Interactive multiobjective fuzzy random programming through the level set-based probability model

This paper considers a multiobjective linear programming problem involving fuzzy random variable coefficients. A new fuzzy random programming model is proposed by extending the ideas of level set-based optimality and a stochastic programming model. The original problem involving fuzzy random variables is transformed into a deterministic equivalent problem through the proposed model. An interactive algorithm is provided to obtain a satisficing solution for a decision maker from among a set of newly defined Pareto optimal solutions. It is shown that an optimal solution of the problem to be solved iteratively in the interactive algorithm is analytically obtained by a combination of the bisection method and the simplex method.     

Convergence of multi-objective evolutionary algorithms to a uniformly distributed representation of the Pareto front

In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent.     

Logic-based automated multi-issue bilateral negotiation in peer-to-peer e-marketplaces

We present a novel logic-based framework to automate multi-issue bilateral negotiation in e-commerce settings. The approach exploits logic as communication language among agents, and optimization techniques in order to find Pareto-efficient agreements. We introduce , a propositional logic extended with concrete domains, which allows one to model relations among issues (both numerical and non-numerical ones) via logical entailment, differently from well-known approaches that describe issues as uncorrelated. Through it is possible to represent buyer’s request, seller’s supply and their respective preferences as formulas endowed with a formal semantics, e.g., “if I spend more than 30000 € for a sedan then I want more than a two-years warranty and a GPS system included”. We mix logic and utility theory in order to express preferences in a qualitative and quantitative way. We illustrate the theoretical framework, the logical language, the one-shot negotiation protocol we adopt, and show we are able to compute Pareto-efficient outcomes, using a mediator to solve an optimization problem. We prove the computational adequacy of our method by studying the complexity of the problem of finding Pareto-efficient solutions in our setting.     

Type II robotic assembly line balancing problem: An evolution strategies algorithm for a multi-objective model

In this paper a different type II robotic assembly line balancing problem (RALB-II) is considered. One of the two main differences with the existing literature is objective function which is a multi-objective one. The aim is to minimize the cycle time, robot setup costs and robot costs. The second difference is on the procedure proposed to solve the problem. In addition, a new mixed-integer linear programming model is developed. Since the problem is NP-hard, three versions of multi-objective evolution strategies (MOES) are employed. Numerical results show that the proposed hybrid MOES is more efficient.     

New polynomial time algorithms to compute a set of Pareto optimal paths for multi-objective shortest path problems

Multi-objective shortest path problem (MOSPP) is an active area of research because of its application in a large number of systems such as transportation systems, communication systems, power transmission systems, pipeline distribution systems of water, gas, blood and drainage, neural decision systems, production planning and project planning. In these networks it becomes necessary to find the best path from one node to a specified or all other nodes. The computational complexity of the existing algorithms in the literature to compute all Pareto minimum paths from a specified source node to all other nodes in an MOSPP is of exponential order in the worst case. Instead of generating all the values of the Pareto minimum paths in exponential time, we propose an algorithm to find a set of values of the Pareto minimum paths in polynomial time, which is very significant in many contexts. If an MOSPP of a network is having negative cycle, all the existing algorithm only indicate the existence of the negative cycle, that too after exponential number of operations. However, applying the proposed algorithm, we can find a set of Pareto minimum paths of any MOSPP of a network even if it contains negative cycles. The proposed algorithm is illustrated with examples.     

飞机环控/发动机系统多目标优化分析

一种以系统熵产最小为目标函数的优化方法,应用到飞机环控/发动机系统的综合优化计算。由于在不同飞行阶段为使系统总的熵产减小对设计变量的要求不尽相同,甚至存在冲突,引入多目标优化的思想进行优化计算。将任务剖面内不同飞行阶段系统总的熵产最小视为不同的目标函数,通过分析系统之间交联关系、选取设计变量和分析约束条件建立多目标优化计算模型。采用自适应进化多目标粒子群优化算法对模型进行优化计算,得到非劣最优解集,为方案决策提供理论依据。仿真结果证实该方法的有效性,为飞机系统综合优化提供一种新思路。     

一类带约束动态多目标优化问题的进化算法

动态多目标约束优化问题是一类NP-Hard问题,定义了动态环境下进化种群中个体的序值和个体的约束度,结合这两个定义给出了一种选择算子.在一种环境变化判断算子下给出了求解环境变量取值于正整数集Z+的一类带约束动态多目标优化问题的进化算法.通过几个典型的Benchmark函数对算法的性能进行了测试,其结果表明新算法能够较好地求出带约束动态多目标优化问题在不同环境下质量较好、分布较均匀的Pareto最优解集.     

基于NSGA-II算法的RLV多目标再入轨迹优化设计

传统的再入轨迹优化设计通常只考虑单目标优化问题,例如最小热流、最小大航程、最小控制能量等。随着人们对降低费用和提高性能的期望越来越高,多目标再入轨迹优化问题也引起了注意。以往人们通过加权因子等方法将多目标问题转化为单目标问题,避免了复杂的多目标优化算法的应用。但也引入了新的参数,且每次优化只能获得与该参数相关的1个解。N SGA-II算法是最近发展起来的具有优良性能的多目标遗传算法,它引入了快速分类、约束支配和精英策略,1次运行可以获得多个Pareto最优解。文中利用N SGA-II算法来求解具有最小热载和最大横程的2个目标的再入轨迹优化问题。算例表明N SGA-II算法能够有效地搜索到优化轨迹的Pareto前沿,是RLV初步设计的有力工具。     

基于（μ＋λ）选择策略的多目标优化分段遗传算法

在多目标优化遗传算法中，将整个种群按目标函数值划分成若干子种群，在各子种群内μ个父代经遗传操作产生λ个后代；然后将各子种群的所有父代和后代个体收集起来进行种群排序适应度共享，选取较好的个体组成下一代种群。相邻的非劣解容易分在同一子种群有利于提高搜索效率；各子种群间的遗传操作可采用并行处理；各子种群的所有
有个体收集起来进行适应度共享有利于维持种群的多样性。最后给出了计算实例。