An Adaptive Reference Vector Adjustment Strategy and Improved Angle-Penalized Value Method for RVEA

Decomposition-based evolutionary multiobjective algorithms (MOEAs) divide a multiobjective problem into several subproblems by using a set of predefined uniformly distributed reference vectors and can achieve good overall performance especially in maintaining population diversity. However, they encounter huge difficulties in addressing problems with irregular Pareto fronts (PFs) since many reference vectors do not work during the searching process. To cope with this problem, this paper aims to improve an existing decomposition-based algorithm called reference vector-guided evolutionary algorithm (RVEA) by designing an adaptive reference vector adjustment strategy. By adding the strategy, the predefined reference vectors will be adjusted according to the distribution of promising solutions with good overall performance and the subspaces in which the PF lies may be further divided to contribute more to the searching process. Besides, the selection pressure with respect to convergence performance posed by RVEA is mainly from the length of normalized objective vectors and the metric is poor in evaluating the convergence performance of a solution with the increase of objective size. Motivated by that, an improved angle-penalized distance (APD) method is developed to better distinguish solutions with sound convergence performance in each subspace. To investigate the performance of the proposed algorithm, extensive experiments are conducted to compare it with 5 state-of-the-art decomposition-based algorithms on 3-, 5-, 8-, and 10-objective MaF1–MaF9. The results demonstrate that the proposed algorithm obtains the best overall performance.

Collaborative Product Portfolio Design Based on the Approach of Multichoice Goal Programming

Product portfolio optimization is a typical multiobjective problem. The multichoice goal programming method becomes a popular means of resolving multiobjective decision problems. However, the classic multichoice goal programming method treats the product portfolio optimization in isolation and does not consider the mutual influence between portfolio products. Researchers should consider the interaction between products in portfolio optimization so that they can be adjusted to “real world” problems. The interaction between products can be explained by population dynamics. Logistic model is a classical method to analyze the population interaction. The equilibrium point of logistic model can show the ideal state of product population coordinated development. The combination of logistic and multichoice goal programming method is an effective approach to analyze the interaction of product portfolio. This paper therefore proposes a new alternative method to formulate the multiobjective problem and also uses an illustrative example to demonstrate the usefulness of the proposed method. The comparative analysis of model optimization results shows that logistic multichoice goal programming model can take into account resource constraints, product collaboration, and output maximization. Logistic multichoice goal programming model shows good performance in the aspects of operation complexity, operation time, sensitivity analysis, and collaborative entropy evaluation.

A Negotiation Pricing Model for Innovation Services Based on the Multiobjective Genetic Algorithm

Service pricing is a bottleneck in the development of innovation services, as it is the issue of most concern between the suppliers and demanders. In this paper, a negotiation pricing model that is based on the multiobjective genetic algorithm is developed for innovation service pricing. Regarding the service pricing process as a multiobjective problem, the objective functions, which include the service price, service efficiency, and service quality, for suppliers and demanders are constructed. As the solution of a multiobjective problem is typically a series of alternatives, another negotiation process is necessary for determining the final decision. A learning strategy is adopted during the negotiation process to simulate reality. Finally, the model is implemented for an innovation service transaction, the objective of which is to identify the optimal price plan. The results demonstrate that the model can provide quantitative decision support for the pricing of an innovation service and ultimately yield a win-win result for both the supplier and demander of the innovation service. Furthermore, the influence of the parameters during the negotiation process is analyzed in detail. The effects of the learning strategy on accelerating the negotiation process, as well as the chosen of reasonable parameters are given.

Multiobjective PID controller design for active suspension system: scalarization approach

In this study, the PID tuning method (controller design scheme) is proposed for a linear quarter model of active suspension system installed on the vehicles. The PID tuning scheme is considered as a multiobjective problem which is solved by converting this multiobjective problem into single objective problem with the aid of scalarization approaches. In the study, three different scalarization approaches are used and compared to each other. These approaches are called linear scalarization (weighted sum), epsilon-constraint and Benson’s methods. The objectives of multiobjective optimization are selected from the time-domain properties of the transient response of the system which are overshoot, rise time, peak time and error (in total there are four objectives). The aim of each objective is to minimize the corresponding property of the time response of the system. First, these four objective is applied to the scalarization functions and then single objective problem is obtained. Finally, these single objective problems are solved with the aid of heuristic optimization algorithms. For this purpose, four optimization algorithms are selected, which are called Particle Swarm Optimization, Differential Evolution, Firefly, and Cultural Algorithms. In total,twelve implementations are evaluated with the same number of iterations. In this study, the aim is to compare the scalarization approaches and optimization algorithm on active suspension control problem. The performance of the corresponding cases (implementations) are numerically and graphically demonstrated on transient responses of the system.