A penalty scheme for the Tchebycheff scalarization method to optimize the single screw extrusion

The polymer single screw extruder optimal design has been involving the optimization of six objectives. Multi-objective optimization methods, in particular those based on the weighted Tchebycheff Scalarization (wTS) function, have provided reasonable solutions in a way that good trade-offs between conflicting objectives are identified. In this work, a new penalty term is added to the wTS function aiming to guide the solution toward the Pareto front. The corresponding formulation works similarly to the penalty-based boundary intersection function. The goal of the proposed penalty parameter scheme is to balance convergence and diversity. Since six objectives are simultaneously optimized, the penalty scheme provides large as well as small penalty parameter values to enlarge the improving region. The results show that the set of solutions obtained by the penalty-based wTS algorithm can reasonably well cover the Pareto front.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie grant agreement No. 734205 – H2020-MSCA-RISE-2016

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

Scalarizing Functions in Decomposition-Based Multiobjective Evolutionary Algorithms

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have received increasing research interests due to their high performance for solving multiobjective optimization problems. However, scalarizing functions (SFs), which play a crucial role in balancing diversity and convergence in these kinds of algorithms, have not been fully investigated. This paper is mainly devoted to presenting two new SFs and analyzing their effect in decomposition-based MOEAs. Additionally, we come up with an efficient framework for decomposition-based MOEAs based on the proposed SFs and some new strategies. Extensive experimental studies have demonstrated the effectiveness of the proposed SFs and algorithm