This paper introduces a family of improved variants of the DE/target-to-best/1 scheme that utilize the concept of neighborhoods for each population member. The idea of small neighborhoods, defined over the index-graph of parameter vectors, draws inspiration from the community of PSO algorithms. The proposed schemes balance exploration and exploitation abilities of DE without imposing serious additional burdens in terms of function evaluations. They are shown to be statistically significantly better than or at least comparable to several existing DE variants as well as other significant evolutionary computing techniques over a test suite of 24 benchmark functions. The paper also investigates the applications of the new DE variants to two real-life problems concerning parameter estimation for frequency modulated sound waves and spread spectrum radar poly-phase code design. The DE algorithm starts with a population of NP D-dimensional parameter vectors representing candidate solutions. The algorithm proceeds through mutation, crossover, and selection steps. Mutation creates a donor vector for each population member, crossover combines the donor vector with the target vector to form a trial vector, and selection determines whether the target or trial vector survives to the next generation. Previous research has focused on improving the performance of DE by tuning control parameters such as population size, scaling factor, and crossover rate. Various self-adaptive DE algorithms have been proposed, including FADE, SaDE, ADE, and others, which adapt parameters based on the problem's characteristics. The proposed DE variants use a neighborhood-based mutation operator that combines local and global mutation strategies. The local neighborhood model uses the best vector in a small neighborhood of each vector, while the global mutation model uses the best vector in the entire population. A weight factor is used to balance the effects of the local and global mutation strategies. The weight factor can be increased, randomized, or self-adapted during the algorithm's execution. The runtime complexity of DEGL is analyzed, showing that it does not impose a significant burden on the runtime complexity of existing DE variants. The proposed DE variants are shown to be statistically significantly better than or at least comparable to several existing DE variants over a test suite of 24 benchmark functions. The paper also investigates the applications of the new DE variants to two real-life problems.This paper introduces a family of improved variants of the DE/target-to-best/1 scheme that utilize the concept of neighborhoods for each population member. The idea of small neighborhoods, defined over the index-graph of parameter vectors, draws inspiration from the community of PSO algorithms. The proposed schemes balance exploration and exploitation abilities of DE without imposing serious additional burdens in terms of function evaluations. They are shown to be statistically significantly better than or at least comparable to several existing DE variants as well as other significant evolutionary computing techniques over a test suite of 24 benchmark functions. The paper also investigates the applications of the new DE variants to two real-life problems concerning parameter estimation for frequency modulated sound waves and spread spectrum radar poly-phase code design. The DE algorithm starts with a population of NP D-dimensional parameter vectors representing candidate solutions. The algorithm proceeds through mutation, crossover, and selection steps. Mutation creates a donor vector for each population member, crossover combines the donor vector with the target vector to form a trial vector, and selection determines whether the target or trial vector survives to the next generation. Previous research has focused on improving the performance of DE by tuning control parameters such as population size, scaling factor, and crossover rate. Various self-adaptive DE algorithms have been proposed, including FADE, SaDE, ADE, and others, which adapt parameters based on the problem's characteristics. The proposed DE variants use a neighborhood-based mutation operator that combines local and global mutation strategies. The local neighborhood model uses the best vector in a small neighborhood of each vector, while the global mutation model uses the best vector in the entire population. A weight factor is used to balance the effects of the local and global mutation strategies. The weight factor can be increased, randomized, or self-adapted during the algorithm's execution. The runtime complexity of DEGL is analyzed, showing that it does not impose a significant burden on the runtime complexity of existing DE variants. The proposed DE variants are shown to be statistically significantly better than or at least comparable to several existing DE variants over a test suite of 24 benchmark functions. The paper also investigates the applications of the new DE variants to two real-life problems.