Non-Convex Multi-Objective Optimization

Multi-objective optimization and decision visualization of batch stirred tank reactor based on spherical catalyst particles

“…However, the objective functions of the considered problem are computationally expensive, and the solution of this problem by a meta-heuristic method would take prohibitive long computing time. For such, so called expensive, objective functions, Bayesian methods proved to be efficient [25]. On the other hand, the inherent complexity of standard implementations of Bayesian methods limits the number of values of the objective functions which can be processed.…”

“…2, the rectangular partition of the feasible region is shown at the vertices of which are computed the values of the objective functions. The performance metrics of the proposed algorithm are presented in Table 2, where the performance of metrics of several other algorithms are also presented for comparison [25]. The following notation is used in Table 2: NFE-number of evaluations of the objective functions, ε -tolerance of the termination condition, NGEN-number of generation in the termination criterion of the genetic algorithm, HV-hypervolume computed with respect to the reference point (1, 1) T , NP-number of found non-dominated solutions, UDuniformity of distribution of points approximating the Pareto front.…”

“…The following notation is used in Table 2: NFE-number of evaluations of the objective functions, ε -tolerance of the termination condition, NGEN-number of generation in the termination criterion of the genetic algorithm, HV-hypervolume computed with respect to the reference point (1, 1) T , NP-number of found non-dominated solutions, UDuniformity of distribution of points approximating the Pareto front. For the convenience of readers the definition of the metric UD follows [25]:…”

“…Multi-objective optimization tools provide a mechanism to obtain a certain number of trade-off solutions, known as Pareto-optimal solutions [25]. Establishing an efficient approach to find a set of solutions with good trade-off among different objectives has a great practical significance, as these allow engineers to gain insight into the key characteristics of potentially good configurations before moving on to more detailed simulations and pilot commercial tests [16,22,32].…”

“…However, the mathematical models of bioreactors based on an array of enzyme-loaded particles are described by transient nonlinear partial differential equations and the numerical solution often requires long lasting computations [2-4, 14, 34]. In such cases, the objective functions of the respective optimization problem is so called expensive, and Bayesian approach-based methods can be most appropriate for those optimization problems [24,25].…”