An affective learning agent with Petri-net-based implementation

Abstract

Traditional interactive evolutionary computing approaches are usually susceptible to limited searching ability and human’s strong subjectivity. In response, by extending a traditional Belief-Desire-Intention (BDI) structure, a kind of affective learning agent which can perform affective computing and learning activities in human-computer interaction environment is explicitly introduced. In solving human-computer interactive multi-objective decision-making problems whose objectives are usually far from well structured and quantified, this kind of agent may help reduce human’s subjective fatigue as well as make decisions more objective and scientific. Specifically, a conceptual model of the agent, affective learning-BDI (AL-BDI) agent, is proposed initially, along with corresponding functional modules to learn human’s affective preference. After that, a kind of high level Petri nets, colored Petri nets are employed to realize the components and scheduler of the AL-BDI agents. To exemplify applications of the approaches, test functions are suggested to case studies, giving rise to satisfied results and showing validity of the contribution.

Appendix: Complexity analysis of the affective learning algorithms

As a technique of computer science, algorithm’s complexity analysis is typically concerned with time and space complexity which is meant to measure the costs of the algorithm in terms of time and space. In this sense, we briefly present the complexity analysis of the affective learning algorithms as follows.

Time complexity analysis

To facilitate the discussion, initially, we specify some related parameters associated with the algorithms as follows. t denotes the number of human-computer affective interactions; p(t) is the population of tth generation; m is the population size; q is the length of chromosome; p _c is the crossover rate; p _m is the mutation rate; f is the human’s expectation value. Additionally, some parameters are involved in the preferential minimization problem solved by genetic algorithms as well, in which, n is the evolution number; p′(n) is the population of nth generation; k is the population size; l is the length of chromosome; $p_{c}'$ is the crossover rate; $p_{m}'$ is the mutation rate; f′ is the human’s expectation values. Thus, The basic statements involved in the algorithms can be summarized as follows.

Initialize (p _c ,p _m ,t,f);

// initializing parameters of the interactive evolutionary computing algorithm (i.e. crossover rate, mutation rate etc.)

{t=0;

(1) :

initialize p(t); // initiating population randomly;

(2) :

calculate the multi-objective fitness index of the initial chromosome group;

(3) :

for (j=1; j<t+1; j++)

// when the fitness index of the highest chromosome fitness value is less than that of human’s expectations, doing follows;

{

(4) :

select the excellent individuals; //selection operations;

(5) :

crossover of p(t); //crossover operations;

(6) :

mutation of p(t); //mutation operations;

(7) :

achieve chromosome groups, Q (t+1), of the next generation;

// calculating chromosome groups’ multi-objective fitness index of the next generation;

(8) :

according to affective computing metrics, calculate agent’s affective preferences corresponding to each individual;

(9) :

present human’s preferences of each individual by interactions;

//next, solving the minimization problem in terms of the preferential deviation between agents and human:

{

(10) :

initialize ($p_{c}',p_{m}',n,f'$);

// initializing parameters of the genetic algorithm (i.e. crossover rate, mutation rate etc.)

(11) :

initialize p′(n); // initiating population of A, X randomly;

(12) :

calculate fitness index;

(13) :

for (i=1; i<n+1; i++); // when the highest fitness index is still less than the expected one, doing follows;

{

(14) :

selection of p′(n); // selection operations;

(15) :

crossover of p′(n); // crossover operations;

(16) :

mutation of p′(n); // mutation operations;

(17) :

achieve next generation of chromosome groups, Q (n+1); //calculating the chromosome groups’ fitness index of the next generation;

}

(18) :

update the optimized affective computing model parameters A, X;

}

}

}

(19) :

achieve the average multi-objective fitness of the current chromosome groups.

It is obviously that the basic statement which has the most execution time in the algorithm is usually in the innermost loop of the loop body. Taking account of statements (3)–(12) and (13)–(17) forming nested loops, the time complexity of the algorithms is eventually characterized by: T ₁(n)+T ₂(n)+T ₃(n)∗{T ₄(n)+⋯T ₁₂(n)+T ₁₃(n)∗[T ₁₄(n)+T ₁₇(n)]+T ₁₈(n)}+T ₁₉(n)=O[t×((m×q)+n×(k×l))], where, O marks the time performance.

Space complexity analysis

Space complexity is concerned with the required storage space where the algorithms execute in computers. In addition, a general discussion can be conducted on auxiliary storage unit space besides the normal memory overhead. In this sense, the affective learning algorithm’s space complexity could refer to the two nested initial chromosomes’ occupant space. Furthermore, other operations are conducted on the spot. As a result, the affective learning algorithm‘s space complexity is presented as O(m×q+k×l).