1. Introduction

High strength multiphase steel is the one of the com-monly used steels due to its reasonable combination ofstrength and ductility. The maximization of strength with-out much compromise to the ductility is an important ob-jective in designing the alloy along with its processing pa-rameters. The strength of low carbon steel is improved bythe addition of alloying and microalloying elements includ-ing carbide formers and other precipitation hardeners, andalso by modifying the microstructure through introductionof the low temperature transformation products of austen-ite, e.g., bainite and martensite, which generally leads to de-terioration in ductility. The design of steels from fundamen-tal principles is a rather complex task. The determination ofmechanical properties of steels in terms of their composi-tion and process parameters requires adequate models,which can suggest a tailored change in the variables toachieve a certain target property. Thermomechanical pro-cessing is known to improve the mechanical properties ofthese steels. Thermomechanically treated microalloyedsteels are now accepted as a viable alternative to the tradi-

tional steels, and their controlled rolling and controlledcooling are practiced routinely around the world. The pres-ence of the microalloying elements, such as niobium, tita-nium and vanadium, renders these steels particularlyamenable to thermomechanical processing, and their lowcarbon contents cause marked improvement in their tough-ness and weldability.1) Application of thermomechanicalprocessing minimizes, and sometimes even eliminates, theheat treatment and thus saves energy. This is why thermo-mechanical controlled processing (TMCP) is a widely usedprocess for high strength steels. To achieve the required mi-crostructure and mechanical properties of thermomechani-cally processed multiphase steels it is necessary to haveknowledge about the role of composition and process pa-rameters.

The chemistry of the steel and the TMCP parameters,like reheating temperature, amount of deformation in dif-ferent stages of rolling, the finish rolling temperature andthe cooling rate are known to exert appreciable influence onthe structure and property of the finished product. Usuallythe patterns relating these “inputs” and “outputs” in TMCPsteels are qualitatively recognized by the experts in the field

Designing High Strength Multi-phase Steel for ImprovedStrength–Ductility Balance Using Neural Networks and Multi-objective Genetic Algorithms

Shubhabrata DATTA,1) Frank PETTERSSON,2) Subhas GANGULY,1) Henrik SAXÉN2) and Niruopam CHAKRABORTI3)

1) School of Materials Science and Engineering, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.E-mail: sdatta@matsc.becs.ac.in, subhasbecollege@yahoo.com 2) Faculty of Chemical Engineering, Heat EngineeringLaboratory, Åbo Akademi University, Biskopsgatan 8, FIN-20500 Åbo, Finland. E-mail: frank.pettersson@abo.fi, henrik.saxen@abo.fi 3) Department of Metallurgical & Materials Engineering, IndianInstitute of Technology, Kharagpur 721302, West Bengal, India. E-mail: nchakrab@iitkgp.ac.in

(Received on January 15, 2007; accepted on May 30, 2007 )

The properties of steels depend in a complex way on their composition and heat treatment and neuralnetworks have therefore recently been widely used for capturing these relationships. Two different meth-ods of reducing the network connectivity, viz a pruning algorithm and a multi-objective predator prey geneticalgorithm, have been used for neural network modeling of the mechanical properties of high strengthsteels, so that relevant connections within the networks are revealed. This provides important understand-ing on the variables and their relationship with mechanical properties. In the pruning algorithm the lowerlayer of the network is gradually reduced by removing less significant connections. In the predator prey al-gorithm, a genetic algorithm based multi-objective optimization technique is used to train the neural net-work and a Pareto front is developed by minimizing the training error along with the network size. The re-sults of both techniques reveal that they can extract more knowledge from the data, which is difficult to ob-tain from conventional neural models. The relative relevance of the composition and processing parametersdetected could be used for designing steel with tailored property balance. The results developed by the twotechniques are also found to be comparable.

KEY WORDS: high strength multiphase steel; neural network model; pruning algorithm; genetic algorithm;multi-objective optimization; predator prey algorithm; alloy design.

