## The Influence of the Fitness Evaluation Method on the Performance of Multiobjective Search Algorithms (2004)

Venue: | European Journal of Operational Research |

Citations: | 6 - 5 self |

### BibTeX

@ARTICLE{Burke04theinfluence,

author = {E. K. Burke and A Silva and J.D. Landa Silva},

title = {The Influence of the Fitness Evaluation Method on the Performance of Multiobjective Search Algorithms},

journal = {European Journal of Operational Research},

year = {2004},

volume = {169},

pages = {875--897}

}

### OpenURL

### Abstract

In this paper we are concerned with finding the Pareto optimal front or a good approximation to it. Since non-dominated solutions represent the goal in multiobjective optimisation, the dominance relation is frequently used to establish preference between solutions during the search. Recently, relaxed forms of the dominance relation have been proposed in the literature for improving the performance of multiobjective search methods. This paper investigates the influence of different fitness evaluation methods on the performance of two multiobjective methodologies when applied to a highly constrained two-objective optimisation problem. The two algorithms are: the Pareto archive evolutionary strategy and a population-based annealing algorithm. We demonstrate here, on a highly constrained problem, that the method used to evaluate the fitness of candidate solutions during the search affects the performance of both algorithms and it appears that the dominance relation is not always the best method to use.

### Citations

1073 |
Multi-objective optimization using evolutionary algorithms
- Deb
- 2001
(Show Context)
Citation Context ...luding simulated annealing and tabu search have been proposed [19,29,32,46,58]. Moreover, there is a growing interest in applying evolutionary algorithms to solve multiobjective optimisation problems =-=[18,22,27,64]-=-. Several surveys on the application of metaheuristics to multiobjective problems are available in the literature [17,24,41,59]. Also, there are several studies that focus on measuring and comparing t... |

518 |
Evolutionary Algorithms for Solving Multi-Objective Problems. 2007
- Coello, Lamont, et al.
(Show Context)
Citation Context ...luding simulated annealing and tabu search have been proposed [19,29,32,46,58]. Moreover, there is a growing interest in applying evolutionary algorithms to solve multiobjective optimisation problems =-=[18,22,27,64]-=-. Several surveys on the application of metaheuristics to multiobjective problems are available in the literature [17,24,41,59]. Also, there are several studies that focus on measuring and comparing t... |

392 | Comparison of multiobjective evolutionary algorithms: empirical results." Evol Comput 8(2
- Zitzler, Deb, et al.
- 2000
(Show Context)
Citation Context ...e problems are available in the literature [17,24,41,59]. Also, there are several studies that focus on measuring and comparing the performance of different algorithms for multiobjective optimisation =-=[51,56,60,63,65]-=-. In fact, a considerable amount of the available literature on the application of multiobjective metaheuristics concentrates on the competition between different approaches to produce the best result... |

286 | Multiobjective evolutionary algorithms: analyzing the state-of-the-art." Evol Comput 8(2
- Veldhuizen, Lamont
- 2000
(Show Context)
Citation Context ...ng evolutionary algorithms to solve multiobjective optimisation problems [18,22,27,64]. Several surveys on the application of metaheuristics to multiobjective problems are available in the literature =-=[17,24,41,59]-=-. Also, there are several studies that focus on measuring and comparing the performance of different algorithms for multiobjective optimisation [51,56,60,63,65]. In fact, a considerable amount of the ... |

236 | Approximarting the nondominated front using the pareto archived evolution strategy
- Knowles, Corne
- 2000
(Show Context)
Citation Context ...are: an amended version of the population-based hybrid annealing algorithm previously proposed by the authors in [11] and the (1+1)-Pareto archived evolutionary strategy proposed by Knowles and Corne =-=[35]-=-. The first one is a hybrid approach that has been developed as a result of the previous research carried out by the authors into investigating metaheuristic approaches to the space allocation problem... |

152 | Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems
- Deb
- 1999
(Show Context)
Citation Context ...re effective and efficient approaches. Although some research has been published on the effect that some strategies have on the performance of some metaheuristics for multiobjective optimisation (eg. =-=[23,42,48]-=-), we believe that more research on this subject is required. The research presented in this paper aims to be a contribution to the better understanding of the mechanisms and conditions that influence... |

