A multi - Objective evolutionary algorithm using directions of improvement and application

Using evolutionary algorithms for approximating solutions in multi-objective optimization problems has been a popular topic in the field of evolutionary computation. Because EAs can o↵er simultaneously a set of trade-o↵ solutions. Up to date, there has been a large set of MOEAs in the literature addressing a widely range of problems with di↵erent properties. Directions of improvement have been discussed, conceptualized and used to guide MOEAs during the search process towards POF. The major concern of the thesis is how to use the directions of improvement in an e↵ective way to guide the evolutionary process of the MOEAs in both aspects: 1) Automatically guiding the evolutionary process to make MOEAs balanced between exploitation and exploration. 2) Combining decision maker’s preference with directions of improvement to guide the MOEAs during optimal process towards the most preferred region in objective space

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ocess. This information is used during the MOEA reproduction phase. At every genera- tion, the archive is exploited to determine directions of improvement. Randomly- selected parental solutions are then perturbed along those directions in order to produce o↵spring solutions. That type of selection is similar to the conventional selection in evolutionary algorithms. However, the niching mechanism requires to spread solutions along the POF. This is a ’hard’ niching method and it might make the convergence slow, the selection of the parent is also random, it has an e↵ect on the convergence. To avoid this e↵ect the thesis suggests to replace orig- inal selection scheme by a new one in which parent at a loop will be changed by a solution in the population. Note that, the index for that solution ranges from 1 to the half of population size; With new selection scheme, the work’s reasoning is 126 6.1. CONCLUSIONS that more selection pleasure on DMEA is placed so that the convergence will be balanced with diversity. The results of the proposed DMEA-II indicates a better performance of DMEA-II over the original DMEA. The thesis also conducts a comparison between DMEA-II’s perfor- mance with other 5 MOEAs on four metrics: GD, IGD, HYP and SC. DMEA-II and the other techniques were competitive in comparison with these algorithms with respect to both convergence and spread. Several analysis on the behaviors of the algorithm were thoroughly investigated. The main features of the evolutionary process in DMEA-II are: The evolutionary pro- cess is automated guided by directions of improvement to keep the balance between exploitation and exploration. For the keeping, an adaptive ratio of these directions is used in di↵erent stages of the evolutionary process: At early stages, the evolutionary process is guided to give priority to generating individuals of convergence directions, at the later stages, it is guided to give priority to generating individuals of spread direc- tions. During the generations, a system of rays is used for a ray based niching method to maintain the diverse of the main population. It also used for a selection scheme to fill the second half of the population. The e↵ective techniques are individual analyzed in [77, 75, 76] and the algorithm was proposed in [78]. 2. The thesis proposed an e↵ective interactive method for DMEA-II: To use guided information in an e↵ective way for guiding the evolutionary process to make the population towards DM’s preferred region, this thesis proposes a ray based interactive method for DMEA-II with three ray based approaches: • Rays Replacement: The furthest rays from DM’s preferred region are replaced by new rays that generated from a set of reference points. • Rays Redistribution: Redistribute the system of rays to be in DM’s preferred region. • Value Added Niching: Based on the distances from non-dominated solutions in archive to DM’s preferred region, the niching values for the solutions is increased 127 6.1. CONCLUSIONS to be priority selected. With the interactive method, the evolutionary process in DMEA-II can be guided to converge to DM’s preferred regions through information from reference points which are given by DM during the optimization process. The interactive method can help DM to find their optimal solutions more quickly. The interactive method for DMEA-II was proposed in [80, 79]. 3. DMEA-II is applied for a Spam Email Detection System in network security area: A framework applied DMEA-II to solve the problem of a Spam Email Detection System (a SpamAssassin based system) as an applied MOEAs for real applications, which validates the usefulness of distributions on this thesis. In fact, traditional anti- spam approaches have optimized the spam detection rate (SDR) and the false alarm rate (FAR) for years and gained specific results. However, the achievement has been optimized for the single objective only. With the-multi objective optimization with interactive approach, not only one pair of SDR and FAR for each threshold has been worked out but a set of solutions with di↵erent tradeo↵ levels are computed. They are all feasible depending on specific email users’ demands. More importantly, the score set of selected solutions are always ready to use without any training needed. The experiments on Vietnamese database and rules are implemented, the results indicated that, when solving the problem using DMEA-II with the proposed interactive method, it not only achieved more ecient results but also created a set of ready-to-use rule scores. These scores support di↵erent levels of the trade-o↵ between SDR and FAR. Via obtained solutions, it gives users more flexibility and eciency for system configu- ration. The application is introduced in [79, 117]. Through the survey and analysis of methods of using directions of improvement to guide MOEAs, the thesis proposes a new direction based multi-objective evolutionary algorithm - DMEA-II. With the techniques used in choosing the direction, niching and selection approach, and through using diverse of standard problems, well-known measurements in comparison 128 6.2. FUTURE DIRECTIONS with other popular MOEAs, DMEA-II is considered as a relatively good algorithms. Along with an interactive method, DMEA-II is added with interactive feature between human and machine which makes it be able to fit the actual problem. DMEA-II algorithm with interactive feature, which was applied in spam email detection problem in the field of network security, is a testament to the usability of the proposed algorithm. 