ISIJ International, Vol. 47 (2007), No. 8, pp. 1195–1203

1195 © 2007 ISIJ

of metallurgy, but the quantitative relations are not alwaysknown. Artificial neural networks (ANN) are learning sys-tems, which try to learn and map the existing input outputrelationship in an accurate way on the basis of experimentalinformation, and have been found successful in developingprediction model for the properties of TMCP steels.2,3)

ANN methods have also been found superior compared totraditional regression techniques in case of prediction ofproperties of steel.4,5) An ANN analysis usually depends onpublished data or data developed in the laboratories, andthat often implies working with a diminutive databank.Sometimes, due to the large number of potential inputs thepractical limitation may lead to over-fitting of the ANNmodel where the abilities of extracting meaningful informa-tion from the data are lost. An established method foravoiding over-fitting is to restrict the number of connectiv-ity (weights) between the inputs and the hidden nodes andeven to restrict the numbers of inputs and hidden nodes.6,7)

In addition to avoiding over-fitting, with its detrimental ef-fect on model accuracy, a detection of the relevant connec-tions within the network could provide important under-standing on the variables and their relationship.

In the present work two different methods of reducingthe network connectivity have been used for modeling themechanical properties of high strength steels. Firstly an in-tuitive pruning algorithm8) with a large sigmoid networkhaving random initial weights in the lower layer of connec-tions is used and the complexity of the network is graduallyreduced by removing less significant connections. In theother approach, a genetic algorithm based multi-objectiveoptimization technique is used to train the ANN, known aspredator prey algorithm9,10) and a Pareto front is developedminimizing the training error along with the network size.Genetic algorithm has been successfully used for alloy de-sign by previous workers.11–13) Here in both approaches, theupper-layer weights are determined by linear least squares,which makes the approaches computationally feasible. Theresults obtained by the techniques are studied with a viewto design high strength steel with superior strength–ductil-ity balance and a comparative study between the informa-tion generated by the two techniques is also made.

2. Methodology

2.1. The Pruning Algorithm

The pruning method is based on feedforward neural net-works of multi-layer perceptron type (often called back-propagation networks) with a single layer of hidden nonlin-ear units and linear output nodes. For the case of simplicity,the principles of the method will here be explained for thecase with a single hidden output node, even though the gen-eralization to networks with several output nodes is cer-tainly feasible. Fundamentally, the method is based on thefact that for such a network with an arbitrary choice ofweights in its lower layer of connections, W, (cf. Fig. 1)there is usually a weight vector, v, to the output node thatwill lead to a relatively good solution, y, of the approxima-tion problem at hand.

The vector v can be determined by linear least squares.14)

With this as the starting point, the pruning algorithm pro-posed can be compactly written as:

1) Select a set of N potential inputs, x, and the output, y,to be estimated for the observations of the training set.

2) Choose a sufficient number of hidden nodes, m, andgenerate a random weight matrix, W(0), for the lowerpart of the network. Set the iteration index to k�1.

3) Equate to zero, in turn, each non-zero weight, wij(k�1), of

W(k�1), and determine the optimal upper-layer weightvector, v, minimizing F�∑( y�y)2 by linear leastsquares. Save the corresponding value of the objectivefunction, Fij

(k).4) Find the minimum of the objective function values,

� (k)�minij

{Fij(k)}. Set W(k)�W(k�1) and equate to zero

the weight corresponding to the minimum objectivefunction value, wij

(k)�0 with ij�arg minij

{Fij(k)}.

5) Set y ij�k and save this variable in a matrix, YY�{y ij}(with the same dimension as W).

6) Set k�k�1. If k�m ·N, go to 3. Else, end.The book-keeping matrix, YY , stores the iteration number

at which each connection weight has been deleted: Bystudying the elements in the columns (or rows) of the ma-trix it is afterwards easy to deduce when a certain input (orhidden node) has been eliminated.

Repeating the process a number of times, each with arandomly generated weight matrix, W, and considering net-work designs up to a certain complexity, a data set with dif-ferent, potentially important, connections can be obtained.An analysis of this data set with statistical methods maygive answers to questions such as which of the inputs aremost essential and which kind of connections are to be in-cluded to yield a parsimonious model.

2.2. Predator Pray Training

As an alternative approach, the architecture of the lowerpart of the network and its corresponding weight matrixwere treated as variables influencing the objective functionsand evolved by a genetic process, while the upper part ofthe network was, like in the pruning approach, determinedby linear least squares. Since the two objectives, i.e., thetraining error, F1, and the required number of active con-nections in the lower part of the network, F2, are clearlyconflicting, the trade off between them can be representedas a ‘Pareto front.’15,16) A ‘population’ of networks was uti-lized in tackling the multi-objective problem formulationusing a Predator–Prey algorithm designed according to anidea suggested in Ref. 9). The main features of this algo-rithm (see Ref. 10) for details) are described next.

