Objective Function Designing Led by User Preferences Acquisition

Transcription

1 Objective Function Designing Led by User Preerences Acquisition Patrick Taillandier and Julien Gauri Abstract Many real world problems can be deined as optimisation problems in which the aim is to maximise an ective unction. The quality o obtained solution is directly linked to the pertinence o the used ective unction. However, designing such unction, which has to translate the user needs, is usually astidious. In this paper, a method to help user ective unctions designing is proposed. Our approach, which is highly interactive, is based on man-machine dialogue and more particularly on the comparison o problem instance solutions by the user. We propose an experiment in the domain o cartographic generalisation that shows promising results. Index Terms user needs deinition, ective unction designing, man-machine dialogue, cartographic generalisation. I. INTRODUCTION Artiicial systems are more eective than humans to solve many problems. One o the reasons is their computing capacity that allows them to tests many possibilities in a short period o time. However, in order to get good results, an artiicial system has to know what it is searching, i.e. what type o solutions is expected. Unortunately, while human experts can easily give a qualitative evaluation o the quality o a problem solution or order several solutions in terms o quality, it is oten ar more diicult or them to express their expectations in a ormal way that can be used by artiicial systems. This problem is particularly complex when numerous measures are used to characterise a solution and when no simple links can be ound between these measures values and the solution quality. This paper deals with the problem o the ormalisation o the user outcome expectation rom the system, into a orm usable by artiicial systems. In this context, we propose an approach aiming at translating the user needs into an ective unction thanks to dialogue between the user and the system. In Section 2, the general context o our work is introduced. Section 3 is devoted to the presentation o our approach. Section 4 describes an application o our approach to cartographic generalisation. We present a real case study that we carried out P. Taillandier is with the UMI UMMISCO o IRD, 209, 32 avenue Henri Varagnat,9343 Bondy, France and with the UMI 209 o IFI, MSI, ngo 42 Ta Quang Buu, Ha Noi, Viet Nam ( patrick.taillandier@gmail.com. J. Gauri is with the COGIT lab o IGN, 73 avenue De Paris, 9465 Saint-Mandé, France ( julien.gauri@ign.r. as well as its results. Section 5 concludes and presents the perspectives o this work. II. CONTEXT A. Optimisation problem and ective unction Many real world problems can be expressed as optimisation problems. Solving such a problem consists in inding, among all possible solutions o the problems, the one that maximises an ective unction. This unction characterises the quality o a solution. Its deinition is a key point o the resolution o optimisation problems [9]-[20]. Indeed, the goal o the resolution o an optimisation problem is to ind the solution that maximises (or minimises this unction. Thus, i the ective unction is not in adequacy with the real quality o a solution, the solutions that will be ound will never be good. Many works were interested in the deinition o such unction or speciic problems [4]-[2] but ew proposed general approach or helping the user o an optimisation system to deine it. B. Related Works The problem o ective unction deinition and more generally o user need deinition is a complex problem which was studied in various ields. A irst approach to solve this problem is to use supervised machine learning techniques. These techniques consist in inducing a general model rom examples labeled by a user/expert. In this context, it is possible to learn an ective unction rom examples evaluated by a user. This approach was used in several works. For example, [2] used this approach in the domain o computer vision, [6], in the learning o cognitive radio. A second approach consists in establishing a man-machine dialogue to converge toward a ormalisation o the user needs. Reerence [5] proposes to use such approach in order to help users to create original map legends. This work proposed to use map samples to establish a dialogue between the user and the system. This dialogue allows the system to retrieve the user preerences, and thus to design a suitable legend that respects the user expectations as well as cartographic constraints (to ensure the map readability. In the same way, [3] proposes to use map samples to capture user needs in terms o geographic inormation. Our work is taking place in the continuity o these two works. We propose to use the same approach based on a dialogue between the user and the system established through the presentation o samples. ICITA 2009 ISBN:

