In many experiments, the response to a treatment may be affected by other treatments applied to neighboring experimental units. Interference may contribute to variability in experimental results and lead to substantial losses in efficiency. It is recommended then to use designs that are balanced in some sense with respect to neighbors. In such experiments, the interference model with neighbor effects is usually applied. Such designs are applied for example in agriculture, medicine, etc. Let $ be the set of designs with t treatments, blocks and k experimental units per block. An interference model with left-neighbor effects associated with the desig can be written as where and are the vectors of treatment and block effects, respectively, while and are the vectors of random left-neighbor effects and random errors, respectively, with . The matrix is the design matrix of block effects, treatment effects and left-neighbor effects, respectively. This model with random neighbor effects is called a mixed interference model. In the theory of experimental designs, the problem of determining optimal designs is often considered. It is know, that circular neighbor balanced designs (CNBDs) are universally optimal under the mixed interference model. However, such designs cannot exist for each combination of design parameters. In such cases, the efficiency of certain designs or optimality with respect to specified criteria is considered. We prove the universal optimality of circular weakly neighbor balanced designs (CWNBDs), which require a smaller number of blocks than CNBDs and give a construction method for some CWNBDs. In the special cases, characterize E- or D-optimal designs. The aim of this thesis is to characterize E- and D-optimal designs under the interference model with random neighbor effects.