119 |
Multiple Criteria Decision Analysis: An Integrated Approach
- Belton, Stewart
- 2001
(Show Context)
Citation Context ...s. Among these, the classical methods (also called traditional methods in some of the literature) include weighting approaches, goal programming, constraint methods, the Tchebycheff method and others =-=[7,54]-=-. In recent years, multiobjective metaheuristics have received considerable attention. For example, adaptations of local search methods including simulated annealing and tabu search have been proposed... |

117 |
Facility Layout and Location: An Analytical Approach, 2nd ed
- Francis, McGinnis, et al.
- 1992
(Show Context)
Citation Context ... for the conservation of all protected species (e.g. [16]). The optimal utilisation of physical space is a concern in many other scenarios that range from industrial and commercial environments (e.g. =-=[8,28,62]-=-) to computer systems [53]. For a more detailed description of the space allocation problem considered in this paper see [14,40]. A brief discussion about why this problem is considered as a two-objec... |

113 | Combining convergence and diversity in evolutionary multiobjective optimization
- Laumanns, Thiele, et al.
- 2002
(Show Context)
Citation Context ...rovide more freedom to explore by the searching mechanism [36]. Also, relaxed forms of the dominance relation have been proposed as a means of improving the performance of some multiobjective methods =-=[13,39,43,48]-=-. Although arguments have been put forward in favor of either aggregating functions or the dominance relation for multiobjective optimisation, there has been no previous study to investigate the influ... |

89 | A survey and annotated bibliography of multiobjective combinatorial optimization
- Ehrgott, Gandibleux
- 2000
(Show Context)
Citation Context ...ng evolutionary algorithms to solve multiobjective optimisation problems [18,22,27,64]. Several surveys on the application of metaheuristics to multiobjective problems are available in the literature =-=[17,24,41,59]-=-. Also, there are several studies that focus on measuring and comparing the performance of different algorithms for multiobjective optimisation [51,56,60,63,65]. In fact, a considerable amount of the ... |

79 | On metrics for comparing nondominated sets
- Knowles, Corne
- 2002
(Show Context)
Citation Context ...tric was selected because it directly compares the quality of two non-dominated sets, it is not required to know the Pareto optimal front and it is simple to compute (various metrics are described in =-=[3,26,38,49]-=-). This metric is described by equation 13, where A, B are sets of non-dominated vectors. C (A, B) = |{b ∈ B; ∃a ∈ A : a � b}| |B| (13) With the above metric, a value of C(A, B) = 1 indicates that all... |

40 |
Local-Search and Hybrid Evolutionary Algorithms for Pareto Optimization
- Knowles
- 2002
(Show Context)
Citation Context ...tiobjective optimisation technique that is simple to implement, has been tested across a range of problems and is considered to be competitive with other modern multiobjective evolutionary algorithms =-=[37,56]-=-. The two approaches above are alike in the sense that both evolve solutions based on self-adaptation, i.e. the current solution is modified by mutation or local search and no recombination is used. A... |

33 | Reducing local optima in single-objective problems by multi-objectivization
- Knowles, Watson, et al.
- 2001
(Show Context)
Citation Context ...est that by the ‘multi-objectivization’ of single objective optimisation problems the number of local optima can be reduced in an attempt to provide more freedom to explore by the searching mechanism =-=[36]-=-. Also, relaxed forms of the dominance relation have been proposed as a means of improving the performance of some multiobjective methods [13,39,43,48]. Although arguments have been put forward in fav... |

29 |
Genetic local search for multiobjective combinatorial optimization
- Jaszkiewicz
- 2002
(Show Context)
Citation Context ... In recent years, multiobjective metaheuristics have received considerable attention. For example, adaptations of local search methods including simulated annealing and tabu search have been proposed =-=[19,29,32,46,58]-=-. Moreover, there is a growing interest in applying evolutionary algorithms to solve multiobjective optimisation problems [18,22,27,64]. Several surveys on the application of metaheuristics to multiob... |

