An Improved Differential Evolution Method Based on the Dynamic Search Strategy to Solve Dynamic Economic Dispatch Problem with Valve-Point Effects

Algorithm 1

Procedure of global search strategy.

Parameters:

𝑥_𝑖,𝐺: Target vector; 𝑣_𝑖,𝐺: Mutant vector; 𝑢_𝑖,𝐺: Trial vector; 𝑥_𝑖: 𝑖th individual in population;

𝑃_infeasible: The set of all the infeasible solution of current population;

Step  1.  Choose the smallest of 𝑓(𝑥) value forms the feasible solutions, denoted as 𝑃_best

Step  2.  For 𝑖=1,…,NP, do

   Step  2.1. Generate a 𝑣_𝑖,𝐺 by DE/rand/1

   Step  2.2. If (𝑥_𝑖=𝑃_best)

        Step  2.2.1. Mix 𝑣_𝑖,𝐺 and 𝑥_𝑖,𝐺 by making use of QOX based on

            𝐿_𝑀(𝑄^𝑘) to generate 𝑀 trial vectors. Calculation 𝑓(𝑥) values

            and 𝐺(𝑥) values of 𝑀 trial vectors

        Step  2.2.2. Choose the one feasible solutions with the smallest of 𝑓(𝑥)

            value as 𝑢_𝑖,𝐺 in 𝑀 trial vectors.

        Step  2.2.3. If there are infeasible solutions in 𝑀 trial vectors, it will

            be added into set 𝑇

       Else

        Step  2.2.4. Mix 𝑣_𝑖,𝐺 and 𝑥_𝑖,𝐺 by (8) to generate 𝑢_𝑖,𝐺.

       End if

   Step  2.3. Calculate the 𝑓(𝑥) value and the 𝐺(𝑥) value for the trial vector 𝑢_𝑖,𝐺.

   Step  2.4. If 𝑢_𝑖,𝐺≺𝑥_𝑖,𝐺,𝑢_𝑖,𝐺 will replace the 𝑥_𝑖,𝐺, else no replacement occurs.

Step  3.  If 𝑇 are not empty set. Select the best infeasible individual (i.e., the infeasible

   solution with the lowest degree of constraint violation) of the non-dominated

   individuals in the set 𝑇, denoted as 𝑀^best_infeasible.

Step  4.  If 𝑀^best_infeasible exists. Compared with pareto dominance between 𝑀^best_infeasible and

   𝑃_infeasible,𝑀^best_infeasible is used to replace a randomly selected pareto dominated

   individual in 𝑃_infeasible.