Traditional Multi-objective Optimization Algorithms Research Articles

An integrated cultural particle swarm algorithm for multi-objective reliability-based design optimization

Uncertainties in design variables and problem parameters are often inevitable in multi-objective optimizations, and they must be considered in an optimization task if reliable Pareto optimal solutions are to be sought. Multi-objective reliability-based design optimization has been raised as a question in design for reliability, but the disadvantages of fixed evolutionary parameters, nonuniformly distributed Pareto optimal solutions and high computational cost hinder engineering applications of reliability-based design. To deal with it, this work proposes an integrated multi-objective cultural-based particle swarm algorithm to solve the double-loop reliability-based design optimization. In the inner optimization loop, the cultural space is composed of the elitism, situational and normative knowledge to adjust the parameters for swarm space, and the crowding distance ranking is introduced to update the global and local optimum and control the maximum number of solutions in elitism knowledge. The hybrid mean value method is improved to perform reliability analysis in the outer loop to suit both concave and convex types of performance functions. In addition, the car side-impact and the injection molding machine are chosen as multi-objective reliability design examples to demonstrate the effectiveness of the proposed approach. Simultaneously, results of car side-impact problem are compared with two traditional multi-objective reliability optimization algorithms, i.e., nondominated sorting genetic algorithm and crowding distance ranking-based multi-objective particle swarm optimizer, to assess the efficiency of the proposed approach. The results denote the proposed cultural-based multi-objective particle swarm optimizer is effective and feasible to solve the reliability-based design optimization problems.

Multi-objective Distinct Candidates Optimization: Locating a few highly different solutions in a circuit component sizing problem

Abstract Traditional multi-objective optimization algorithms typically return several hundred non-dominated solutions. From a practical point of view, a small set of 5–10 distinct candidates is often preferred because post-processing many solutions may be too costly, too time-consuming, or it may be too difficult to compare design differences. In this paper, we introduce Multi-objective Distinct Candidates Optimization (MODCO) as an approach to find a user-defined low number of clearly different solutions wrt. performance and design. To demonstrate the potential of the MODCO approach, we suggest the General Cluster-Forming Differential Evolution (GCFDE) algorithm and test it on five well-known mechanical engineering problems and a new five-objective constrained problem from electrical engineering – the circuit component sizing problem of the Alpha Pro pump. The experiments showed that GCFDE significantly outperformed all competing MOEAs on the many-objective circuit problem and had slightly better performance on the mechanical problems. Furthermore, our algorithm was able to return result sets in accordance with the user’s settings for result set cardinality as well as performance and design distinctiveness.