27 | On the effects of archiving, elitism, and density based selection in evolutionary multi-objective optimization
- Laumanns, Zitzler, et al.
- 2001
(Show Context)
Citation Context ...re effective and efficient approaches. Although some research has been published on the effect that some strategies have on the performance of some metaheuristics for multiobjective optimisation (eg. =-=[23,42,48]-=-), we believe that more research on this subject is required. The research presented in this paper aims to be a contribution to the better understanding of the mechanisms and conditions that influence... |

27 |
A swarm metaphor for multi-objective design optimization. Engineering Optimization
- Ray, T
- 2002
(Show Context)
Citation Context ... to a wide range of application areas which include personnel scheduling (e.g. [12,25,31]), university timetabling (e.g. [9,15,50]), production scheduling (e.g. [4,5]), engineering optimisation (e.g. =-=[6,55,57]-=-), and many others. Various different methods have been applied to tackle multiobjective optimisation problems over the years. Among these, the classical methods (also called traditional methods in so... |

26 | A critical survey of performance indices for multiobjective optimisation
- Okabe, Jin, et al.
- 2003
(Show Context)
Citation Context ...tric was selected because it directly compares the quality of two non-dominated sets, it is not required to know the Pareto optimal front and it is simple to compute (various metrics are described in =-=[3,26,38,49]-=-). This metric is described by equation 13, where A, B are sets of non-dominated vectors. C (A, B) = |{b ∈ B; ∃a ∈ A : a � b}| |B| (13) With the above metric, a value of C(A, B) = 1 indicates that all... |

25 |
A multicriteria approach to examination timetabling
- Burke, Petrovic
- 2001
(Show Context)
Citation Context ...pending upon the problem domain. Multiobjective methodologies have been applied to a wide range of application areas which include personnel scheduling (e.g. [12,25,31]), university timetabling (e.g. =-=[9,15,50]-=-), production scheduling (e.g. [4,5]), engineering optimisation (e.g. [6,55,57]), and many others. Various different methods have been applied to tackle multiobjective optimisation problems over the y... |

21 | R.: Approximation algorithms for the multiple knapsack problem with assignment restrictions
- Dawande, Kalagnanam, et al.
- 2000
(Show Context)
Citation Context ...reported for a highly constrained combinatorial optimisation problem with two objectives: the space allocation problem which is a variant of the class of knapsack problems with assignment constraints =-=[21,34]-=-. Three ways of deal3sing with the two objectives are compared: an aggregation of the objectives, the dominance relation and a relaxed form of this dominance relation. The results presented here show ... |

21 | Efficient and Scalable Pareto Optimization by Evolutionary Local Selection Algorithms
- Menczer
- 2000
(Show Context)
Citation Context ... In recent years, multiobjective metaheuristics have received considerable attention. For example, adaptations of local search methods including simulated annealing and tabu search have been proposed =-=[19,29,32,46,58]-=-. Moreover, there is a growing interest in applying evolutionary algorithms to solve multiobjective optimisation problems [18,22,27,64]. Several surveys on the application of metaheuristics to multiob... |

18 |
A metaheuristic approach to multiple objective nurse scheduling
- Jaszkiewicz
- 1997
(Show Context)
Citation Context ...ion space, the objective space or both, depending upon the problem domain. Multiobjective methodologies have been applied to a wide range of application areas which include personnel scheduling (e.g. =-=[12,25,31]-=-), university timetabling (e.g. [9,15,50]), production scheduling (e.g. [4,5]), engineering optimisation (e.g. [6,55,57]), and many others. Various different methods have been applied to tackle multio... |

16 |
Fogel DB: How to solve it: Modern heuristics
- Michalewicz
(Show Context)
Citation Context ...Annealing Algorithm The approach described next is based on the simulated annealing algorithm but it also incorporates elements of other metaheuristics such as tabu search and evolutionary algorithms =-=[47]-=-. Simulated annealing is a local search approach that attempts to improve the current solution and in which the acceptance of worse solutions is controlled by an annealing schedule [1]. Initially, a h... |

14 |
V.: A multiobjective genetic algorithm for the class/teacher timetabling problem
- Carrasco, Pato
- 2001
(Show Context)
Citation Context ...pending upon the problem domain. Multiobjective methodologies have been applied to a wide range of application areas which include personnel scheduling (e.g. [12,25,31]), university timetabling (e.g. =-=[9,15,50]-=-), production scheduling (e.g. [4,5]), engineering optimisation (e.g. [6,55,57]), and many others. Various different methods have been applied to tackle multiobjective optimisation problems over the y... |