6.2 Future directions There are several possibilities to extend the research on the using directions of improvement in the thesis: • Design of more mechanisms that allow an automated control of the pa- rameters of DMEA-II : the concepts of using directions of improvement and related techniques which are used in DMEA-II should be analysed. The properties of the used techniques might suggest to determine e↵ective parameters to make the DMEA-II qual- ity to be better in convergence and diversity. In other words, it might make DMEA-II to be good keeping balanced in exploitation and exploration automatically. • Parallelization the optimization process of DMEA-II : this is an interesting idea to improve the algorithm performance when calculating during the evolutionary process. The Parallel computation might make DMEA-II to be faster than existed sequential computation during the evolutionary process on the fitness functions assess- ment. A parallel computation is capable of multi-threading on a large scale, it can simultaneously process several calculations of fitness functions. • Extending the capacity of DMEA-II on multi-objective discrete optimiza- tion problem : DMEA-II was experimented and validated in real space, however, there are many multi-objective discrete optimization problems in the real world, so the idea of extending DMEA-II to work with discrete multi-objective discrete optimization problems is a meaningful research to make DMEA-II widely applied in many areas of real applications. 129 6.2. FUTURE DIRECTIONS Publications Journal articles [1] Long Nguyen, Lam Thu Bui, Hussein Abbass. DMEA-II: A Direction based Multi- objective Evolutionary Algorithm-II. Journal of Soft Computing, Volume 18, Issue 11, pp. 2119–2134, 2014, Springer-Verlag.[ISI Journal]. [2] Long Nguyen, Lam Thu Bui. A Decomposition-Based Interactive Method for Multi- Objective Evolutionary Algorithm. Journal of Development and Application on Information and Telecommunication Technology, pp. 17–24, Volume E-2, No.5 (9), 2012. [3] Long Nguyen, Lam Thu Bui. A New Selection Strategy for the Direction-based Multi- objective Evolutionary Algorithm. Journal of Development and Application on Information and Telecommunication Technology, pp. 35–48, Volume E-2, No.6 (10), 2013. [4] Long Nguyen, Lam Thu Bui, Anh Quang Tran. Toward an Interactive Method for DMEA- II and Application to the Spam-Email Detection System. VNU Journal of Computer Science and Communication Engineering, Volume 1, No.4, pp. 29–44, 2014. Conference papers [1] Long Nguyen, Lam Thu Bui, Hussein Abbass. A new niching method for the direction- based multi-objective evolutionary algorithm. In proceeding of Computational Intelligence in Multi-Criteria Decision-Making (MCDM), IEEE Symposium Series on Computational Intel- ligence, Volume 1, No.8, pp. 16–19, Singapore, 2013, IEEE. [2] Long Nguyen, Lam Thu Bui. A Ray Based Interactive Method for Direction Based Multi- objective Evolutionary Algorithm. In proceeding of The fifth International Conference on Knowledge and Systems Engineering (KSE 2013), Volume 2, pp. 173–184, Hanoi, Vietnam, 2013, Springer-Verlag. [3] Long Nguyen, Lam Thu Bui. A Multi-Point Interactive Method For Multi-objective Evo- lutionary Algorithms. In proceeding of The fourth International Conference on Knowledge and Systems Engineering (KSE 2012), Volume 1, pp. 107–112, Da nang, Vietnam, 2013, IEEE. 130 6.2. FUTURE DIRECTIONS [4] Long Nguyen, Lam Thu Bui. The e↵ects of di↵erent selection schemes on the direction based multi-objective evolutionary algorithm. In proceeding of The first NAFOSTED Con- ference on Information and Computer Science 2014 (NICS14), pp. 428–437, Hanoi, Vietnam, 2014. [5] Long Nguyen, Quang Anh Tran, Lam Thu Bui. DMEA-II and its application on spam email detection problems. In proceeding of Seventh IEEE Symposium on Computational Intelligence for Security and Defense Applications (IEEE CISDA 2014), Hanoi, Vietnam, 2014. 131 Appendix A Benchmark sets 132 Tab. A.1: ZDT Problems MOP POF ZDT1 : f1( !x ) = x1, f2( !x , g) = g(!x ).(1 s f1( !x ) g(!x ) ), g(!x ) = 1 + 9 n 1 nX i=2 xi. where n = 30, and xi 2 [0, 1]; g(!x ) = 1. The POF is convex. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 ZDT2 : f1( !x ) = x1, f2( !x , g) = g(!x ).(1 (f1( !x ) g(!x ) ) 2), g(!x ) = 1 + 9 n 1 nX i=2 xi. where n = 30, and xi 2 [0, 1]; g(!x ) = 1. The POF is concave. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 ZDT3 : f1( !x ) = x1, f2( !x , g) = g(!x ).(1 s f1( !x ) g(!x ) f1( !x ) g(!x ) . sin(10⇡f1( !x ))), g(!x ) = 1 + 9 n 1 nX i=2 xi. where n = 30, and xi 2 [0, 1]; g(!x ) = 1. The POF is disconnected and convex. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 F1 F2 133 MOP POF ZDT4 : f1( !x ) = x1, f2( !x , g) = g(!x ).(1 s f1( !x ) g(!x ) ), g(!x ) = 1 + 10.(n 1) + nX i=2 (x2i 10 cos(4⇡xi)). where n = 10, x1 2 [0, 1] and x2, ..., xn 2 [5, 5]; g(!x ) = 1. The POF is multi-modal. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 ZDT6 : f1( !x ) = 1 exp(4x1). sin6(6⇡x1), f2( !x , g) = g(!x ).(1 (f1( !x ) g(!x ) ) 2), g(!x ) = 1 + 9(1 9 . nX i=2 (xi)). where n = 10, xi 2 [0, 1]; g(!x ) = 1. The POF is non-convex. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 134 Tab. A.2: DTLZ Problems MOP POF DTLZ1 : f1( !x ) = 1 2 x1x2...xM1(1 + g(!xM )), f2(!x ) = 1 2 x1x2...