This article presents mathematical models for designing GRID systems to solve resource-intensive problems. The study aims to enhance the efficiency of distributed solutions for structural-parametric synthesis of neural network models of complex systems using GRID technology, integrating evolutionary optimization and queuing theory. New mathematical models for assessing GRID system performance and reliability are developed, along with a multi-criteria optimization model for designing GRID systems to solve high-resource computing problems. A decision support system using a multi-criteria genetic algorithm is proposed to optimize GRID system design. The study uses a genetic algorithm with a dynamic penalty function to solve the multi-constrained optimization problem. The developed system is applied to select an effective structure for a centralized GRID system configured to solve structural-parametric synthesis of neural network models. A Pareto-optimal configuration of the GRID system is tested, achieving an average performance of 103.483 GFLOPS, a cost of 500 rubles per day, an availability rate of 99.92%, and a minimum performance of 51 GFLOPS. The study highlights the importance of GRID systems in solving complex resource-intensive problems, emphasizing the need for efficient resource allocation, performance, and reliability. The research contributes new mathematical models, a multi-criteria optimization model, and a decision support system for GRID systems. The study also discusses the application of parallel genetic algorithms for neural network structure synthesis and the development of a multi-criteria multi-population parallel genetic algorithm with topology restructuring of linkages between populations. The paper presents a performance evaluation model for GRID systems, considering factors such as resource availability, communication speed, and system configuration. The reliability assessment model evaluates the system's ability to maintain performance despite failures and reconfiguration. The study concludes that GRID systems are essential for solving complex resource-intensive problems, and the proposed models and algorithms enhance their efficiency and reliability.This article presents mathematical models for designing GRID systems to solve resource-intensive problems. The study aims to enhance the efficiency of distributed solutions for structural-parametric synthesis of neural network models of complex systems using GRID technology, integrating evolutionary optimization and queuing theory. New mathematical models for assessing GRID system performance and reliability are developed, along with a multi-criteria optimization model for designing GRID systems to solve high-resource computing problems. A decision support system using a multi-criteria genetic algorithm is proposed to optimize GRID system design. The study uses a genetic algorithm with a dynamic penalty function to solve the multi-constrained optimization problem. The developed system is applied to select an effective structure for a centralized GRID system configured to solve structural-parametric synthesis of neural network models. A Pareto-optimal configuration of the GRID system is tested, achieving an average performance of 103.483 GFLOPS, a cost of 500 rubles per day, an availability rate of 99.92%, and a minimum performance of 51 GFLOPS. The study highlights the importance of GRID systems in solving complex resource-intensive problems, emphasizing the need for efficient resource allocation, performance, and reliability. The research contributes new mathematical models, a multi-criteria optimization model, and a decision support system for GRID systems. The study also discusses the application of parallel genetic algorithms for neural network structure synthesis and the development of a multi-criteria multi-population parallel genetic algorithm with topology restructuring of linkages between populations. The paper presents a performance evaluation model for GRID systems, considering factors such as resource availability, communication speed, and system configuration. The reliability assessment model evaluates the system's ability to maintain performance despite failures and reconfiguration. The study concludes that GRID systems are essential for solving complex resource-intensive problems, and the proposed models and algorithms enhance their efficiency and reliability.