13 |
Tabu search based procedure for solving the 0-1 multiobjective knapsack problem: The two objectives case
- Gandibleux, Freville
- 2000
(Show Context)
Citation Context ... In recent years, multiobjective metaheuristics have received considerable attention. For example, adaptations of local search methods including simulated annealing and tabu search have been proposed =-=[19,29,32,46,58]-=-. Moreover, there is a growing interest in applying evolutionary algorithms to solve multiobjective optimisation problems [18,22,27,64]. Several surveys on the application of metaheuristics to multiob... |

13 |
Failure of Pareto-based MOEAs: Does non-dominated really mean near to optimal
- Ikeda, Kita, et al.
- 2001
(Show Context)
Citation Context ...minance relation is not well-suited for approaches that employ local search [32]. Furthermore, Kokolo et.al. discuss whether non-dominated solutions represent good approximations to optimality or not =-=[39]-=-, while Knowles et.al. suggest that by the ‘multi-objectivization’ of single objective optimisation problems the number of local optima can be reduced in an attempt to provide more freedom to explore ... |

13 | A multiobjective optimisation technique for exam timetabling based on trajectories
- Petrovic, Bykov
- 2002
(Show Context)
Citation Context ...pending upon the problem domain. Multiobjective methodologies have been applied to a wide range of application areas which include personnel scheduling (e.g. [12,25,31]), university timetabling (e.g. =-=[9,15,50]-=-), production scheduling (e.g. [4,5]), engineering optimisation (e.g. [6,55,57]), and many others. Various different methods have been applied to tackle multiobjective optimisation problems over the y... |

12 | An introduction to multiobjective metaheuristics for scheduling and timetabling - Landa-Silva, Burke, et al. |

11 |
taboo search based approach to find the Pareto optimal set in multiple objective optimization
- Baykasoglu, Owen, et al.
- 1999
(Show Context)
Citation Context ... to a wide range of application areas which include personnel scheduling (e.g. [12,25,31]), university timetabling (e.g. [9,15,50]), production scheduling (e.g. [4,5]), engineering optimisation (e.g. =-=[6,55,57]-=-), and many others. Various different methods have been applied to tackle multiobjective optimisation problems over the years. Among these, the classical methods (also called traditional methods in so... |

11 |
A simulated annealing algorithm for multiobjective optimization
- Suppapitnarm, Seffen, et al.
(Show Context)
Citation Context ... to a wide range of application areas which include personnel scheduling (e.g. [12,25,31]), university timetabling (e.g. [9,15,50]), production scheduling (e.g. [4,5]), engineering optimisation (e.g. =-=[6,55,57]-=-), and many others. Various different methods have been applied to tackle multiobjective optimisation problems over the years. Among these, the classical methods (also called traditional methods in so... |

10 |
Cardinality constrained bin-packing problems
- Kellerer, Pferschy
- 1999
(Show Context)
Citation Context ...reported for a highly constrained combinatorial optimisation problem with two objectives: the space allocation problem which is a variant of the class of knapsack problems with assignment constraints =-=[21,34]-=-. Three ways of deal3sing with the two objectives are compared: an aggregation of the objectives, the dominance relation and a relaxed form of this dominance relation. The results presented here show ... |

10 |
Fleming ” The Multiobjective Genetic Algorithm Applied to Benchmark Problems–an Analysis
- Purshouse, J
- 2001
(Show Context)
Citation Context ...e problems are available in the literature [17,24,41,59]. Also, there are several studies that focus on measuring and comparing the performance of different algorithms for multiobjective optimisation =-=[51,56,60,63,65]-=-. In fact, a considerable amount of the available literature on the application of multiobjective metaheuristics concentrates on the competition between different approaches to produce the best result... |

10 |
Evolutionary Algorithms for Multi-Objective Optimization: Performance Assessments and Comparisons
- Tan, Lee, et al.
- 2002
(Show Context)
Citation Context ...e problems are available in the literature [17,24,41,59]. Also, there are several studies that focus on measuring and comparing the performance of different algorithms for multiobjective optimisation =-=[51,56,60,63,65]-=-. In fact, a considerable amount of the available literature on the application of multiobjective metaheuristics concentrates on the competition between different approaches to produce the best result... |