(1 xM 1)(1 + g(!xM )), ..., fM1(!x ) = 1 2 x1(1 x2)(1 + g(!xM )), fM ( !x ) = 1 2 (1 x1)(1 + g(!xM )). subject to 0  xi  1, 8i = 1, 2, ..., n where: !xM = M,M +1, ..., xn and g(!xM ) = 100[|!xM |+P xi2!xM (xi 0.5)2 cos(20⇡(xi 0.5))]. The Pareto-optimal solution corresponds to !x ⇤M = 0.5 and the objective function values on the linear hyper-plane: PM m=1 fi = 0.5. The POF is linear, separable and multi-modal. 00.10.20.30.40.5 0 0.1 0.2 0.3 0.4 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 f1 f2 f3 DTLZ2 : f1( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 ) cos(x2 ⇡ 2 )... cos(xM2 ⇡ 2 ) cos(xM1 ⇡ 2 ), f2( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 ) cos(x2 ⇡ 2 )... cos(xM2 ⇡ 2 ) sin(xM1 ⇡ 2 ), f3( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 )cos(x2 ⇡ 2 )...sin(xM2 ⇡ 2 ), ..., fM1(!x ) = (1 + g(!xM )) cos(x1 ⇡ 2 )sin(x2 ⇡ 2 ), fM ( !x ) = (1 + g(!xM ))sin(x1 ⇡ 2 ). subject to 0  xi  1, 8i = 1, 2, ..., n where: !xM = M,M + 1, ..., xn and g(!xM ) = P xi2!xM (xi 0.5)2 The Pareto-optimal solutions corresponds to xi = 0.5 for all xi 2 !xM , 8i = M,M + 1, ..., n and all objective function values must satisfy:PM i=1(fi) 2 = 1. The POF is concave, scalable and multi-modal. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f1 f2 f3 135 MOP POF DTLZ3 : f1( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 ) cos(x2 ⇡ 2 )... cos(xM2 ⇡ 2 ) cos(xM1 ⇡ 2 ), f2( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 ) cos(x2 ⇡ 2 )... cos(xM2 ⇡ 2 ) sin(xM1 ⇡ 2 ), f3( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 )cos(x2 ⇡ 2 )... sin(xM2 ⇡ 2 ), ..., fM1(!x ) = (1 + g(!xM )) cos(x1 ⇡ 2 )sin(x2 ⇡ 2 ), fM ( !x ) = (1 + g(!xM ))sin(x1 ⇡ 2 ). subject to 0  xi  1, 8i = 1, 2, ..., n where: !xM = M,M + 1, ..., xn and g(!xM ) = 100[|!xM |+ P xi2!xM (xi0.5)2cos(20⇡(xi0.5))] It is suggested that k = |xM | = 10 ; g⇤ = 1. 00.10.20.30.40.5 0 0.1 0.2 0.3 0.4 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 f1 f2 f3 DTLZ4 : f1( !x ) = (1 + g(!xM )) cos(x⇡1 ⇡ 2 ) cos(x⇡2 ⇡ 2 )... cos(x⇡M2 ⇡ 2 ) cos(x⇡M2 ⇡ 2 ), f2( !x ) = (1 + g(!xM )) cos(x⇡1 ⇡ 2 ) cos(x⇡2 ⇡ 2 )... cos(x⇡M2 ⇡ 2 ) sin(x⇡M1 ⇡ 2 ), f3(x) = (1 + g( !xM )) cos(x⇡1 ⇡ 2 ) cos(x⇡2 ⇡ 2 )... sin(x⇡M2 ⇡ 2 ), ..., fM1(x) = (1 + g(!xM )) cos(x⇡1 ⇡ 2 ) sin(x⇡2 ⇡ 2 ), fM(x) = (1 + g(!xM )) sin(x⇡1 ⇡ 2 ). subject to 0  xi  1, 8i = 1, 2, ..., n where: !xM = M,M + 1, ..., xn and g(!xM ) = P xi2!xM (xi 0.5)2. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f1 f2 f3 136 MOP POF DTLZ5 : f1( !x ) = (1 + g(!xM )) cos(1 ⇡ 2 ) cos(2 ⇡ 2 )... cos(M2 ⇡ 2 ) cos(M1 ⇡ 2 ), f2( !x ) = (1 + g(!xM )) cos(1 ⇡ 2 ) cos(2 ⇡ 2 )... cos(M2 ⇡ 2 ) sin(M1 ⇡ 2 ), f3( !x ) = (1 + g(!xM )) cos(1 ⇡ 2 )cos(2 ⇡ 2 )... sin(M2 ⇡ 2 ), ..., fM1(!x ) = (1 + g(!xM )) cos(1 ⇡ 2 )sin(2 ⇡ 2 ), fM ( !x ) = (1 + g(!xM ))sin(1 ⇡ 2 ). subject to 0  xi  1, 8i = 1, 2, ..., n where: i = ⇡ 4(1+g(!xM )) (1+2g( !xM )xi), for i = 2, 3, ..., (M1) and g(!xM ) = P xi2!xM (xi 0.5)2. 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f2 f1 f3 DTLZ6 : f1( !x ) = (1 + g(!xM )) cos(1 ⇡ 2 ) cos(2 ⇡ 2 )... cos(M2 ⇡ 2 ) cos(M1 ⇡ 2 ), f2( !x ) = (1 + g(!xM )) cos(1 ⇡ 2 ) cos(2 ⇡ 2 )... cos(M2 ⇡ 2 ) sin(M1 ⇡ 2 ), f3( !x ) = (1 + g(!xM )) cos(1 ⇡ 2 )cos(2 ⇡ 2 )... sin(M2 ⇡ 2 ), ..., fM1(!x ) = (1 + g(!xM )) cos(1 ⇡ 2 )sin(2 ⇡ 2 ), fM ( !x ) = (1 + g(!xM ))sin(1 ⇡ 2 ). subject to 0  xi  1, 8i = 1, 2, ..., n where: i = ⇡ 4(1+g(!xM )) (1 + 2g( !xM )xi), for i = 2, 3, ..., (M1) and g(!xM ) = P xi2!xM (xi) 0.1. 0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f2f1 f3 137 MOP POF DTLZ7 : f1( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 ) cos(x2 ⇡ 2 )... cos(xM2 ⇡ 2 ) cos(xM1 ⇡ 2 ), f2( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 ) cos(x2 ⇡ 2 )... cos(xM2 ⇡ 2 ) sin(xM1 ⇡ 2 ), f3( !x ) = (1 + g(!xM )) cos(x1 ⇡ 2 )cos(x2 ⇡ 2 )...sin(xM2 ⇡ 2 ), ..., fM1(!x ) = (1 + g(!xM )) cos(x1 ⇡ 2 )sin(x2 ⇡ 2 ), fM ( !x ) = (1 + g(!xM ))sin(x1 ⇡ 2 ). subject to 0  xi  1, 8i = 1, 2, ..., n where: !xM = M,M + 1, ..., xn and g(!xM ) = P xi2!xM (xi 0.5)2 The Pareto-optimal solutions corresponds to xi = 0.5 for all xi 2 !xM , 8i = M,M + 1, ..., n and all objective function values must satisfy:PM i=1(fi) 2 = 1. The POF is concave, scalable and multi-modal. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 2.5 3 3.5 4 4.5 5 5.5 6 f1 f2 f3 138 Tab. A.3: UF Problems MOP POF UF1 : f1( !x ) = x1 + 2| J1| X j2J1 [xj sin(6⇡x1 + j⇡ n )]2, f2( !x ) = 1px1 + 2|J2| X j2J2 [xj sin(6⇡x1 + j⇡ n ]2 where J1 = {j|j is odd and (2  j  n} and J2 = {j|j is even and 2  j  n}. The search space is [0, 1]⇥ [1, 1]n1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 UF2 : f1( !x ) = x1 + 2|J1| X j2J1 y2j , f2( !x ) = 1px1 + 2|J2| X j2J2 y2j where J1 = {j|j is odd and (2  j  n} and J2 = {j|j is even and 2  j  n} and yj = 8>: xj [0.3x21 cos(24⇡x1 + 4j⇡n ) + 0.6x1] cos(6⇡x1 + j⇡n )j 2 J1 xj [0.3x21 cos(24⇡x1 + 4j⇡n ) + 0.6x1] sin(6⇡x1 + j⇡n )j 2 J2 The search space is [0, 1]⇥ [1, 1]n1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 UF3 : f1( !x ) = x1 + 2|J1| (4 X j2J1 y2j 2 Y j2J1 cos( 20yj⇡p j ) + 2), f2( !x ) = 1px1 + 2|J2| (4 X j2J2 y2j 2 Y j2J2 cos( 20yj⇡p j ) + 2) where J1 and J2 are the same as those of UF1, and yj = xj x 0.5(1.0+ 3(j2) n2 ) 1 , j = 2, ..., n,. The search space is [0, 1]n. