基于空间网格划分的多目标进化算法

为了有效求解多目标优化问题,找到分布宽广、均匀的Pareto解集,提出了一个基于空间网格划分的进化算法。将目标空间网格化,利用网格的位置,删除大量被支配个体。在杂交算子中利用了单个目标最优的个体信息,以增加非劣解的宽广性。利用一种新设计的基于最大距离排序的方法删除非劣解集中多余个体。数值实验表明提出的算法是可行有效的。     

PRODUCT QUALITY MULTI-OBJECTIVE DRYER DESIGN

ABSTRACT

Design of conveyor-belt dryers constitutes a mathematical programming problem involving the evaluation of appropriate structural and operational process variables so that total annual plant cost involved is optimized. The increasing need for dehydrated products of the highest quality, imposes the development of new criteria that, together with cost, determine the design rules for drying processes. Quality of dehydrated products is a complex resultant of properties characterizing the final products, where the most important one is color. Color is determined as a three-parameter resultant, whose values for products undergone drying should deviate from the corresponding ones of natural products, as little as possible. In this case, product quality dryer design is a complex multi-objective optimization problem, involving the color deviation vector as an objective function and as constraints the ones deriving from the process mathematical model. The mathematical model of the dryer was developed and the fundamental color deterioration laws were determined for the drying process. Non-preference multi-criteria optimization methods were used and the Pareto-optimal set of efficient solutions was evaluated. An example covering the drying of sliced potato was included to demonstrate the performance of the design procedure, as well as the effectiveness of the proposed approach.     

Utopian point based decomposition for multi-objective optimization problems with complicated Pareto fronts

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been considered as a promising method for solving multi-objective optimization problems (MOPs). It devotes most of its effort on convergence by optimizing a set of scalar optimization subproblems in a collaborative manner, while maintaining the diversity by using a set of uniformly distributed weight vectors. However, more recent studies illustrated that MOEA/D faces difficulties on MOPs with complicated Pareto fronts, mainly because the uniformity of weight vectors no longer lead to an evenly scattered approximation of the Pareto fronts in these cases. To remedy this, we suggest replacing the ideal point in the reciprocal Tchebycheff decomposition method with a more optimistic utopian point, with the aim of alleviating the sensitivity of MOEA/D to the Pareto front shape of MOPs. Experimental studies on benchmark and real-world problems have shown that such simple modification can significantly improve the performances of MOEA/D with reciprocal Tchebycheff decomposition on MOPs with complicated Pareto fronts.     

Comprehensive Pareto Efficiency in robust counterpart optimization

In this paper, an innovative concept named Comprehensive Pareto Efficiency is introduced in the context of robust counterpart optimization, which consists of three sub-concepts: Pareto Robust Optimality (PRO), Global Pareto Robust Optimality (GPRO) and Elite Pareto Robust Optimality (EPRO). Different algorithms are developed for computing robust solutions with respect to these three sub-concepts. As all sub-concepts are based on the Probability of Constraint Violation (PCV), formulations of PCV under different probability distributions are derived and an alternative way to calculate PCV is also presented. Numerical studies are drawn from two applications (production planning problem and orienteering problem), to demonstrate the Comprehensive Pareto Efficiency. The numerical results show that the Comprehensive Pareto Efficiency has important significance for practical applications in terms of the evaluation of the quality of robust solutions and the analysis of the difference between different robust counterparts, which provides a new perspective for robust counterpart optimization.     

基于平行多种群与冗余基因策略的置信规则库优化方法

置信规则库(Belief rule base, BRB)的参数学习和结构学习共同影响着置信规则库的建模精度和复杂度. 为了提高BRB结构学习和参数学习的优化效率, 本文提出了一种基于平行多种群(Parallel multi-population)策略和冗余基因(Redundant genes)策略的置信规则库优化方法. 该方法采用平行多种群策略以实现对具有不同数量规则BRB同时进行优化的目的, 采用冗余基因策略以确保具有不同数量规则的BRB能够顺利进行(交叉, 变异等)相关优化操作. 最终自动生成具有不同数量规则BRB的最优解, 并得出帕累托前沿(Pareto frontier), 决策者可以根据自身偏好和实际问题需求, 综合权衡并在帕累托前沿中筛选最优解. 最后以某输油管道泄漏检测问题作为示例验证本文提出方法的有效性, 示例分析结果表明本文提出的方法可以一次生成具有多条规则BRB的最优解, 并且可以准确绘制出帕累托前沿, 为综合决策提供较强的决策支持.     

基于自适应多种群遗传算法的多目标配电网故障恢复

包含分布式电源(distributed generation,DG)的配电系统,在发生大面积断电时,其供电恢复是一个多目标、多约束的复杂优化问题.文章考虑用户优先等级,基于负荷恢复量,手动开关和遥控开关的动作次数以及恢复供电后的网损,建立了包含DG的配电系统的多目标供电恢复模型,并提出一种改进的遗传算法来处理配电网故障...     

基于改进智能水滴算法的多目标供应链最优模型

为了最大限度地降低制造型供应链的销售成本并缩短供货时间,提出了一种基于改进智能水滴算法的多目标供应链优化模型。该模型通过在选项选择期间同时考虑成本和时间来提高供应链效率,并能够将制造型供应链中的销售成本和交货时间最小化。通过使用帕累托最优准则对传统的智能水滴算法进行修改,从而得到一个帕累托集,以实现两个目标的最小化。通过3个实例对所提算法进行了测试,并采用世代距离和超区域比指标将其与蚁群优化算法进行了比较。实验结果显示,所提方法的性能更优,生成的解集更接近真实帕累托集,能够覆盖更大的解区域面积,且计算效率较高。     

Pareto-optimal solutions for multicriteria optimization of a chemical engineering process using a diploid genetic algorithm

In many, if not most, optimization problems, industrialists are often confronted with multi‐objective decision problems. For example, in manufacturing processes, it may be necessary to optimize several criteria to take into account all the market constraints. Hence, the purpose is to choose the best trade‐offs among all the defined and conflicting objectives. This paper presents a multi‐objective optimization procedure based on a diploid genetic algorithm, which yields an optimal zone containing the solution under the concept of Pareto dominance. Pair‐wise points are compared, and non‐dominated points are collected in the Pareto region. Then a ranking is established, and the decision maker selects the first‐best solution. Finally, the procedure is applied to the chemical engineering process of cattle feed manufacture.     

Stability criteria in vector combinatorial bottleneck problems in terms of binary relations

The paper considers a vector (multiobjective) path problem with minimax partial criteria. Solving this problem means finding a Pareto set. Binary relations on a set of paths are used to formulate the necessary and sufficient conditions for five types of problem stability against perturbations of the parameters of a vector criterion. Some sufficient stability conditions in terms of Pareto, Smale, and Slater sets are obtained as corollaries. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 103–111, May–June 2008.