, 2005
"... Abstract. The problem of computing spanning trees along with specific constraints is mostly NPhard. Many approximation and stochastic algorithms which yield a single solution, have been proposed. In this paper, we formulate the generic multiobjective spanning tree (MOST) problem and consider edge ..."
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Abstract. The problem of computing spanning trees along with specific constraints is mostly NPhard. Many approximation and stochastic algorithms which yield a single solution, have been proposed. In this paper, we formulate the generic multiobjective spanning tree (MOST) problem and consider edgecost and diameter as the two objectives. Since the problem is hard, and the Paretofront is unknown, the main issue in such probleminstances is how to assess the convergence. We use a multiobjective evolutionary algorithm (MOEA) that produces diverse solutions without needing a priori knowledge of the solution space, and generate solutions from multiple tribes in order to assess movement of the solution front. Since no experimental results are available for MOST, we consider three well known diameterconstrained minimum spanning tree (dcMST) algorithms including randomized greedy heuristics (RGH) which represents the current state of the art on the dcMST, and modify them to yield a (near) optimal solutionfronts. We quantify the obtained solution fronts for comparison. We observe that MOEA provides superior solutions in the entirerange of the Paretofront, which none of the existing algorithms could individually do. 1
Multiobjective network design for realistic traffic models
 In Proceedings of generic and evolutionary computation conference (GECCO’07
, 2007
"... Network topology design problems find application in several real life scenarios. However, most designs in the past either optimize for a single criterion like delay or assume simplistic traffic models like Poisson. Such assumptions make the solutions inapplicable in the practical world. In this pap ..."
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Network topology design problems find application in several real life scenarios. However, most designs in the past either optimize for a single criterion like delay or assume simplistic traffic models like Poisson. Such assumptions make the solutions inapplicable in the practical world. In this paper, we formulate and solve a multiobjective network topology design problem for a realistic Internet traffic model which is assumed to be self similar. We optimize for the average packet delivery delay and network layout cost to construct realistic network topologies. We present a multiobjective evolutionary algorithm (MOEA) to obtain the diverse nearoptimal network topologies. For fair comparison, we design a multiobjective deterministic heuristic based on branch exchange – we call the heuristic Pareto Branch Exchange (PBE). We empirically show that the MOEA used performs well for real networks of various sizes, and generated topologies are quite different with significantly larger delays for the self similar traffic model.
Concurrent Topology and Routing Optimization in Automotive Network Integration
"... In this paper, a novel automatic approach for the concurrent topology and routing optimization that achieves a high quality network layout is proposed. This optimization is based on a specialized binary Integer Linear Program (ILP) in combination with a MultiObjective Evolutionary Algorithm (MOEA). ..."
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In this paper, a novel automatic approach for the concurrent topology and routing optimization that achieves a high quality network layout is proposed. This optimization is based on a specialized binary Integer Linear Program (ILP) in combination with a MultiObjective Evolutionary Algorithm (MOEA). The ILP is formulated such that each solution represents a topology and routing that fulfills all requirements and demands of the network. Thus, in an iterative process, this ILP is solved to obtain feasible networks whereas the MOEA is used for the optimization of multiple even nonlinear objectives and ensures a fast convergence towards the optimal solutions. Additionally, a domain specific preprocessing algorithm for the ILP is presented that decreases the problem complexity and, thus, allows to optimize large and complex networks efficiently. The experimental results validate the performance of this methodology on two stateoftheart prototype automotive networks.
A Comparative Assessment of Memetic, Evolutionary, and Constructive Algorithms for the Multiobjective dMST Problem
 Proc. of 2001 Genetic and Evolutionary Computation Conference Workshop Program
, 1997
"... Finding a minimumweight spanning tree ..."
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Fixed Parameter Evolutionary Algorithms and Maximum Leaf Spanning Trees: A Matter Of Mutation
, 2010
"... Evolutionary algorithms have been shown to be very successful for a wide range of NPhard combinatorial optimization problems. We investigate the NPhard problem of computing a spanning tree that has a maximal number of leaves by evolutionary algorithms in the context of fixed parameter tractability ..."
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Evolutionary algorithms have been shown to be very successful for a wide range of NPhard combinatorial optimization problems. We investigate the NPhard problem of computing a spanning tree that has a maximal number of leaves by evolutionary algorithms in the context of fixed parameter tractability (FPT) where the maximum number of leaves is the parameter under consideration. Our results show that simple evolutionary algorithms working with an edgeset encoding are confronted with local optima whose size of the inferior neighborhood grows with the value of an optimal solution. Investigating two common mutation operators, we show that an operator related to spanning tree problems leads to an FPT running time in contrast to a general mutation operator that does not have this property.
Multiobjective branchandbound. Application to the biobjective spanning tree problem
"... This paper focuses on a multiobjective derivation of branchandbound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multiobjective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points ra ..."
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This paper focuses on a multiobjective derivation of branchandbound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multiobjective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that a node in the search tree can be discarded if one can define a separating hypersurface in the objective space between the set of feasible solutions in the subtree and the set of points corresponding to potential Pareto optimal solutions. Numerical experiments on the biobjective spanning tree problem are provided that show the efficiency of the approach. Key words: multiobjective combinatorial optimization; branchandbound; biobjective spanning tree problem 1.