2 A. General approach III. PROPOSED APPROACH As stated in the introduction, i experts oten have diiculties to express in a ormal way their needs rom a system, it is ar easier or them to compare dierent solutions o a problem and to point out their preerences. Thus, we propose to base our user need deinition approach on the presentation o comparisons between solutions to the user. Each comparison is composed o two solutions or a same problem instance. The user can give his preerences toward these two solutions to the system, i.e. the solution that he preers i there is one. The system then automatically build the evaluation unction rom the whole set o preerences. Our general approach, presented Figure, is composed o 3 steps: the irst one consists in generating a set o pairs o solutions to compare (called comparisons set ; the second one consists in capturing the user preerences by asking the user to select its avourite solution or each comparison; the last step consists in using these captured preerences to automatically build the ective unction that will represent the user expectations toward the optimisation system. C. Capture o the user preerences The second step o our approach consists in capturing the user preerences. Figure 2 presents our approach: at each iteration, a comparison is selected between all available ones (the comparison set. Then, the user deines its preerences, i.e. between the two solutions, the one that he inds better. The user can also deine that the two solutions are as good or as bad. This sequence is reiterated until an ending criterion is checked. An example o ending criterion can be to stop the cycle when a speciic number o comparisons have been presented to the user. Fig. 2. User preerence capture approach The main question o this step concerns the choice o a comparison to propose to the user at each iteration. How to choose that comparison? To guide this choice, we propose to use comparison choice strategies: a comparison choice strategy allows the choice o the next comparison among a set o comparisons according to a speciic strategy. Fig.. General approach In the ollowing sections, we described each o these three steps. B. Initialisation o the comparison set The irst step o our approach consists in generating a set o comparisons that will be used to capture the user needs. We deined a comparison as a set o two solutions or a same problem instance. The generation o the comparison set depends on the context o use o our approach. For example, in the case where a set o instances o the considered problem is available and where this set is too big to take into account all available instances, a sampling method has to be used in order to select a subset o problem instances. The subset has to be representative o the whole set in order to capture more pertinently the user preerences in a generic ective unction. Each selected instance has to be solved in order to obtain at least two solutions or it. For each couple o solutions, a comparison is created and is added to the comparison set. In this paper, we propose our dierent comparison choice strategies: Measure consistency analysis: this strategy consists in choosing a comparison where the two solutions are equivalent in terms o measure values. The goal is to analyse the consistency o the measure set. I the user preers one o the two solutions whereas they are equivalent in terms o measure values, it means that the measure set is not pertinent and does not allow to well-characterised the solution quality. Measure evolution analysis: this strategy consists in choosing a comparison where the value o only one measure changes between the two solutions. The goal is to analyse how the quality o a solution evolves according to the evolution o the value o this measure. Order o preerence between two measures: this strategy consists in choosing a comparison where the values o only two measures change between the two solutions. The goal is to compare the relative importance o each measure or the computation o the solution quality. Random comparison: this strategy consists in choosing randomly a comparison in the comparison set. In order to deine a global strategy o user preerence capture,

3 we propose to chain dierent comparison choice strategies. Indeed, in a irst step, we propose to apply the measure consistency analysis strategy in order to check the pertinence o the measure set. I this one is not pertinent, the ective unction obtained at the end o the user need deinition process will certainly not be perect. Then, in a second step, we propose to apply the measure evolution analysis strategy or each measure. This step allows a better understanding o the link existing between the evolution o a measure and the evolution o the solution quality. The third step consists in applying the order o preerence between two measures strategy to compare by couple the relative importance o each measure. In the last step, we propose to apply he random comparison strategy. D. Deinition o the ective unction The last step o our approach consists in designing