Genetic Algorithm (GA) as Optimization Technique

Genetic Algorithm (GA) as Optimization TechniquePreference knowledge (or preference elicitation) is a critical job in m both scientific fields, such as decision theory 1,2, economics 3,4, logistic ref and database 5. When modeling user preference, researchers oft model the preferences as a solution to an optimization problem which maximizes some utility function. In reality, however, we are non a-priori given a utility but give only access to a finite historical user choice data. Therefore, the passive preference learning problem, that is, how to learn user preferences using her historical choice data, has gained a lot of attention in novel years.When dealing with preference learning, it is often assumed that user preference over the values of each evaluate is independent of the values of other attributes. However, this assumption is not a sound in many world scenarios. For example, as it is shown in Fig. 1 for cloth shopping problem, one might choose the color of her place depending on the color of dress she will buy, i.e. her preference over shoes color is conditioned by the available dresses. More formally, we say the preferences induced by the users behavior are intrinsically related to textitconditional preferential independence, a key notion in multi-attribute decision theory20.Conditional preference networks (CP-nets) have been proposed for such problems 4 and have received a great deal of attention due to the compact and natural representation of ordinal preferences in multi-attribute domains 8-12, 17-19,22. Briefly, a CP-net, fig. 1, is a digraph, whose nodes correspond to alternative attributes and edges correspond to the dependency between nodes and each node is annotated with a conditional preference table which describe the preferences over that particular attribute (chapter 3).It is sometimes claimed that CP-nets are easy to elicit 16. That is, we first explain CP-nets to the user, and then ask her to write down the CP-net that best descr ibes her decision-making process 18,30. However, it has been shown that when facing the choices, people often act differently from what they described previously as their preferences 39,40,97,103. As an example, Kamishima and Akaho 53 point out that when customers were asked to rank ten sushi items and then later to assign rating rack up to the same items, in 68% of the cases, the ordering implied by the ratings did not agree with the ranking elicited directly only minutes before. Based on these experiments, several(prenominal) CP-net learning algorithms have been developed depend on the users choice data. Some algorithms work on the historical choice data 23,64, a process cognize as passive learning. Others actively offer solutions in an attempt to learn the users preferences as they choose 23,29,47,58. The work of this paper falls into the category of passive learning, in which the learner uses the recorded users choices and then fits a CP-net model to the observed data. Formall y, we collect the set of samples $S = o_i succ o_i$, where $o_i succ o_i$ means that the user strictly prefers core $o_i$ over case $o_i$ and then find a model $N$ that can best describe $S$. Such set of samples may be ga on that pointd, for instance, by observant online users choices.Table1 shows the number of binary CP-nets up to 7 nodes, i.e. each outcome consists of 7 attributes A250110. From the values, it is evident that, even for a small number of attributes, finding the best CP-net is not a trivial task due to the huge size of the search space. textbfinja np-completo begoo. To the best of our knowledge, there is no existing approach that can perform headspring on problem with more than 7 attributes hence they are not practical when facing real world problems, in which the alternatives usually consist of tens or even hundreds of attributes.Another problem that rises when learning preferences from human subjects is the possibility of noise or comparison data that are ultima tely inconsistent in the chose data-set $S$. While noise is results of the observation of the users behavior, inconsistency is the result of randomicity of the users behaviors that is, the transitive closure of data-set may result in a cycle in which some outcome $o$ is seen to be preferred to itself. The objective of most CP-net learning techniques is to learn (i.e. rebuild) a CP-net that can describe the whole data-setref. However, since the $S$ is not usually clean, there is no possibility of finding such a CP-net, that is consistent with every example in $S$. This fact motivated us to frame the CP-net learning problem as an optimization problem that is, to identify a model that maximizes some objective function, $f$, with respect to choice data-set.In this work, we utilized the role of Genetic Algorithm (GA) as an optimization technique. GA is an optimization algorithm inspired from the mechanism of natural selection and natural genetics, which can work without any a-priori kno wledge about the problem domain and have received a growing interest in solving the complex combinatorial optimization problems oddly for their scalability as compared with the deterministic algorithms 1. In this work, we investigate the feasibility of implementing the GA to solve the passive CP-net learning problem.