The ‘preys’ are initiated as randomly generated sparseneural networks that constitute an initial ‘population’ in theusual GA sense. Any ‘individual’ in the prey populationdiffers from its other members both by the nature of thelower part connections and the weight values associated

ISIJ International, Vol. 47 (2007), No. 8

1196© 2007 ISIJ

Fig. 1. Feed forward neural network and notation.

with it. The ‘predators’ are externally induced entitieswhose role is to prune the prey population based upon a‘fitness’ value, F , which is related to both objective func-tion values. The effective fitness of any prey i evaluated bya predator j is given as a weighted sum of Fi,1 and Fi,2

F ij�w jFi,1�(1�w j)Fi,2 ; 0�w j�1..............(1)

where the weight value, w j, is given by a uniform randomnumber.15) Initially, the preys and the predators are ran-domly introduced into a two-dimensional computationallattice, where for any predator or prey a neighborhood,given by the adjacent elements in the lattice, plays an im-portant role in the algorithm. A predator is allowed to moveone step at a time, up to a maximum number of steps that isdynamically adjusted at the end of a generation, and duringthis movement it kills the weakest prey in its neighborhoodand takes its position. The weakest here means the prey thatperforms worst in terms of its F value. If the neighborhoodis empty of preys, the predator makes one random move inany direction, unless it has exhausted its allowed number ofmoves. Initially, a target size of the prey population, �prey, isset and at the onset of any generation the allowed numberof moves, M, for a predator is determined as

......................(2)

where int( · ) rounds downwards to the closest integer, andNprey and Npred are the number of preys and predators re-spectively; this controls the population of preys. Whenkilling stops, the survivors in the prey population are (witha given probability) allowed to move randomly one step at atime (up to a prescribed maximum number of steps) to anempty position in the lattice. This establishes a new neigh-borhood, where the preys are allowed to mate (by‘crossover’) and mutate. Each prey chooses a random matein its neighborhood, provided at least one more prey residesthere. The applied crossover process, illustrated schemati-cally in Fig. 2, swaps identically-positioned hidden nodesof two parents. Each hidden node is swapped with a prede-fined probability, and the recipient individual thus inheritsboth the connectivity and the weights of the yielding node.It should be stressed that this step is crucial for the successof the algorithm, since it serves to retain well-working enti-ties, i.e., hidden nodes that show transition in appropriatepoints in the input space. In this sense, the approach showsfundamental similarities with the pruning approach out-lined in Subsec. 2.1. Next, the offspring are subjected tomutation, but only of the real coded weight values, follow-ing the procedures of ‘differential evolution’.17) The mu-tated version of any weight belonging to a population mem-ber, m, connecting an input j to a hidden node i was deter-mined as

wijmm�wij

m�l(wkij�wl

ij) ........................(3)

where the superscript m denotes the mutated version of theweight wij

m, the superscripts k and l refer to two randomlypicked weights from the network population, both connect-ing input j to hidden node i, while l is a user defined muta-tion constant. It should be noted that the probability of mu-tation must be kept high to allow novel weight combination

to emerge during the process.Two ‘children’ are produced as a result of a crossover op-

eration and the corresponding mutation, and are randomlyplaced in any unoccupied location in the lattice: This ‘mi-gration’ facilitates better mixing of the available gene pool.Predators are not allowed to evolve by any means and theirnumber is kept constant. The objective function is deter-mined for all the preys in the population, ranking them ac-cording to the Fonseca procedure,18) where the rank of anyindividual, n, is given by

ℜn�1�Qn ..................................(4)

where Qn denotes the number of individuals dominatingn.16) Prey members worse than rank 4 are removed aftereach ranking operation, since this was found to be highlyeffective in pruning a large number of superfluous solu-tions. Instead new randomly generated prey individuals areintroduced in the population, but to create an effectivesearch from dense to sparse networks (i.e., high to lowcomplexity, F2) hidden nodes were omitted in this randompopulation with a specified probability. Once the presetupper limit of the number of generations is reached, thenon-dominating set of rank 1 is accepted as the final Pareto-solution.