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 139 MOP POF UF4 : f1( !x ) = x1 + 2|J1| X j2J1 h(yj), f2( !x ) = 1 x21 + 2 |J2| X j2J2 h(yj) where J1 = {j|j is odd and (2  j  n} and J2 = {j|j is even and 2  j  n} yi = xj sin(6⇡x1 + j⇡n ), j = 2, ..., n and h(t) = |t|1+e2|t| . The search space is [0, 1]⇥ [2, 2]n1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 UF5 : f1( !x ) = x1 + ( 1 2N + ✏)| sin(2N⇡x1)|+ 2|J1| X j2J1 h(yj), f2( !x ) = 1 x1 + ( 1 2N + ✏)| sin(2N⇡x1)|+ 2|J2| X j2J2 h(yj) where J1 = {j|j is odd and (2  j  n} and J2 = {j|j is even and 2  j  n} yi = xjsin(6⇡x1+ j⇡n ), j = 2, ..., n and h(t) = 2t2cos(4⇡t)+1. The search space is [0, 1]⇥ [1, 1]n1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 140 MOP POF UF6 : f1( !x ) = x1 +max{0, 2( 1 2N + ✏) sin(2N⇡x1)} + 2 |J1| (4 X j2J1 y2j 2 Y j2J1 cos( 20yj⇡p j ) + 2), f2( !x ) = 1 x1 +max{0, 2( 1 2N + ✏) sin(2N⇡x1)} + 2 |J2| (4 X j2J2 y2j 2 Y j2J2 cos( 20yj⇡p j ) + 2) where J1 = {j|j is odd and (2  j  n} and J2 = {j|j is even and 2  j  n} yi = xj sin(6⇡x1 + j⇡n ), j = 2, ..., n. The search space is [0, 1]⇥ [1, 1]n1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 UF7 : f1( !x ) = 5px1 + 2 J1 X j2J1 y2j , f2( !x ) = 1 5px1 + 2 J2 X j2J2 y2j where J1 = {j|j is odd and (2  j  n} and J2 = {j|j is even and 2  j  n} yi = xj sin(6⇡x1 + j⇡n ), j = 2, ..., n. The search space is [0, 1]⇥ [1, 1]n1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F1 F2 UF8 : f1( !x ) = cos(0.5x1⇡) cos(0.5x2⇡)+ 2 |J1| X j2J1 (xj 2x2 sin(2⇡x1 + j⇡ n ))2, f2( !x ) = cos(0.5x1⇡) sin(0.5x2⇡)+ 2 |J2| X j2J2 (xj 2x2 sin(2⇡x1 + j⇡ n ))2, f3( !x ) = sin(0.5x1⇡) + 2|J3| X j2J3 (xj 2x2 sin(2⇡x1 + j⇡ n ))2, where J1 = {j|3  j  n, and j 1 is a multiplication of 3}, J1 = {j|3  j  n, and j 2 is a multiplication of 3}, J1 = {j|3  j  n, and j is a multiplication of 3}. The search space is [0, 1]2 ⇥ [2, 2]n2. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 f1f2 f3 141 MOP POF UF9 : f1( !x ) = 0.5[max{0, (1 + ✏)(1 4(2x1 1)2)}+ 2x1]]x2 + 2 |J1| X j2J1 (xj 2x2 sin(2⇡x1 + j⇡ n ))2, f2( !x ) = 0.5[max{0, (1 + ✏)(1 4(2x1 1)2)} 2x1 + 2]x2 + 2 |J2| X j2J2 (xj 2x2 sin(2⇡x1 + j⇡ n ))2, f3( !x ) = 1 x2 + 2|J3| X j2J3 (xj 2x2 sin(2⇡x1 + j⇡ n ))2 where J1 = {j|3  j  n, and j 1 is a multiplication of 3}, J1 = {j|3  j  n, and j 2 is a multiplication of 3}, J1 = {j|3  j  n, and j is a multiplication of 3} and ✏ = 0.1. The search space is [0, 1]2 ⇥ [2, 2]n2. 00.010.020.030.040.05 0 0.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f1f2 f3 UF10 : f1( !x ) = cos(0.5x1⇡) cos(0.5x2⇡) + 2 J1 X j2J1 [4y2j cos(8⇡yj) + 1], f2( !x ) = 0 cos(0.5x1⇡) sin(0.5x2⇡) + 2 J2 X j2J1 [4y2j cos(8⇡yj) + 1], f3( !x ) = sin(0.5x2⇡) + 2 J3 X j2J1 [4y2j cos(8⇡yj) + 1] where J1 = {j|3  j  n, and j1 is a multiplication of 3}, J1 = {j|3  j  n, and j2 is a multiplication of 3}, J1 = {j|3  j  n, and j is a multiplication of 3} and yj = xj 2x2 sin(2⇡x1 + j⇡ n ), j = 3, ..., n. The search space is [0, 1] 2 ⇥ [2, 2]n2. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 f1f2 f3 142 Bibliography [1] Schwartz A. SpamAssassin. O’Reilly, 2004. [2] H.A. Abbass, R.A. Sarker, and C.S. Newton. PDE: A pareto-frontier di↵erential evo- lution approach for multi-objective optimization problems. In Proceedings of the IEEE Congress on Evol. Compt (CEC2001), volume 2, pages 971–978, Piscataway, NJ, 2001. IEEE Press. [3] Hussein A. Abbass. An economical cognitive approach for bi-objective optimization using bliss points, visualization, and interaction. Soft Computing, 10(8):687–698, 2006. [4] Hussein A Abbass. An economical cognitive approach for bi-objective optimization using bliss points, visualization, and interaction. Soft Computing, 10(8):687–698, 2006. [5] Hussein A Abbass, Adil M Bagirov, and Jiapu Zhang. The discrete gradient evolu- tionary strategy method for global optimization. In IEEE Congress on Evolutionary Computation (1), pages 435–442, 2003. [6] E. Aggelogiannaki and H. Sarimveis. A simulated annealing algorithm for prioritized multiobjective optimization—implementation in an adaptive model predictive control configuration. Trans. Sys. Man Cyber. Part B, 37(4):902–915, August 2007. [7] Shubham Agrawal, K.B. Panigrahi, and M.K. Tiwari. Multiobjective particle swarm al- gorithm with fuzzy clustering for electrical power dispatch. Evolutionary Computation, IEEE Transactions on, 12(5):529–541, Oct 2008. [8] Bilal Alatas, Erhan Akin, and Ali Karci. Modenar: Multi-objective di↵erential evolu- tion algorithm for mining numeric association rules. Appl. Soft Comput., 8(1):646–656, January 2008. 143 BIBLIOGRAPHY [9] D Balasubramanian, Murali C Krishna, and R Murugesan. Multi-objective ga- optimized interpolation kernels for reconstruction of high resolution emr images from low-sampled k-space data. International Journal of Computational Intelligence and Applications, 8(02):127–140, 2009. [10] Vitor Basto-Fernandes, Iryna Yevseyeva, and Jose´ R. Me´ndez. Optimization of anti- spam systems with multiobjective evolutionary algorithms. Inf. Resour. Manage. J., 26(1):54–67, January 2000. [11] P.A.N. Bosman and D. Thierens. Multi-objective optimization with the naive midea. In J.A. Lozano et al, editor, Towards a New Evolutionary Computation. Advances in Estimation of Distribution Algorithms, pages 123–157. Springer-Verlag, Berlin, 2006. [12] Peter A. N. Bosman and Edwin D. de Jong. Exploiting gradient information in numer- ical multi–objective evolutionary optimization. In Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, GECCO ’05, pages 755–762, New York, NY, USA, 2005. ACM. [13] Martin Brown and Robert E Smith. E↵ective use of directional information in multi-objective evolutionary computation. In Genetic and Evolutionary Computation (GECCO 2003), pages 778–789. Springer, 2003. [14] Lam T Bui, Hussein A Abbass, and Daryl Essam. Local models-an approach to dis- tributed multi-objective optimization. Computational Optimization and Applications, 42(1):105–139, 2009. [15] Lam T Bui, Hussein A Abbass, and Daryl Essam. Localization for solving noisy multi- objective optimization problems. Evolutionary computation, 17(3):379–409, 2009. [16] Lam T. Bui and Sameer Alam. Multi-Objective Optimization in Computation Intelli- gence: Theory and Practice. Information Science Reference. IGI Global, 5 2008. [17] Lam Thu Bui. Advances in Multi-objective evolutionary algorithms. People army pub- lishing house, 2013. 