an ective unction rom the user preerences. We propose to ormulate the ective unction as a set o regression rules. Each regression rule is associated to a weighted means. The interest o such representation is to be easily interpretable by domain experts and thus to acilitate the ective unction validation. Let M be the set o measures, w i the weight associated to the measure i and Val i (sol, the value o the measure i or the solution sol belonging to the whole possible solution set SOL. We deine the measures o M such as: sol SOL, i M, VAL _ MIN vali ( sol VAL _ MAX with VAL_MIN and VAL_MAX real. Each regression rule is deined as ollows: i condition then quality( sol = wi Vali ( sol w i i M i M An Example o ective unction is presented in Section IV.E.3. Building an ective unction consists in inding a set o regression rules (with, or each o them, a condition and the weight values rom the preerences given by the users on the samples. As presented Figure 3, to solve this problem, we propose to use an approach based on the search o the best weights and eventually on the partitioning o the measures set (which correspond to the addition o new regression rules. At the initial stage, the ective unction is composed o only one regression rule, such as the measure space is composed o only one partition. At the irst step, the system searches a weight assignment that maximises the adequacy between the ective unction and the user preerences. I this weight assignment is in total adequacy with the user preerences, the process ends; the ective unction is composed o only one regression rule. Otherwise, new regression rules are introduced: the system computes partitions o the measure set in order to detect the parts o the measure set that are not compatible with the others. Then, a new weight assignment is searched again or all regression rules, by considering all partitions built at the same time. I the weight assignment obtained ater the partitioning allows to get a better result than the previous one, it is kept; otherwise, the system backtracks to the previous ective unction and end the evaluation unction building process. This partitioning procedure is recursively repeated until the learnt ective unction allows to obtain the given user preerences or until no more improvement o the ective unction is obtained. Fig. 3. Approach o evaluation unction building Search o the best weight assignment We propose to ormulate the problem o best weight assignment as a minimisation problem. We deine a global error unction that represents the inadequacy between the evaluation unction (and thus the weight assignment and the user preerences. The goal o the best weight assignment search is to ind the weights that allow to minimise the global error unction. Let (sol be the current ective unction that evaluates the quality o a solution sol. Let c sol,sol2 be a comparison between two solutions, sol and sol 2. Let p c be the user preerence or the comparison c. p c can be either {sol } (the user preers the solution sol, {sol 2 } (the user preers the solution sol 2 or {sol, sol 2 } (the two solutions have the same quality or the user. We deine the unction comp(, p c that determines or a comparison c i the user preerence p c is compatible with the ective unction, i.e. i the preerence ormulated by the user is consistent with the quality order obtained by applying the ective unction on the solutions. I the user preerence p c is compatible with the ective unction or the comparison comp(, p c is equal to 0; otherwise it is equal to. pc = { sol, sol2} and ( sol = ( sol2 0 i or pc = { sol} and ( sol > ( sol2 { } or pc = sol2 and ( sol2 > ( sol comp(, pc = otherwise

4 We deine the unction error(, p c that returns the error value or a comparison c. This unction is deined as: error(, pc = val error + 0 ( sol ( sol i i comp( comp( 2 c, p = 0 c, p = In this unction, we integrated a parameter val error that represents the minimum importance o an error whatever the values o the ective unction or the two solutions are. The higher the value o this parameter, the more important it will be to minimise the number o incompatible comparisons. Finally, the global error unction proposed corresponds to the mean error obtained with the ective unction on the comparison sample Comp: Error (, Comp = error(, pc Comp c Comp The aims o the weight assignment step is to ind a weight assignment that minimises Error(, Comp. The size o the search space will be most o time too high to carry out a complete search. Thus, it will be necessary to proceed by incomplete search. In this context, we propose to use a metaheuristic to ind the best weight assignment. In the literature, numerous metaheuristics were introduced [8]-[]-[5]. In this paper, we propose to use genetic algorithms [2] which are particularly eective when the search space is well-structured as it is in our search problem. 