3. Database

The alloy composition and the TMCP parameters viz. theslab reheating temperature (SRT), deformation in differenttemperature zones, finish rolling temperature (FRT) andcooling rate (CR) have been taken as input parameters,whereas tensile strength (UTS), yield strength (YS) andpercentage elongation (%El) are designated as the outputvariables. Within the alloy chemistry, the concentrations ofelements like carbon, manganese, silicon, nickel, copper,molybdenum, niobium, chromium, titanium, and boron areconsidered. Deformation percentages given in three differ-ent temperature regions viz. region of recrystallization, re-gion of non-recrystallization and that of two-phase (g�a)region are denoted as D1, D2 and D3 respectively. The dataused for the present exercise have been mostly generated inthe laboratory. The chemical analyses are done in atomicspectrometer. Controlled rolling has been carried out in alaboratory scale rolling mill, and the mechanical testing hasbeen carried out in an INSTRON 4204 machine. Some datafrom the open literature19,20) has also been taken into con-sideration to cover a wider range of the variables and a totalof 120 data has been used. The variable bounds are detailedin Table 1.

MN

N�

�int prey prey

pred

�

ISIJ International, Vol. 47 (2007), No. 8

1197 © 2007 ISIJ

Fig. 2. Crossover scheme, where shaded regions participate.

4. Results and Discussion

4.1. Modeling with Pruning Algorithm

The pruning of the connections between the inputs andthe hidden nodes have been done for four cases; one withthree outputs taken together and the other three with thethree outputs used for separate ANN models. Figure 3(a)shows the mean square error (MSE) values with decreasingnumber of weights for 100 separate runs with different ini-tial weight matrices for the lower layer of the network hav-ing all the three steel properties as output. Fig. 3(b) showsan example of the model’s fit on the data using ten connec-tions, which was found to make reasonable prediction forthe three properties under consideration. It should be men-tioned here that the models’ fit improved appreciably, as ex-pected, when the steel properties are modeled separatelytaking one output at a time, but at the same time increasingthe total number of parameters.

The numbers of occurrences of the weights connecting a

particular input to any hidden nodes during the pruning op-eration are plotted as a bar diagram for all the four cases inFig. 4. As the connection to a hidden node for a particularinput during pruning depends on the relevance or impor-tance of that input in respect to the output, these numbersmay be treated as the relative importance of the inputs fordescribing the outputs. It also suggest the extent of nonlin-earity between the particular input and output, as a highernumber of connections for a particular input with the hid-den nodes means that a higher number of sigmoid functionare needed to describe the relation. Figures 4(a) and 4(b),which correspond to connection results for networks havingYS and UTS as outputs respectively, show that in bothcases almost all the inputs have certain importance exceptFRT. It is known that lowering the FRT below the recrystal-lization temperature increases the amount of dislocationand thus can affect the properties significantly, but in thepresent dataset the FRT is maintained sufficiently higher formost of the cases, and the network actually reveals this fact.The major factors influencing these kinds of steels are mi-crostructure (phase constituents) and the precipitation hard-ening. In case of possible precipitations, it is seen that car-bide forming microalloying elements have lesser role thanthat of Cu, particularly in the case of UTS. The copper pre-cipitates have been crucial for the strain hardening of thealloys. The microstructural constituents chiefly depend onthe post rolling cooling rate, and in both the cases it isfound to be the most important variable. It is interesting tonote that cooling rate is found to be the most importantvariable for the %El also (Fig. 4(c)), though it should benoted here that presence of harder phases play the oppositerole for the ductility of the steel. Here also copper is foundto have some role to play.

When all the outputs are taken together, similar observa-tions are found (Fig. 4(d)). In conclusion, it can be statedthat copper and the post rolling cooling rate are the mostimportant factors determining the mechanical properties ofsuch steel.

When the connections are being pruned to minimize er-rors, it is seen in all the four models that some inputs have apreference to be connected to a hidden node in combinationto some other particular inputs. This is natural since it is

ISIJ International, Vol. 47 (2007), No. 8

1198© 2007 ISIJ

Fig. 3. Typical results of the pruning algorithm, showing (a) the variation of MSE with the number of remaining connec-tions and (b) the target (solid lines) and predicted (dashed lines) outputs of a particular network.

