DDMOA2: Improved Descent Directions-Based Multiobjective Algorithm,

In this paper, we propose an improved version of descent direction-based multiobjective algorithm (DDMOA2). Significant modifications are introduced comparing with the originally proposed algorithm (DDMOA). DDMOA2 does not rely on the concept of Pareto dominance instead a scalarizing fitness assignment is used. Now, all population members have a probability of creating offspring. We define the concept of search matrix and population leaders for which local search is used to find descent directions. Moreover to improve efficiency, descent directions are found only for two randomly chosen objectives. The experimental study shows that the proposed approach outperforms the previous version of the algorithm with respect to the convergence to the Pareto optimal front and the diversity among obtained solutions, especially on three-objective test problems. At the same time, it provides highly competitive results with respect to other state-ofthe-art multiobjective optimizers.

[1]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[2]  Lino A. Costa,et al.  Stochastic algorithms assessment using performance profiles , 2011, GECCO '11.

[3]  Hisao Ishibuchi,et al.  Incorporation of Scalarizing Fitness Functions into Evolutionary Multiobjective Optimization Algorithms , 2006, PPSN.

[4]  Lino Costa,et al.  DDMOA: Descent Directions based Multiobjective Algorithm , 2012 .

[5]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[6]  Dirk Thierens,et al.  The balance between proximity and diversity in multiobjective evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[7]  Virginia Torczon,et al.  On the Convergence of Pattern Search Algorithms , 1997, SIAM J. Optim..

[8]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[9]  Kalyanmoy Deb,et al.  On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods , 2007, Eur. J. Oper. Res..

[10]  Lino A. Costa,et al.  A New Hybrid Evolutionary Multiobjective Algorithm Guided by Descent Directions , 2013, J. Math. Model. Algorithms Oper. Res..

[11]  M. K. Luhandjula.  Studies in Fuzziness and Soft Computing , 2013 .

[12]  Evan J. Hughes,et al.  MSOPS-II: A general-purpose Many-Objective optimiser , 2007, 2007 IEEE Congress on Evolutionary Computation.

[13]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[14]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[15]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[16]  Wei-Liem Loh.  On Latin hypercube sampling , 1996 .

[17]  Joshua D. Knowles,et al.  Memetic Algorithms for Multiobjective Optimization: Issues, Methods and Prospects , 2004 .

[18]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.