144 BIBLIOGRAPHY [18] Lam Thu Bui, Kalyanmoy Deb, Hussein A Abbass, and Daryl Essam. Interleaving guidance in evolutionary multi-objective optimization. Journal of Computer Science and Technology, 23(1):44–63, 2008. [19] Lam Thu Bui, Jing Liu, Axel Bender, Michael Barlow, Slawomir Wesolkowski, and Hussein A. Abbass. Dmea: a direction-based multiobjective evolutionary algorithm. Memetic Computing, pages 271–285, 2011. [20] K. Piromsopa C. Na Songkhla. Statistical rules for thai spam detection. Proceeding of: Future Networks, pages 178–184, 2010. [21] Oscar Castillo, Leonardo Trujillo, and Patricia Melin. Multiple objective genetic algo- rithms for path-planning optimization in autonomous mobile robots. Soft Computing, 11(3):269–279, 2007. [22] Pei-Chann Chang, Jih-Chang Hsieh, and Chih-Yuan Wang. Adaptive multi-objective genetic algorithms for scheduling of drilling operation in printed circuit board industry. Appl. Soft Comput., 7(3):800–806, June 2007. [23] Fan Yang Chung Kwan and Che Chang. A di↵erential evolution variant of nsga ii for real world multiobjective optimization. Proceeding ACAL’07 Proceedings of the 3rd Australian conference on Progress in artificial life, pages 345–356, 2007. [24] C. A.C. Coello, G. T. Pulido, and M. S. Lechuga. Handling multiple objectives with particle swarm optimization. Trans. Evol. Comp, 8(3):256–279, June 2004. [25] C.A. Coello, D.A. Van Veldhuizen, and G.B. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic publishers, New York, 2002. [26] K. Deb. Multiobjective Optimization using Evolutionary Algorithms. John Wiley and Son Ltd, New York, 2001. [27] K. Deb and T. Goel. Controlled elitist non-dominated sorting genetic algorithm for bet- ter convergence. In Evolutionary Multi-Criteria Optimization, volume 1993 of Lecture Notes in Computer Science, pages 67–81. Springer, 2001. 145 BIBLIOGRAPHY [28] K. Deb and A. Kumar. Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In GECCO ’07, pages 781–788, 2007. [29] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. A fast and elitist multiobjec- tive genetic algorithm: Nsga-ii. Evolutionary Computation, IEEE Transactions on, 6(2):182–197, 2002. [30] K. Deb and J. Sundar. Reference point based multi-objective optimization using evo- lutionary algorithms. In GECCO ’06: Proceedings of the 8th annual conference on Genetic and Evolutionary Computation, pages 635–642, New York, NY, USA, 2006. ACM Press. [31] K. Deb, L. Thiele, M. Laumanns, and E. Zitzler. Scalable test problems for evolu- tionary multi-objective optimization, TIK-Report no. 112. Technical report, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich, 2001. [32] Satchidananda Dehuri, Srikanta Patnaik, Ashish Ghosh, and Rajib Mall. Application of elitist multi-objective genetic algorithm for classification rule generation. Applied Soft Computing, 8(1):477–487, 2008. [33] Kenneth Alan DeJong. An analysis of the behavior of a class of genetic adaptive systems. PhD thesis, University of Michigan, Ann Arbor, 1975. [34] G.Nildem Demir, A.Sima Uyar, and Sule Gunduz-Oguducu. Multiobjective evolution- ary clustering of web user sessions: a case study in web page recommendation. Soft Computing, 14(6):579–597, 2010. [35] R. C. Eberhart and Y. Shi. Particle swarm optimization: developments, applications and resources. In Proceedings of the Congress on Evolutionary Computation. IEEE Press, 2001. [36] Francis Ysidro Edgeworth. Mathematical psychics: An essay on the application of mathematics to the moral sciences. C. Keagann Paul, 1881. 146 BIBLIOGRAPHY [37] Ronald Aylmer Fisher. Statistical methods for research workers. Genesis Publishing Pvt Ltd, 1925. [38] Jorg Fliege and Benar Fux Svaiter. Steepest descent methods for multicriteria opti- mization. Mathematical Methods of Operations Research, 51(3):479–494, 2000. [39] C.M. Fonseca and P.J. Fleming. Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In Proceedings of the Fifth Int. Conf. on Genetic Algorithms, San Mateo, California, pages 416–423. Morgan Kau↵man Pub- lishers, 1993. [40] Mar´ıa Jose´ Gacto, Rafael Alcala´, and Francisco Herrera. Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems. Soft Computing, 13(5):419–436, 2009. [41] Ashish Ghosh and Bhabesh Nath. Multi-objective rule mining using genetic algorithms. Information Sciences, 163(1):123–133, 2004. [42] Maoguo Gong, Fang Liu, Wei Zhang, Licheng Jiao, and Qingfu Zhang. Interactive moea/d for multi-objective decision making. In GECCO’ 2011, pages 721–728, 2011. [43] Julia Handl and Joshua Knowles. An evolutionary approach to multiobjective cluster- ing. Evolutionary Computation, IEEE Transactions on, 11(1):56–76, 2007. [44] Thomas Hanne and Stefan Nickel. A multiobjective evolutionary algorithm for schedul- ing and inspection planning in software development projects. European Journal of Operational Research, 167(3):663–678, 2005. [45] Ken Harada and Shigenobu Kobayashi. Local search for multiobjective function opti- mization: Pareto descent method. In In The 8th Annual Conference on Genetic and Evolutionary Computation (GECCO-2006), pages 659–666. ACM Press, 2006. [46] Joel Hewlett, Bogdan Wilamowski, and G Dundar. Merge of evolutionary computation with gradient based method for optimization problems. In Industrial Electronics, 2007. ISIE 2007. IEEE International Symposium on, pages 3304–3309. IEEE, 2007. 147 BIBLIOGRAPHY [47] J. Horn, N. Nafpliotis, and D.E. Goldberg. A niched pareto genetic algorithm for multiobjective optimization. In Proceedings of the First IEEE Conf. on Evolutionary Computation, volume 1, pages 82–87. IEEE World Congress on Computational Intelli- gence, Piscataway, New Jersey, 1994. [48] Juan Gayta´n Iniestra and Javier Garc´ıa Gutie´rrez. Multicriteria decisions on interde- pendent infrastructure transportation projects using an evolutionary-based framework. Applied Soft Computing, 9(2):512–526, 2009. [49] Antony W Iorio and Xiaodong Li. Incorporating directional information within a dif- ferential evolution algorithm for multi-objective optimization. In Proceedings of the 8th annual conference on Genetic and evolutionary computation, pages 691–698. ACM, 2006. [50] Stefan Janson, Daniel Merkle, and Martin Middendorf. Molecular docking with multi- objective particle swarm optimization. Appl. Soft Comput., 8(1):666–675, January 2008. [51] Mehmet Kaya. Multi-objective genetic algorithm based approaches for mining opti- mized fuzzy association rules. Soft Computing, 10(7):578–586, 2006. [52] Hyoungjin Kim and Meng-Sing Liou. Adaptive directional local search strategy for hybrid evolutionary multiobjective optimization. Applied Soft Computing, 19(0):290 – 311, 2014. [53] J. Knowles and D. Corne. Approximating the nondominated front using the pareto archived evolution strategy. Evol. Comp, 8(2):149–172, 2000. [54] J. D. Knowles and D. Corne. ”M-PAES: A memetic algorithm for multi-objective optimization”. In Proceedings of the Congress on Evolutionary Computation, pages 325–332. IEEE Press, 2000. [55] Tjalling C Koopmans and John Michael Montias. On the description and comparison of economic systems. Comparison of Economic Systems, 14, 1971. 