Table 1. Minimum and maximum limits of the variables.

known that in this type of steel the alloying elements aswell as processing parameters have some combined effecton the properties in addition to their individual effects. Forexample, microalloy additions like Nb–B and Ti–B have asynergistic effect on the steel strength.21) Therefore, it wasdeemed worthwhile to study if the evolved combined con-nections in the models could yield some additional infor-mation. Table 2 shows a list of the highest numbers ofcombined connections that have occurred in all the fourmodels. It is seen that combinations like Ni–CR, Mo–CRand Cr–CR are present in all the cases. Elements like Ni, Crand Mo are known to have a role in determining the mi-crostructure and thus their combination with the coolingrate is also logical. These results also point out to the factthat microstructural constituents play an important role forthe final property of the steel. It is to be noted here that theother important parameter found through counting the num-ber of connections, i.e., Cu, has not occurred in combina-tion to other inputs in a single case. It is known that Cu pre-cipitation is increased if the dislocation density of the ma-trix is increased, which here depends mostly on the defor-mation in two phase region and the FRT. However, thedataset used for training in this particular work has alreadyrevealed that these variables do not have much importancefor the properties concerned (cf. Fig. 4), so these variablesmay not have much effect on the precipitation of Cu.

4.2. Modeling with Predator Prey Algorithm

As in the case of networks developed by the pruning al-gorithm, the Predator Prey algorithm was also used toevolve networks for four cases, one with three outputs takentogether and the other three with outputs used separately.Figure 5(a) shows the MSE values versus the number of

weights for 200 generations, illustrating the progressiveevolution of the Pareto front, and Fig. 5(b) shows an exam-ple on the model’s fit on the data using 20 connections. Inthis case also, the fit is found to be good enough for makingreasonable predictions. Here also the models’ fits improvewhen the properties are modeled separately, taking one out-put at a time.

In an analogous analysis to that carried out for the net-works created by the pruning approach, the occurrences ofthe weights connecting a particular input to any hiddennodes in the networks trained by the evolutionary approachwere studied. To increase the number of networks underconsideration and to make sure that good networks are notomitted, all the networks having 7 to 25 connections be-tween the inputs and the hidden nodes on the Pareto frontsafter 100, 150 and 200 generations were studied. The re-sults are illustrated in Fig. 6, which shows that in all thecases almost all the inputs have certain importance, asshown in.22) Here also it is seen that Cu and cooling ratehave a significant role to play. The figures also reveal someadditional information: The importance of Cu is found to

ISIJ International, Vol. 47 (2007), No. 8

1199 © 2007 ISIJ

Fig. 4. Number of connections of the individual inputs with the hidden nodes for pruned networks having (a) YS, (b)UTS, (c) %El and (d) all three variables as outputs.

Table 2. Preferred combinations of input connections in thehidden nodes.

be higher in the case of UTS than YS (cf. Figs. 6(a) and6(b)). This is logical since the presence of Cu precipitatesincreases the strain hardening and thus increases the UTSvalue. The role of Cr, Ni and Mo are almost similar in thissteel, and they all increase the hardenability of the steel, butit is seen that Mo is significantly more important than theothers for UTS. This may reflect a higher ability of Mo thanCr in carbide forming and resistance to grain coarsening inthis steel, which has a positive effect on the strain harden-ing. The role of SRT is found quite important in the case ofUTS, but not in the other cases. This could have reflectedthe dissolution of microalloy carbides, but in all cases theinsignificance of Ti, Nb and B does not lead to such justifi-cation. Clearly, this topic needs further study before conclu-

sive statements can be made.

4.3. Simulation Results

Another way, and perhaps the most common way of ex-tracting information about a system from its experimentaldata through neural networks, is to study the response ofthe trained networks. In our case, it is difficult to choose asingle network from so many reasonably good candidatesdeveloped through the pruning or the predator prey algo-rithms. For networks created by the pruning algorithm, asno training or adjustments of weight is being done in theclassical sense, we studied the effect of the hidden nodescarrying connections to more than one inputs to find the na-ture of consequence of the connected input variables on the

ISIJ International, Vol. 47 (2007), No. 8

1200© 2007 ISIJ

Fig. 5. Typical results of predator prey algorithm, showing (a) the progressive change in Pareto front with generations,and (b) target (solid lines) and predicted (dahed lines) outputs of a particular network.

