Comparative study of different approaches to solve batch process scheduling and optimisation problems

Effective approaches are important to batch process scheduling problems, especially those with complex constraints. However, most research focus on improving optimisation techniques, and those concentrate on comparing their difference are inadequate. This study develops an optimisation model of batch process scheduling problems with complex constraints and investigates the performance of different optimisation techniques, such as Genetic Algorithm (GA) and Constraint Programming (CP). It finds that CP has a better capacity to handle batch process problems with complex constraints but it costs longer time

Una metodología eficiente para manejo de restricciones en algoritmos evolutivos multiobjetivo

RESUMEN: Este artículo presenta un nuevo enfoque para resolver problemas de optimización restrictos (POR) basado en la filosofía de programación lexicografita de objetivos. En este caso se utiliza una metodología de dos fases usando una estrategia multi-objetivo. En la primera fase se concentra el esfuerzo en encontrar por lo menos una solución factible, descartando completamente la función objetivo. En la segunda fase se aborda el problema como bi-objetivo, convirtiendo el problema de optimización restricta a un problema de optimización irrestricto de dos objetivos. Los dos objetivos resultantes son la función objetivo original y el grado de violación de las restricciones. En la primera fase se propone una metodología basada en el endurecimiento progresivo de restricciones blandas para encontrar soluciones factibles. El desempeño de la metodología propuesta es validado a través de 11 casos de prueba bastante conocidos en la literatura especializada.ABSTRACT: This paper presents a new approach for solving constraint optimization problems (COP) based on the philosophy of lexicographical goal programming. A two-phase methodology for solving COP using a multiobjective strategy is used. In the first phase, the objective function is completely disregarded and the entire search effort is directed towards finding a single feasible solution. In the second phase, the problem is treated as a bi-objective optimization problem, turning the constraint optimization into a two-objective optimization. The two resulting objectives are the original objective function and the constraint violation degree. In the first phase a methodology based on progressive hardening of soft constraints is proposed in order to find feasible solutions. The performance of the proposed methodology was tested on 11 well-known benchmark functions

COIL: Constrained optimization in learned latent space: learning representations for valid solutions

Constrained optimization problems can be difficult because their search spaces have properties not conducive to search, e.g., multimodality, discontinuities, or deception. To address such difficulties, considerable research has been performed on creating novel evolutionary algorithms or specialized genetic operators. However, if the representation that defined the search space could be altered such that it only permitted valid solutions that satisfied the constraints, the task of finding the optimal would be made more feasible without any need for specialized optimization algorithms. We propose Constrained Optimization in Latent Space (COIL), which uses a VAE to generate a learned latent representation from a dataset comprising samples from the valid region of the search space according to a constraint, thus enabling the optimizer to find the objective in the new space defined by the learned representation. Preliminary experiments show promise: compared to an identical GA using a standard representation that cannot meet the constraints or find fit solutions, COIL with its learned latent representation can perfectly satisfy different types of constraints while finding high-fitness solutions

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

Incremental approximation of nonlinear constraint functions for evolutionary constrained optimization

This paper proposes an alternative approach to efficient solving of nonlinear constrained optimization problems using evolutionary algorithms. It is assumed that the separate-ness of the feasible regions, which imposes big difficulties for evolutionary search, is partially resulted from the complexity of the nonlinear constraint functions. Based on this hypothesis, an approximate model is built for each constraint function with an increasing accuracy, starting from a simple linear approximation. As a result, the feasible region based on the approximate constraint functions will be much simpler, and the isolated feasible regions will become more likely connected. As the evolutionary search goes on, the approximated feasible regions should gradually change back to the original one by increasing the accuracy of the approximate models to ensure that the optimum found by the evolutionary algorithm does not violate any of the original constraints. Empirical studies have been performed on 13 test problems and four engineering design optimization problems. Simulation results suggest that the proposed method is competitive compared to the state-of-the-art techniques for solving nonlinear constrained optimization problems

Application of Genetic Algorithm in Multi-objective Optimization of an Indeterminate Structure with Discontinuous Space for Support Locations

In this thesis, an indeterminate structure was developed with multiple competing objectives including the equalization of the load distribution among the supports while maximizing the stability of the structure. Two different coding algorithms named “Continuous Method” and “Discretized Method” were used to solve the optimal support locations using Genetic Algorithms (GAs). In continuous method, a continuous solution space was considered to find optimal support locations. The failure of this method to stick to the acceptable optimal solution led towards the development of the second method. The latter approach divided the solution space into rectangular grids, and GAs acted on the index number of the nodal points to converge to the optimality. The average value of the objective function in the discretized method was found to be 0.147 which was almost onethird of that obtained by the continuous method. The comparison based on individual components of the objective function also proved that the proposed method outperformed the continuous method. The discretized method also showed faster convergence to the optima. Three circular discontinuities were added to the structure to make it more realistic and three different penalty functions named flat, linear and non-linear penalty were used to handle the constraints. The performance of the two methods was observed with the penalty functions while increasing the radius of the circles by 25% and 50% which showed no significant difference. Later, the discretized method was coded to eliminate the discontinuous area from the solution space which made the application of the penalty functions redundant. A paired t-test (α=5%) showed no statistical difference between these two methods. Finally, to make the proposed method compatible with irregular shaped discontinuous areas, “FEA Integrated Coded Discretized Method (FEAICDM)” was developed. The manual elimination of the infeasible areas from the candidate surface was replaced by the nodal points of the mesh generated by Solid Works. A paired t-test (α=5%) showed no statistical difference between these two methods. Though FEAICDM was applied only to a class of problem, it can be concluded that FEAICDM is more robust and efficient than the continuous method for a class of constrained optimization problem