Genetic algorithm learning--Genetic algorithm in multiobjective optimization

Ext.: https://www.cnblogs.com/lomper/p/3831428.html

In the application of engineering, it is often the multi-criteria and the optimum design of the target. To solve the optimization problem with multi-objective and multi-constraints is called multi-Objective optimization problem . Often, these goals are conflicting. such as investment in the least capital, the best returns, the least risk ~ ~

The general mathematical model of multi-objective optimization problem can be described as:

Pareto Optimal solution (Pareto Optimal solution)

Using genetic algorithm to solve Pareto optimal solution:

• Weight coefficient Transformation Method:

• Parallel Selection Method:

Basic idea:

The whole population is divided into sub-groups according to the number of sub-objective functions, assigning a target function to each sub-group, selecting a new sub-group of individuals with high adaptability, and then merging all these subgroups into a complete group, in which the cross-mutation operation is performed. Generate the next generation of complete groups, so cycle, and ultimately generate Pareto optimal solutions. Such as:

• Permutation selection Method:

Based on the premise of Pareto optimal individual, each individual in the group is sorted and selected according to the order, so that the Pareto optimal individual in front will have greater possibility to enter the next generation group.

• Shared Function Method:

Techniques for using niche genetic algorithms. The algorithm adds a limit to the number of identical individuals or similar individuals, so that they can produce different optimal solutions of many kinds.

For an individual x, it is possible to measure the number of similar individuals around it, known as niche numbers. Calculation method:

S (d) is a shared function, which is a monotonically decreasing function of distance d between individuals. D (x, y) is the Hamming distance between individual x, Y .

After the number of niches is calculated, it is possible that individuals with small niche numbers can have more opportunities to be selected and inherit into next-generation groups, where less-similar individuals have more opportunities to be inherited into next-generation groups.

In order to solve the problem of multiobjective optimization, the solution can be scattered as much as possible in the whole Pareto optimal solution set rather than in a small area of the Pareto optimal solution set.

• Mixing method:

1. Side-by-side selection process: According to the number of sub-objective functions of multiobjective optimization problem, the whole group is divided into sub-groups, each sub-objective function in the corresponding sub-group to produce its next-generation sub-group.
2. Preserving Pareto optimal individual processes: for Pareto optimal individuals in subgroups, they are not allowed to participate in individual crossover and mutation operations, but are retained directly into the next generation sub-group.
3. Shared function Processing: If the number of Pareto optimal individuals has exceeded the defined group size, then a shared function is used to select them to form a new generation of groups of defined size.

Genetic algorithm learning--Genetic algorithm in multiobjective optimization