Fig. 6. Number of connections of the individual inputs with the hidden nodes for networks in the Pareto front having (a)YS, (b) UTS, (c) %El and (d) all three variables as outputs.

final property of the steel. In these cases the signals gener-ated from the hidden nodes were taken as outputs to specifi-cally study the effect of the nodes. Figure 7 shows the re-sults for the combined effect of Ni and cooling rate, whichwas found to be quite significant for the predicted proper-ties of the steel (cf. Table 2). Figure 7(a) depicts the effectof those variables on YS and it is seen that both Ni and CRdelays yielding of the steel, with the effect of CR beingmarginally more significant than Ni. This also indicates thatthe presence of harder phases has more influence onstrength than solution hardening of ferrite. But when bothare increased simultaneously the effect reaches a plateau. Itsignifies that the YS cannot be increased beyond a certain

level by increasing Ni and CR, i.e. by modification of themicrostructure, if we generalize it to a certain extent. Thisphenomenon is more apparent in the case of UTS (Fig.7(b)), where already a minor increase in Ni leads to a satu-ration of the output of the hidden node. The ability of Ni tostabilize austenite to a certain extent and thus promotingharder low temperature transformation products of austen-ite may heavily influence the hardening of the softer phases.This will increase the UTS, but may be equally detrimentalfor the ductility of the steel.

In the direction of further studies on the variables, partic-ularly with those of more concern, the networks generatedthrough the predator prey technique have been further ana-

ISIJ International, Vol. 47 (2007), No. 8

1201 © 2007 ISIJ

Fig. 7. Effects of Ni and cooling rate on (a) YS and (b) UTS predicted by networks with pruned connectivity.

Fig. 8. Effects of Ni and Cu on (a) YS, (b) UTS and (c) %El predicted by networks developed by the predator prey algo-rithm.

lyzed. As stated earlier about the difficulties in choosingfrom so many good models, we preferred to be on the saferside and carried out the simulation study with a network ofcomparatively high (20) connections between the 16 inputsand 10 hidden nodes, chosen from the Pareto front gener-ated after 200 generations. In the foregoing studies, it wasfound that Cu and post-rolling cooling rate along with ele-ments like Ni, Mo and Cr were most important for decidingthe mechanical properties of this steel, so this study was fo-cused on the role of these variables with some other combi-nations. Figure 8 shows the effect of Cu and Ni on thethree properties of the steel. In the case of YS (Fig. 8(a)), itis seen that the role of Ni is a little bit higher than Cu, andboth have a positive effect. This can be true if a significantamount of Cu is precipitated, and Ni is utilized fully forsolid solution hardening. Another important feature re-vealed from the figure is that the effect of Cu is almost sat-urated after it reaches an amount of around 1.5 wt%. This isquite expected, as this amount of Cu gives highest precipi-tation hardening effect.23) For YS, the effects of microstruc-tural features still dominate over those of precipitates. Inthe case of UTS (Fig. 8(b)), the situation is reversed. Here itis seen that the effect of Cu is significantly higher than thatof Ni, as strain hardening due to presence of precipitatesdominates. Still, both have a significant negative effect onductility individually as well as in combination (Fig. 8(c)).The effect of Ni in solid solution hardening and assisting todevelop harder phases makes the microstructure to be con-

sisting of Cu precipitates in hard matrix. This effect de-creases the dislocation mobility and thus the ductility dete-riorates.

Finally, the effect of the cooling rate on the properties ofthe steel along with the amount of carbon was studied (Fig.9). The interstitial elements, particularly C, have a majorrole to play in determining the phase constituents in thefinal microstructure at varying cooling rate. It is seen thatYS increases with an increase in the cooling rate, and theincrease in YS is further enhanced with higher C content(Fig. 9(a)), as this situation promotes higher amount of lowtemperature phases. In the case of UTS the effect of coolingis not so prominent after it reaches a certain rate (Fig. 9(b)).This again points out that microstructure is not the majorcriterion in the case of UTS. Figure 9(c) shows the effect ofC and CR on the %El, and as expected, the ductility of thesteel decreases with increased CR.

5. Conclusion

The studies presented in this paper converge in somegeneral findings. It is seen that in this type of steel YS de-pends mostly on the solid solution hardening and the mi-crostructural constituents. On the other hand, UTS is moreinfluenced by the precipitation hardening, but all thesestrengthening mechanisms have a negative effect on theductility of the steel. These factors in general and the roleof individual variables in particular, could easily be used to

ISIJ International, Vol. 47 (2007), No. 8

1202© 2007 ISIJ

Fig. 9. Effects of C and cooling rate on (a) YS, (b) UTS and (c) %El predicted by networks developed by predator preyalgorithm.

control the strength–ductility ratio and even the yield-ten-sile ratio of the steel. It may be noted here that the effect ofmicroalloy carbide precipitates are not seen in this steel.Though it is not entirely fair to make any statement in thisregard, it should be mentioned here that some further inves-tigations are needed to find out the effect of these precipi-tates on the properties, particularly on the ductility of thesteel. Another important factor that was not considered inthis study is grain refinement. Indeed, the SRT, amount ofdeformation, Ti and some other factors determine the grainsize of this steel, but it is found to be difficult to make anycomment in this regard from the results.