2 Partitioning o the measure space For some user need deinition problems, it will not be possible to ind a weight assignment compatible with all user preerences. Thus, we propose to partition the measure set space and to deine or each partition a regression rule with its own weight assignment. We propose to base our partitioning method on the utilisation o supervised learning techniques. The goal is to search the parts o the measure space that have a dierent behaviour in terms o ective unction. Thus, we search to detect the parts o the measure space which contain solutions linked to an incompatible comparison. We built an example set composed o solutions described by its measures values. The conclusion could be either compatible i the comparison which contains the solution is compatible with the ective unction or incompatible i it is not. Then, a supervised learning algorithm is used to partition the measure space. We remind that we proposed to express the partition in the orm o rules. Thus, it is necessary to use a supervised learning algorithm that allows to build a predictive model expressed by rules. Dierent algorithms could be used or this partitioning problem such as RIDOR [0] or C4.5 algorithm [6]. In this paper, we propose to use the eective and well-established RIPPER algorithm [7]. Figure 4 presents an example o partitioning or a measure set composed o two measures. Fig. 4. Partitioning method Once the partitioning is carried out, the user need deinition module perorms a new search o the best weights assignment. All partitions are considered at the same time or this search. I the weights assignment ound is better (in terms o minimisation o the global error value than the assignment obtained beore the partitioning, the new ective unction is kept. Otherwise, the module keeps the previously obtained ective unction. IV. APPLICATION TO CARTOGRAPHIC GENERALISATION A. Automatic cartographic generalisation We propose to test our ective unction designing approach in the domain o cartographic generalisation. Cartographic generalisation is the process that aims at simpliying geographic data to suit the scale and purpose o a map. The ective o this process is to ensure the readability o the map while keeping the essential inormation o the initial data. Figure 5 gives an example o cartographic generalisation. Fig. 5. Cartographic Generalisation The automation o the generalisation process is an interesting industrial application context which is ar rom being solved. Moreover, it directly interests the mapping agencies that wish to improve their map production lines. At last, the multiplication o web sites allowing creating one s own map increases the needs o reliable and eective automatic generalisation processes. One classical approach to automate the generalisation process is to use a local, step-by-step and knowledge-based method [4]: each vector ect o the database (representing a building, a road segment, etc. is transormed by application o a sequence o generalisation algorithms realising atomic transormations. The choice o the applied sequence algorithms is not predetermined but built on the ly or each ect according to heuristics and to its characteristics.

5 B. The generalisation system The generalisation system that we use or our experiment is based on the AGENT model [3]-[7]. The AGENT model has been urther described in [8]. In this model, geographic ects (roads, buildings, etc are modelled as agents. Geographic agents manage their own generalisation, choosing and applying generalisation operations to themselves. Each state o the agent represents the geometric state o the considered geographic ects. During its generalisation process, each agent is guided by a set o constraints that represents the speciications o the desired cartographic product. An example o constraint is, or a building agent, to be big enough to be readable. Each constraint has a satisaction level between 0 (constraint not satisy at all and 00 (constraint perectly satisy. For each state, the agent computes its own satisaction according to the values o its constraint satisaction. To satisy its constraints as well as possible, a geographical agent carries out a cycle o actions during which it tests dierent actions in order to reach a perect state (where all o its constraints are perectly satisied or at least the best possible state. The action cycle results in an inormed exploration o a state tree. Each state represents the geometric state o the considered geographic ects. Figure 6 gives an example o a state tree obtained with the generalisation system. Fig. 6. Example o a state tree or the generalisation o a building C. Diiculties o the agent satisaction unction deinition The AGENT model has been the core o numerous research works and is used or map production in several mapping agencies. However, the question o the evaluation o the state o an agent is still asked. The unction usually used is a mean o the constraint satisaction weighted by their importance (which is oten an integer ranged between and 0. The problem o this unction is to give