9 | Space Allocation: An analysis of higher education requirements. The Practice and Theory of Automated Timetabling
- Burke, Varley
- 1998
(Show Context)
Citation Context ...cenarios that range from industrial and commercial environments (e.g. [8,28,62]) to computer systems [53]. For a more detailed description of the space allocation problem considered in this paper see =-=[14,40]-=-. A brief discussion about why this problem is considered as a two-objective optimisation problem in this paper is provided in the next section. 2.2 The Conflicting Objectives Using the dominance rela... |

8 |
Berghe, “A multi criteria meta-heuristic approach to nurse rostering
- Burke, Causmaecker, et al.
(Show Context)
Citation Context ...ion space, the objective space or both, depending upon the problem domain. Multiobjective methodologies have been applied to a wide range of application areas which include personnel scheduling (e.g. =-=[12,25,31]-=-), university timetabling (e.g. [9,15,50]), production scheduling (e.g. [4,5]), engineering optimisation (e.g. [6,55,57]), and many others. Various different methods have been applied to tackle multio... |

8 |
independence: relationships in evolutionary multi-criterion optimisation
- Purshouse, Fleming, et al.
- 2003
(Show Context)
Citation Context ...xt section. 2.2 The Conflicting Objectives Using the dominance relation when dealing with a multiobjective optimisation problem makes sense only if the objectives are partially or totally conflicting =-=[52]-=-. If the objectives are uncorrelated or reinforce each other, it is often adequate to combine all of them into a single scalar value and approach the problem as a single-objective one. More than two o... |

8 |
Steuer,Multiple Criteria Optimization: Theory, Computation, and Application
- E
- 1986
(Show Context)
Citation Context ...ometimes more than one decision-maker is involved in selecting an appropriate solution. At present, three broad typical approaches can be identified in the literature to deal with multiple objectives =-=[30,54]-=-: (1) Optimising one objective at a time while imposing constraints on the other objectives. (2) Combining all objectives into a single objective. (3) Optimising all objectives simultaneously. Frequen... |

8 |
G.B.: A Statistical Comparison of Multiobjective Evolutionary Algorithms Including the MOMGA-II
- Zydallis, Veldhuizen, et al.
- 1993
(Show Context)
Citation Context |

7 |
Preliminary statement on the current progress of multiobjective evolutionary algorithm performance measurement
- Ang, Chong, et al.
- 2002
(Show Context)
Citation Context ...tric was selected because it directly compares the quality of two non-dominated sets, it is not required to know the Pareto optimal front and it is simple to compute (various metrics are described in =-=[3,26,38,49]-=-). This metric is described by equation 13, where A, B are sets of non-dominated vectors. C (A, B) = |{b ∈ B; ∃a ∈ A : a � b}| |B| (13) With the above metric, a value of C(A, B) = 1 indicates that all... |

7 |
Space planning by ant colony optimisation
- Bland
- 1999
(Show Context)
Citation Context ... for the conservation of all protected species (e.g. [16]). The optimal utilisation of physical space is a concern in many other scenarios that range from industrial and commercial environments (e.g. =-=[8,28,62]-=-) to computer systems [53]. For a more detailed description of the space allocation problem considered in this paper see [14,40]. A brief discussion about why this problem is considered as a two-objec... |

7 | Applying Genetic Algorithms to Multiobjective Land Use Planning
- MATTHEWS, CRAW, et al.
- 2000
(Show Context)
Citation Context ...raphic management. For example, an important resource allocation problem in geographic research is the goal of optimising the allocation of land use to each of the cells forming an area of land (e.g. =-=[2,45]-=-. In forest management, the maximal covering location problem consists of selecting reserve areas that maximise the coverage of species with the aim of having enough forest areas for the conservation ... |

7 |
Fortemps Ph., Tuyttens D.. MOSA method: a tool for solving multiobjective combinatorial optimization problems
- Ulungu, Teghem
- 1999
(Show Context)
Citation Context |