The authors wish to conclude that the pruning and preda-tor prey algorithms applied in this study have been demon-strated to be able to extract more knowledge from the data,which is difficult to reveal by conventional ANN analysis.In this work the relative relevance of the composition andTMCP parameters have been detected in a way that it couldbe used for designing steel with tailored property balance.Furthermore, the results of the two techniques are found tobe comparable and also commensurate the fundamentalprinciples of physical metallurgy. These techniques are def-initely suitable for mining knowledge from the experimen-tal data of materials systems.

REFERENCES

1) A. J. DeArdo: HSLA Steels: Processing, Properties and Applica-tions, ed. by G. Tither and Z. Shouhua, The Minerals, Metals & Ma-terials Society, Warrendale, PA, (1992).

2) S. Datta and M. K. Banerjee: Scand. J. Metall., 33 (2004), 310.3) S. Datta and M. K. Banerjee: Mater. Sci. Eng. A, A420 (2006), 254.4) Z. Y. Liu, W.-D. Wang and W. Gao: J. Mater. Process. Technol., 57

(1996), 332.

5) H. K. D. H. Bhadeshia: ISIJ Int., 39 (1999), 966.6) J. C. Principe, N. R. Euliano and W. C. Lefebvre: Neural and Adap-

tive Systems: Fundamentals through Simulations, John Wiley &Sons, New York, (1999).

7) G. Thimm and E. Fiesler: Int. Symp. on Artificial Neural Network(ISANN ’95), Taiwan, ROC, (1995), A2-20-25.

8) H. Saxén and F. Pettersson: Comp. Chem. Eng., 30 (2006), 1038.9) X. Li: 2nd Int. Conf. on Evolutionary Multi-Criterion Optimization,

Lecture Notes in Computer Science, LNCS 2632, ed. by C. M. Fon-seca, P. J. Fleming, E. Zitzler, K. Deb and L. Thiele, (2003), 207.

10) F. Pettersson, N. Chakraborti and H. Saxén: Appl. Soft Comput., 7(2007), 387.

11) I. N. Egorov-Yegorov and G. S. Dulikravich: Mater. Manuf. Process.,20 (2005), 569.

12) M. Mahfouf, M. Jamei and D. A. Linkens: Mater. Manuf. Process.,20 (2005), 553.

13) S. Ganguly, S. Datta and N. Chakraborti: Mater. Manuf. Process., 22(2007), 650.

14) J. Hinnelä, H. Saxén and F. Pettersson: Ind. Eng. Chem. Res., 42,(2003), 2314.

15) K. Deb: Multi-objective Optimization Using Evolutionary Algo-rithms, John-Wiley, Chichester, (2001).

16) C. A. Coello Coello, D. A. Van Veldhuizen and G. B. Lamont: Evo-lutionary Algorithms for Solving Multi-objective Problems, KluwerAcademic Publishers, New York, (2002).

17) K. Price and R. Storn: Dr Dobbs J., 22 (1997), 18.18) C. M. Fonseca: PhD thesis, Department of Automatic Control and

Systems Engineering, University of Sheffield, Sheffield, UK, (1995).19) L. Meyer, C. Straßburger and C. Schneider: Proc. of Int. Conf. on

HSLA Steels, Beijing, China, ASM Int., DH, USA, (1985), 29.20) M. K. Banerjee, P. S. Banerjee and S. Datta: ISIJ Int., 41 (2001),

257.21) H. Tamehiro, M. Murata, R. Habu and M. Nagumo: Trans. Iron Steel

Inst. Jpn., 27 (1987), 120.22) M. Helle, F. Pettersson, N. Chakraborti and H. Saxén: Steel Res. Int.,

77 (2006), 75.23) S. Datta, P. S. Banerjee and M. K. Banerjee: Ironmaking

Steelmaking, 31 (2004), 312.

ISIJ International, Vol. 47 (2007), No. 8

1203 © 2007 ISIJ