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3.PROPOSED ALGORITHM
The proposed dynamic evolutionary algorithm exploits evolutionary progress history to adapt the current population to the new environment.The algorithm introduces shifts in the decision space,the so-called relocations,which try to account for the estimated amount of change in the objective space.A complete description of the proposed algorithm is presented in detail next.represents the DOP we want to optimize; represents the -dimensional decision vector,and denotes the th-dimension decision variable.A nomenclature table is given in Appendix A for quick reference.For the discussion of this paper,the DOP is assumed to be a maximization problem.Note that a minimization problem can be converted into a maximization problem by multiplying with .denotes the child’s evolutionary progress in the th-dimension of the decision variable with respect to its parents.It is measured as the difference between the th-dimension decision variable of a child and that of the centroid of its parents.This can be mathematically expressed as (2) The evolutionary fitness progress,,of a child with respect to its parents is measured as the difference between the fitness,,of a child and the interpolated fitness of its parents.The interpolation is based on the distance between a child and its parents .The farther a parent is from its child,the lesser is its contribution to the interpolated fitness,as shown in (3a)–(4) at the bottom of the page.The average evolutionary progress in the th-dimension decision variable of a child can be obtained as the weighted sum of the child’s and the average evolutionary progress in the th-dimension decision variable of its parents.The same is true for the child’s average evolutionary fitness progress ,except that we use the interpolated value of its parents’ average fitness progress,as shown in (5) and (6) at the bottom of the next page,where denotes the total number of generations either from the start of an evolutionary process or the last occurrence of change,whichever was more recent,up to the current generation.On the other hand,represents the weight given to previous evolutionary progresses relative to the current one.Using ,the weighted average is equivalent to taking a simple average of all the individual progresses (total sum divided by number of generation).This means that the effect of all the previous and values starting from the recent occurrence of change is accumulated and does not diminish through time.
3.PROPOSED ALGORITHM
The proposed dynamic evolutionary algorithm exploits evolutionary progress history to adapt the current population to the new environment.The algorithm introduces shifts in the decision space,the so-called relocations,which try to account for the estimated amount of change in the objective space.A complete description of the proposed algorithm is presented in detail next.represents the DOP we want to optimize; represents the -dimensional decision vector,and denotes the th-dimension decision variable.A nomenclature table is given in Appendix A for quick reference.For the discussion of this paper,the DOP is assumed to be a maximization problem.Note that a minimization problem can be converted into a maximization problem by multiplying with .denotes the child’s evolutionary progress in the th-dimension of the decision variable with respect to its parents.It is measured as the difference between the th-dimension decision variable of a child and that of the centroid of its parents.This can be mathematically expressed as (2) The evolutionary fitness progress,,of a child with respect to its parents is measured as the difference between the fitness,,of a child and the interpolated fitness of its parents.The interpolation is based on the distance between a child and its parents .The farther a parent is from its child,the lesser is its contribution to the interpolated fitness,as shown in (3a)–(4) at the bottom of the page.The average evolutionary progress in the th-dimension decision variable of a child can be obtained as the weighted sum of the child’s and the average evolutionary progress in the th-dimension decision variable of its parents.The same is true for the child’s average evolutionary fitness progress ,except that we use the interpolated value of its parents’ average fitness progress,as shown in (5) and (6) at the bottom of the next page,where denotes the total number of generations either from the start of an evolutionary process or the last occurrence of change,whichever was more recent,up to the current generation.On the other hand,represents the weight given to previous evolutionary progresses relative to the current one.Using ,the weighted average is equivalent to taking a simple average of all the individual progresses (total sum divided by number of generation).This means that the effect of all the previous and values starting from the recent occurrence of change is accumulated and does not diminish through time.
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