148 BIBLIOGRAPHY [56] Pekka J Korhonen and Jukka Laakso. A visual interactive method for solving the multiple criteria problem. European Journal of Operational Research, 24(2):277–287, 1986. [57] Adriana Lara, Sergio Alvarado, Shaul Salomon, Gideon Avigad, Carlos A Coello Coello, and Oliver Schu¨tze. The gradient free directed search method as local search within multi-objective evolutionary algorithms. In EVOLVE-A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II, pages 153–168. Springer, 2013. [58] Beatrice Lazzerini, Francesco Marcelloni, and Massimo Vecchio. A multi-objective evo- lutionary approach to image quality/compression trade-o↵ in jpeg baseline algorithm. Applied Soft Computing, 10(2):548–561, 2010. [59] Loo Hay Lee, Chul Ung Lee, and Yen Ping Tan. A multi-objective genetic algorithm for robust flight scheduling using simulation. European Journal of Operational Research, 177(3):1948–1968, 2007. [60] Bin-Bin Li and Ling Wang. A hybrid quantum-inspired genetic algorithm for multi- objective flow shop scheduling. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 37(3):576–591, June 2007. [61] Hui Li and Qingfu Zhang. Comparison between nsga-ii and moea/d on a set of multi- objective optimization problems with complicated pareto sets. [62] Hui Li and Qingfu Zhang. Multiobjective optimization problems with complicated pareto sets, moea/d and nsga-ii. Evolutionary Computation, IEEE Transactions on, 13(2):284–302, 2009. [63] Hui Li and Qingfu Zhang. Multiobjective optimization problems with complicated pareto sets, moea/d and nsga-ii. IEEE Trans. Evol. Comp, pages 284–302, 2009. [64] Ming-Jeng LIN and Ching-Lai HWANG. Group decision making under multiple crite- ria. Springer, 1987. [65] Bo Liu, Francisco V Ferna´ndez, Qingfu Zhang, Murat Pak, Suha Sipahi, and Georges 149 BIBLIOGRAPHY Gielen. An enhanced moea/d-de and its application to multiobjective analog cell sizing. In Evolutionary Computation (CEC), 2010 IEEE Congress on, pages 1–7. IEEE, 2010. [66] AG Lo´pez-Herrera, E Herrera-Viedma, and F Herrera. A multiobjective evolutionary algorithm for spam e-mail filtering. In Intelligent System and Knowledge Engineering, 2008. ISKE 2008. 3rd International Conference on, volume 1, pages 366–371. IEEE, 2008. [67] Samir W Mahfoud. Niching methods for genetic algorithms. Urbana, 51(95001), 1995. [68] Engin Masazade, Ramesh Rajagopalan, Pramod K Varshney, Chilukuri K Mohan, Gullu Kiziltas Sendur, and Mehmet Keskinoz. A multiobjective optimization approach to obtain decision thresholds for distributed detection in wireless sensor networks. Sys- tems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 40(2):444– 457, 2010. [69] K. Miettinen. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston, USA, 1999. [70] Yu Chen Minzhong Liu, Xiufen Zou and Zhijian Wu. Performance assessment of dmoea- dd with cec 2009 moea competition test instances. Proceeding CEC’09 Proceedings of the 11th conference on Congress on Evol. Comp, pages 2913–2918, 2009. [71] F. Jiang V.Q. Tran M.T. Vu, Q.A. Tran. Multilingual rules for spam detection. Proceed- ings of the 7th International Conference on Broadband and Biomedical Communications (IB2COM 2012), pages 106–110, 2012. [72] Anirban Mukhopadhyay and Ujjwal Maulik. A multiobjective approach to mr brain image segmentation. Applied Soft Computing, 11(1):872–880, 2011. [73] Long Nguyen and Lam Thu Bui. A decomposition-based interactive method for multi- objective evolutionary algorithms. The Journal on Information Technologies and Com- munications (JITC), E-2(5(9)):17–24, 2012. [74] Long Nguyen and Lam Thu Bui. A multi-point interactive method for multi-objective 150 BIBLIOGRAPHY evolutionary algorithms. In The fourth International Conference on Knowledge and Systems Engineering (KSE 2012), Da Nang, Vietnam, 7 2012. [75] Long Nguyen and Lam Thu Bui. A new selection strategy for the direction-based multi-objective evolutionary algorithm. Journal of Development and Application on Information and Telecommunication Technology (JITC), E-2(6(10)):35–48, 2013. [76] Long Nguyen and Lam Thu Bui. The e↵ects of di↵erent selection schemes on the direc- tion based multi-objective evolutionary algorithm. In The first NAFOSTED Conference on Information and Computer Science 2014 (NICS’14), Ha Noi, Vietnam, March 2014. [77] Long Nguyen, Lam Thu Bui, and Hussein Abbass. A new niching method for the direction-based multi-objective evolutionary algorithm. In 2013 IEEE Symposium Se- ries on Computational Intelligence, Singapore, 4 2013. [78] Long Nguyen, Lam Thu Bui, and Hussein. Abbass. DMEA-II: the direction-based multi-objective evolutionary algorithm-II. Soft Computing, 18(11):2119–2134, 2014. [79] Long Nguyen, Lam Thu. Bui, and Tran Quang. Anh. Toward an interactive method for dmea-ii and application to the spam-email detection system. VNU Journal of Computer Science and Communication Engineering, 30(4):29–44, 2014. [80] Long Nguyen and LamThu Bui. A ray based interactive method for direction based multi-objective evolutionary algorithm. In Van Nam Huynh, Thierry Denoeux, Dang Hung Tran, Anh Cuong Le, and Son Bao Pham, editors, Knowledge and Sys- tems Engineering, volume 245 of Advances in Intelligent Systems and Computing, pages 173–184. Springer International Publishing, 2014. [81] SN Omkar, J Senthilnath, Rahul Khandelwal, G Narayana Naik, and S Gopalakrish- nan. Artificial bee colony (abc) for multi-objective design optimization of composite structures. Applied Soft Computing, 11(1):489–499, 2011. [82] Levent O¨zgu¨r, Tunga Gu¨ngo¨r, and Fikret S. Gu¨rgen. Adaptive anti-spam filtering for agglutinative languages: a special case for turkish. Pattern Recognition Letters, 25(16):1819–1831, 2004. 