6 |
Pareto Simulated Annealing - a Metaheuristic for Multiple-Objective Combinatorial Optimization
- Czyzak, Jaszkiewicz
- 1998
(Show Context)
Citation Context |

6 |
A study on shelf space allocation and management
- Yang, Chen
- 1999
(Show Context)
Citation Context ... for the conservation of all protected species (e.g. [16]). The optimal utilisation of physical space is a concern in many other scenarios that range from industrial and commercial environments (e.g. =-=[8,28,62]-=-) to computer systems [53]. For a more detailed description of the space allocation problem considered in this paper see [14,40]. A brief discussion about why this problem is considered as a two-objec... |

5 | Hybrid population-based metaheuristic approaches for the space allocation problem
- Burke, Cowling, et al.
- 2001
(Show Context)
Citation Context ...tive Approaches Tested 4.1 Justification The two algorithms used in this investigation are: an amended version of the population-based hybrid annealing algorithm previously proposed by the authors in =-=[11]-=- and the (1+1)-Pareto archived evolutionary strategy proposed by Knowles and Corne [35]. The first one is a hybrid approach that has been developed as a result of the previous research carried out by ... |

4 | Three Methods to Automate the Space Allocation Process in UK Universities, Practice, and Theory of Automated Timetabling
- Burke, Cowling, et al.
- 2000
(Show Context)
Citation Context ...out being biased by the algorithm design. Also, the authors’s previous experience is that the recombination of solutions in this highly constrained problem almost always produces infeasible solutions =-=[10,40]-=-. Of course this only means that good crossover operators or repairing heuristics need to be designed and therefore the applicability of recombination-based multiobjective evolutionary algorithms to t... |

3 |
Talbi E.-G.: Design of multi-objective evolutionary algorithms: Application to the flow-shop scheduling problem
- Basseur, Seynhaeve
- 2002
(Show Context)
Citation Context ...jective methodologies have been applied to a wide range of application areas which include personnel scheduling (e.g. [12,25,31]), university timetabling (e.g. [9,15,50]), production scheduling (e.g. =-=[4,5]-=-), engineering optimisation (e.g. [6,55,57]), and many others. Various different methods have been applied to tackle multiobjective optimisation problems over the years. Among these, the classical met... |

3 |
Improving the Performance of Multiobjective Optimizers by Using Relaxed Dominance
- Burke, D
- 2002
(Show Context)
Citation Context ...rovide more freedom to explore by the searching mechanism [36]. Also, relaxed forms of the dominance relation have been proposed as a means of improving the performance of some multiobjective methods =-=[13,39,43,48]-=-. Although arguments have been put forward in favor of either aggregating functions or the dominance relation for multiobjective optimisation, there has been no previous study to investigate the influ... |

3 |
Multiobjective Decision Analysis With Engineering and Business Applications
- Giocoechea, Hansen, et al.
- 1982
(Show Context)
Citation Context ...ometimes more than one decision-maker is involved in selecting an appropriate solution. At present, three broad typical approaches can be identified in the literature to deal with multiple objectives =-=[30,54]-=-: (1) Optimising one objective at a time while imposing constraints on the other objectives. (2) Combining all objectives into a single objective. (3) Optimising all objectives simultaneously. Frequen... |

3 | Adaptive Diversity Maintenance and Convergence Guarantee in Multiobjective Evolutionary Algorithms
- Jin, Wong
- 2003
(Show Context)
Citation Context ...al set and maintain a wide diversity in the population at the same time [43]. The ɛ-dominance has also been proposed to implement specialised archiving mechanisms for multiobjective search algorithms =-=[33,48]-=-. In some sense, the relaxed forms of dominance (α-dominance and ɛ-dominance) are similar to establishing preferences among the objectives using weights in an aggregating function. In both cases, a de... |

3 |
Methods for the one-dimensional space allocation problem
- Romero, Sánchez-Flores
- 1990
(Show Context)
Citation Context ...otected species (e.g. [16]). The optimal utilisation of physical space is a concern in many other scenarios that range from industrial and commercial environments (e.g. [8,28,62]) to computer systems =-=[53]-=-. For a more detailed description of the space allocation problem considered in this paper see [14,40]. A brief discussion about why this problem is considered as a two-objective optimisation problem ... |