satisaction values too homogenous. More over, it does not allow to take into account discontinuities in the satisaction unction. At last, the deinition o the importance values is oten complex and astidious when more than ive constraints are in stake [2]. Thus, having an approach like the one described in this paper allowing to design the agent satisaction unction is particularly interesting in the context o the AGENT model. D. Implementation o our approach or the AGENT model We experiment our approach on an implementation o our user need deinition module in Java, using GéOxygene [2] or geographical data transormation, and WEKA [22] or the partitioning part using RIPPER algorithm. Figure 7 presents our implemented interace. On the top panel, the initial state or a building is presented to the user, with, under, the two possible solutions. The user gives its preerence or this sample. E. Case study Fig. 7. Implemented graphic interace Setting o the case study We propose to apply our user need deinition approach or the learning o the satisaction unction o the generalisation o building agents or :25000 scaled maps. We deined six constraints or the building agents: Size constraint: the building shape should be big enough. Let S sz be the value o this constraint satisaction. Granularity constraint: the building shape should not contain too small details. Let S gr be the value o this constraint satisaction. Squareness constraint: the angles o the building that are nearly square should be square. Let S sq be the value o this constraint satisaction. Convexity constraint: the convexity o the building should be preserved. Let S cv be the value o this constraint satisaction Elongation constraint: the elongation o the building should be preserved. Let S el be the value o this constraint satisaction Orientation constraint: the orientation o the building should be preserved. Let S or be the value o this constraint satisaction 2 Experiment protocol 50 comparisons (the learning set were presented to a generalisation expert to learn an ective unction. Then, we tested the learnt ective unction on 50 new comparisons (the test set which were selected in a new area and or which the

6 expert expressed its preerences. The value used or val error (c. Section III.D. is 40. This value is high enough to limit the number o incompatible comparisons and, at the same time, not too high in order to take into account the dierence o values o the ective unction value in case o errors. Thus, in our application context, the value o the global error is ranged between 0 and Results The learnt ective unction (with S, the satisaction o the building agent is the ollowing: i ( Scv < 83 S = 6 Scv + 2 Sel + 9 Ssq + 2 Sgr + 2 Sor + 7 Ssz 28 i (83 Scv < 93 S = ( 7 Scv + 7 Sel + Ssq + 7 S gr + 6 Ssz 28 i ( Scv > 93 S = ( 9 Scv + 9 Sel + 3 Ssq + 2 S gr + 7 Ssz 30 ( Table presents the results obtained on the two comparison sets. The learnt ective unction allowed to get, or both comparison sets, a global error value lower than 5 and a number o incompatible comparisons equals to 5. Nb o incompatible comparisons Global error Learning set Test set Table. Results o the learnt ective unction on the learning set and on the test set. These results show that our approach allowed to learn a pertinent ective unction. Indeed, the results obtained by the learnt unction are both good on the learning set and on the test set. For both comparison sets, the global error value is very low and only 5 o the 50 comparisons are incompatible. Among these incompatible comparisons, several can be explained by the lack o pertinent measures used to describe the generalisation results. Indeed, the Measure consistency analysis comparison choice strategy allowed us to detect that, or some comparisons, two states can be identical in terms o constraint satisactions but dierent in terms o generalisation quality. V. CONCLUSION In this paper, we presented an approach dedicated to the deinition o user needs. Thus, we proposed an approach based on a man-machine dialogue aiming at deining an ective unction representing the user expectations toward an optimisation system. An experiment, carried out in the domain o cartographic generalisation, showed that our approach can help users to ormalise their needs and can allow to detect lacks o pertinent measures. Our approach is based on the utilisation o comparison choosing strategies. In this paper, we deined our dierent strategies. Other strategies, more complex, could be proposed, such as strategies that take more into account the preerences initially ormalised by the user. Concerning the exploration part as well as the partitioning part, we just tested one search algorithm and one supervised learning algorithm. An interesting study could be to test others algorithms and to compare the results with the ones obtained. A last perspective could be to pass rom an acquisition problem to a revision problem. 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