151 BIBLIOGRAPHY [83] Siddharth Pal, Swagatam Das, and Aniruddha Basak. Design of time-modulated linear arrays with a multi-objective optimization approach. Progress In Electromagnetics Research B, 23:83–107, 2010. [84] Marco A Panduro, Carlos A Brizuela, David Covarrubias, and Claudio Lopez. A trade- o↵ curve computation for linear antenna arrays using an evolutionary multi-objective approach. Soft Computing, 10(2):125–131, 2006. [85] Jose´ Maria A Pangilinan and Gerrit K Janssens. Evolutionary algorithms for the multiobjective shortest path problem. Enformatika, 19, 2007. [86] Vilfredo Pareto. Cours d’economie politique. Librairie Droz, 1964. [87] Eskelinen Petri and Miettinen Kaisa. Trade-o↵ analysis approach for interactive non- linear multiobjective optimization. In OR Spectrum, pages 1–14, 2011. [88] Huyen N.T.M Phuong L.H, Azim Roussanaly, and Ho Tuong Vinh. A hybrid approach to word segmentation of vietnamese texts. 5196:240–249, 2008. [89] Ken Price, Rainer Storn, and Jouni Lampinen. Di↵erential Evolution - A Practical Approach to Global Optimization. Springer, Berlin, Germany, 2005. [90] S.Z. Zhao P.N. Suganthan W. Liu S. Tiwari Q. Zhang, A. Zhou. Multiobjective opti- mization test instances for the cec 2009 special session and competition. [91] X. Li Q.A. Tran, H. Duan. Real-time statistical rules for spam detection. Proceedings of the International Journal of Computer Science and Network Security, pages 178–184, 2006. [92] Bin Qian, Ling Wang, De-Xian Huang, and Xiong Wang. Multi-objective no-wait flow-shop scheduling with a memetic algorithm based on di↵erential evolution. Soft Computing, 13(8-9):847–869, 2009. [93] Gang Quan, Garrison W Greenwood, Donglin Liu, and Sharon Hu. Searching for multi- objective preventive maintenance schedules: Combining preferences with evolutionary algorithms. European Journal of Operational Research, 177(3):1969–1984, 2007. 152 BIBLIOGRAPHY [94] Daniel Radu and Yvon Besanger. A multi-objective genetic algorithm approach to optimal allocation of multi-type facts devices for power systems security. In Power Engineering Society General Meeting, 2006. IEEE, pages 8–pp. IEEE, 2006. [95] A.R. Rahimi-Vahed, S.M. Mirghorbani, and M. Rabbani. A new particle swarm al- gorithm for a multi-objective mixed-model assembly line sequencing problem. Soft Computing, 11(10):997–1012, 2007. [96] Margarita Reyes-Sierra and CA Coello Coello. Multi-objective particle swarm optimiz- ers: A survey of the state-of-the-art. International journal of computational intelligence research, 2(3):287–308, 2006. [97] AlanP. Reynolds and Beatriz Iglesia. A multi-objective grasp for partial classification. Soft Computing, 13(3):227–243, 2009. [98] Isabel Espirito Santo Roman Denysiuk, Lino Costa. Ddmoa: Descent directions based multiobjective algorithm. In Proceedings of the Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 12), pages 460–471. IEEE, 2012. [99] Isabel Espirito Santo Roman Denysiuk, Lino Costa. Ddmoa2: Improved descent directions-based multiobjective algorithm. In 13th International Conference on Com- putational and Mathematical Methods in Science and Engineering. IEEE, 2013. [100] Rocıo C Romero-Zaliz, Cristina Rubio-Escudero, J Perren Cobb, Francisco Herrera, Oscar Cordo´n, and Igor Zwir. A multiobjective evolutionary conceptual clustering methodology for gene annotation within structural databases: a case of study on the gene ontology database. Evolutionary Computation, IEEE Transactions on, 12(6):679– 701, 2008. [101] RP Runyon, A Haber, DJ Pittenger, and KA Coleman. Statistical inference: categorical variables. Fundamentals of Behavioral Statistics. McGraw Hill, New York, pages 592– 594, 1996. 153 BIBLIOGRAPHY [102] Mohammad Saadatseresht, Ali Mansourian, and Mohammad Taleai. Evacuation plan- ning using multiobjective evolutionary optimization approach. European Journal of Operational Research, 198(1):305–314, 2009. [103] Luciano Sanchez, Jose Otero, and Ines Couso. Obtaining linguistic fuzzy rule-based regression models from imprecise data with multiobjective genetic algorithms. Soft Computing, 13(5):467–479, 2009. [104] R Saravanan, S Ramabalan, N Ebenezer, and C Dharmaraja. Evolutionary multi criteria design optimization of robot grippers. Applied Soft Computing, 9(1):159–172, 2009. [105] Ruhul Sarker and Tapabrata Ray. An improved evolutionary algorithm for solving multi-objective crop planning models. Comput. Electron. Agric., 68(2):191–199, Octo- ber 2009. [106] Stefan Scha¨✏er, Reinhart Schultz, and Klaus Weinzierl. Stochastic method for the so- lution of unconstrained vector optimization problems. Journal of Optimization Theory and Applications, 114(1):209–222, 2002. [107] O. Schutze, A. Lara, and Carlos A. Coello Coello. On the influence of the number of objectives on the hardness of a multiobjective optimization problem. Evolutionary Computation, IEEE Transactions on, 15(4):444–455, Aug 2011. [108] Soo-Yong Shin, In-Hee Lee, Dongmin Kim, and Byoung-Tak Zhang. Multiobjective evolutionary optimization of dna sequences for reliable dna computing. Evolutionary Computation, IEEE Transactions on, 9(2):143–158, 2005. [109] Pradyumn Kumar Shukla. On gradient based local search methods in unconstrained evolutionary multi-objective optimization. In Evolutionary Multi-Criterion Optimiza- tion, pages 96–110. Springer, 2007. [110] Valceres VR Silva, Peter J Fleming, Jungiro Sugimoto, and Ryuichi Yokoyama. Multi- objective optimization using variable complexity modelling for control system design. Applied Soft Computing, 8(1):392–401, 2008. 154 BIBLIOGRAPHY [111] Christine Solnon and Khaled Ghe´dira. Ant colony optimization for multi-objective optimization problems. Internation Journal on computer science, 2010. [112] James C Spall. Implementation of the simultaneous perturbation algorithm for stochas- tic optimization. Aerospace and Electronic Systems, IEEE Transactions on, 34(3):817– 823, 1998. [113] Wolfram Stadler. Multicriteria Optimization in Engineering and in the Sciences, vol- ume 37. Springer, 1988. [114] Rainer Storn and Kenneth Price. Di↵erential evolution - a simple and ecient adaptive scheme for global optimization over continuous spaces, 1995. [115] Reza Tavakkoli-Moghaddam, Alireza Rahimi-Vahed, and Ali Hossein Mirzaei. A hy- brid multi-objective immune algorithm for a flow shop scheduling problem with bi- objectives: Weighted mean completion time and weighted mean tardiness. Information Sciences, 177(22):5072 – 5090, 2007. [116] G Timmel. Ein stochastisches suchverrahren zur bestimmung der optimalen kompro- milsungen bei statischen polzkriteriellen optimierungsaufgaben. Wiss. Z. TH Ilmenau, 6(1):5, 1980. [117] Long Nguyen Anh Quang Tran and Lam Thu Bui. Dmea-ii and its application on spam email detection problems. In Seventh IEEE Symposium on Computational Intelligence for Security and Defense Applications (CISDA 2014), Ha Noi, Vietnam. [118] Steve Uhlig. A multiple-objectives evolutionary perspective to interdomain trac engineering. International Journal of Computational Intelligence and Applications, 5(02):215–230, 2005. [119] D.A.V. Veldhuizen. Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovation. PhD thesis, Department of Electrical Engineering and Computer Engineering, Airforce Institue of Technology, Ohio, 1999. [120] Minh Tuan Vu, Quang Anh Tran, Quang Minh Ha, and Lam Thu Bui. A multi-objective 155 BIBLIOGRAPHY approach for vietnamese spam detection. In Knowledge and Systems Engineering, pages 211–221. Springer, 2014. [121] MinhTuan Vu, QuangAnh Tran, QuangMinh Ha, and LamThu Bui. A multi-objective approach for vietnamese spam detection. In Processding: Knowledge and Systems Engineering 2013, pages 211–221, 2013. [122] Antony Waldock and David Corne. Multiple objective optimisation applied to route planning. In Proceedings of the 13th annual conference on Genetic and evolutionary computation, pages 1827–1834. ACM, 2011. [123] Klaus Weinert, Andreas Zabel, Petra Kersting, Thomas Michelitsch, and Tobias Wag- ner. On the use of problem-specific candidate generators for the hybrid optimiza- tion of multi-objective production engineering problems. Evolutionary computation, 17(4):527–544, 2009. [124] Stefan Wiegand, Christian Igel, and Uwe Handmann. Evolutionary multi-objective optimisation of neural networks for face detection. International Journal of Computa- tional Intelligence and Applications, 4(03):237–253, 2004. [125] A. Wierzbicki. The use of reference objectives in multiobjective optimization. In G. Fan- del and T. Gal, editors, Multiple Objective Decision Making, Theory and Application, pages 468–486, Berlin and New York, 1980. Springer. [126] Li-Ning Xing, Ying-Wu Chen, and Ke-Wei Yang. Multi-objective flexible job shop schedule: Design and evaluation by simulation modeling. Appl. Soft Comput., 9(1):362– 376, January 2009. [127] Iryna Yevseyeva, Vitor Basto-Fernandes, and Jose´ R Me´ndez. Survey on anti-spam single and multi-objective optimization. In ENTERprise Information Systems, pages 120–129. Springer, 2011. [128] Iryna Yevseyeva, Vitor Basto-Fernandes, David Ruano-Orda´s, and Jose´ R Me´ndez. Optimising anti-spam filters with evolutionary algorithms. Expert Systems with Appli- cations, 2013. 156 BIBLIOGRAPHY [129] Po-Lung Yu. A class of solutions for group decision problems. Management Science, 19(8):936–946, 1973. [130] Xinjie Yu and Mitsuo Gen. Introduction to evolutionary algorithms. Springer, 2010. [131] Xianyi Zeng, Yijun Zhu, Ludovic Koehl, Mauricio Camargo, Christian Fonteix, and Franc¸ois Delmotte. A fuzzy multi-criteria evaluation method for designing fashion oriented industrial products. Soft Computing, 14(12):1277–1285, 2010. [132] Q. F. Zhang and H. Li. Moea/d: A multi-objective evolutionary algorithm based on decomposition. 2007. [133] Yang Zhang and Peter I Rockett. A generic multi-dimensional feature extrac- tion method using multiobjective genetic programming. Evolutionary Computation, 17(1):89–115, 2009. [134] Yang Zhang and Peter I Rockett. A generic optimising feature extraction method using multiobjective genetic programming. Applied Soft Computing, 11(1):1087–1097, 2011. [135] Zhuhong Zhang. Multiobjective optimization immune algorithm in dynamic environ- ments and its application to greenhouse control. Applied Soft Computing, 8(2):959–971, 2008. [136] Shuguang Zhao and Licheng Jiao. Multi-objective evolutionary design and knowledge discovery of logic circuits based on an adaptive genetic algorithm. Genetic Programming and Evolvable Machines, 7(3):195–210, 2006. [137] Stanley Zionts. Decision making: Some experiences, myths and observations. In Mul- tiple Criteria Decision Making, pages 233–241. Springer, 1997. [138] E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the strength pareto evo- lutionary algorithm for multiobjective optimization. In K. C. Giannakoglou, D. T. Tsahalis, J. Periaux, K. D. Papailiou, and T. Fogarty, editors, Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, pages 95–100. Int. CMINE, 2001. 157 BIBLIOGRAPHY [139] E. Zitzler and L. Thiele. Multi-objective optimization using evolutionary algorithms - a comparative case study. In Parallel Problem Solving from Nature, volume 1498 of Lecture Notes in Computer Science, pages 292–304. Springer, 1998. [140] E. Zitzler, L. Thiele, and K. Deb. Comparision of multiobjective evolutionary algo- rithms: Emprical results. Evol. Comp, 8(1):173–195, 2000. [141] Xingquan Zuo, Hongwei Mo, and Jianping Wu. A robust scheduling method based on a multi-objective immune algorithm. Information Sciences, 179(19):3359 – 3369, 2009. 158

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