On finding and detecting efficient assignments in the case of multiple inputs and outputs

An interesting variant of the assignment problem is the case where each partial assignment of an individual to a job involves multiple inputs and outputs. In this paper, three issues about this problem are discussed: finding an efficient assignment, verifying the efficiency of a solution and restoring the efficiency of an inefficient assignment. For the first issue, a current method, proposed by Chen and Lu, is compared with a proposed multiobjective formulation and for the second and third ones, a two-phase method is developed, which is based on the simplex method and the Dantzig–Wolfe decomposition algorithm.     

基于自适应变异的多目标鸽群优化的无人机目标搜索

无人机在搜索任务中起着关键的作用,它能够在复杂环境中寻找到目标.无人机搜索问题是一个相对复杂的多约束条件下的多目标优化问题.大多数搜索算法不能满足搜索过程中高效率和低功耗的要求.本文所采用的目标搜索方法是一种基于Agent路由和光传感器的解耦滚动时域方法.为了优化目标搜索方法的参数,本文提出一种基于Agent路由和光传感器的自适应变异多目标鸽群优化(AMMOPIO)算法.利用自适应飞行机制可以获得较好的鸽群分布,种群具有多样性和收敛性.利用变异机制简化了鸽群优化算法中的模型,提高了搜索效率.实验仿真结果验证了所提出的AMMOPIO算法在目标搜索问题中的可行性和有效性.     

DEA nonradial efficiency based on vector properties

Classic data envelopment analysis (DEA) models determine the efficiency of productive units, called decision making units (DMUs). DEA uses as its methodology the equiproportional reduction of inputs or increase of outputs and the finding of a single target for each DMU. This target does not incorporate the preference of the decision maker. Later works propose obtaining alternative targets based on nonradial projections on the efficiency frontier that are obtained through nonproportional variations of inputs or outputs. However, the efficiencies are not calculated for these alternative targets. This impedes a comparison among the DMUs. Thus, diverse nonradial efficiency indexes have been proposed based on mathematical averages or weighted averages that do not consider the vectorial characteristics of the efficiency. In this work, we present a nonradial efficiency index based on the initial concept of efficiency associated with each alternative (nonradial) target obtained through a multiobjective model of an inefficient DMU.     

混合个体选择机制的多目标进化算法

在多目标进化算法中,如何从后代候选集中选择最优解,显著地影响优化过程.当前,最优解的选择方式主要是基于实际目标值或者代理模型估计目标值.然而,这些选择方式往往是非常耗时或者存在精度差等问题,特别是对于一些实际的复杂优化问题.最近,一些研究人员开始利用有监督分类辅助后代选择,但是这些工作难以准备准确的正例和负例样本,或者存在耗时的参数调整等问题.为了解决这些问题,提出了一种新颖的融合分类与代理的混合个体选择机制,用于从后代候选集中选择最优解.在每一代优化中,首先利用分类器选择优良解;然后设计了一个轻量级的代理模型用于估计优良解的目标值;最后利用这些目标值对优良解进行排序,并选择最优解作为后代解.基于典型的多目标进化算法MOEA/D,利用混合个体选择机制设计了新的算法框架MOEA/D-CS.与当前流行的基于分解多目标进化算法比较,实验结果表明,所提出的算法取得了最好的性能.     

A multiobjective approach to fleet, fuel and operating cost efficiency of European airlines

In this paper, a multiobjective DEA approach to airlines target setting has been proposed allowing for more control and flexibility in the determination of the trade-offs among environmental impact, fleet cost and operating cost. These variables are considered as inputs. Revenue Tonne-Kilometres (RTK) is the single output considered. For each airline, the proposed multiobjective Linear Programming model is solved using ADBASE, which finds all extreme efficient points in the Pareto Frontier. The representation of the Pareto Frontier as a function of RTK gives cues about the growth of the inputs and about their trade-offs with increasing output. Also, the technical efficiency of each airline has been assessed using a Slacks-Based Measure (SBM) of efficiency. The results show that about half of the airlines are technically inefficient and that most of the airlines operate below their Most Productive Scale Size which suggests that more industry consolidation is foreseeable in the future. Overall, although operating costs seem to be under control, there is an 8% overcapacity in terms of assets and a 7.2% excess carbon emissions. There is also room for an additional 4.4% overall traffic increase.     

Solving Multiobjective Optimization Problems Using an Artificial Immune System

In this paper, we propose an algorithm based on the clonal selection principle to solve multiobjective optimization problems (either constrained or unconstrained). The proposed approach uses Pareto dominance and feasibility to identify solutions that deserve to be cloned, and uses two types of mutation: uniform mutation is applied to the clones produced and non-uniform mutation is applied to the not so good antibodies (which are represented by binary strings that encode the decision variables of the problem to be solved). We also use a secondary (or external) population that stores the nondominated solutions found along the search process. Such secondary population constitutes the elitist mechanism of our approach and it allows it to move towards the true Pareto front of a problem over time. Our approach is compared with three other algorithms that are representative of the state-of-the-art in evolutionary multiobjective optimization. For our comparative study, three metrics are adopted and graphical comparisons with respect to the true Pareto front of each problem are also included. Results indicate that the proposed approach is a viable alternative to solve multiobjective optimization problems.     

一种基于免疫原理的多目标优化方法

借鉴生物免疫原理中抗体多样性产生及保持的机理，建立了一种多目标优化方法．该方法定义了多目标选择熵和浓度调节选择概率的概念，采用了抗体克隆选择策略和高度变异策略．最后采用四种典型的多目标优化函数，将本方法同几种常用的多目标遗传算法进行了比较研究，证明了所建立的基于免疫原理的多目标优化方法能有效解决多目标优化问题且具有一定的优越性．     

面向多目标流水车间调度的多种群多目标遗传算法

针对制造型企业普遍存在的流水车间调度问题,建立了以最小化最迟完成时间和总延迟时间为目标的多目标调度模型,并提出一种基于分解方法的多种群多目标遗传算法进行求解.该算法将多目标流水车间调度问题分解为多个单目标子问题,并分阶段地将这些子问题引入到算法迭代过程进行求解.算法在每次迭代时,依据种群的分布情况选择各子问题的最好解及与其相似的个体分别为当前求解的子问题构造子种群,通过多种群的进化完成对多个子问题最优解的并行搜索.通过对标准测试算例进行仿真实验,结果表明所提出的算法在求解该问题上能够获得较好的非支配解集.     

Solving multiobjective problems using cat swarm optimization

This paper proposes a new multiobjective evolutionary algorithm (MOEA) by extending the existing cat swarm optimization (CSO). It finds the nondominated solutions along the search process using the concept of Pareto dominance and uses an external archive for storing them. The performance of our proposed approach is demonstrated using standard test functions. A quantitative assessment of the proposed approach and the sensitivity test of different parameters is carried out using several performance metrics. The simulation results reveal that the proposed approach can be a better candidate for solving multiobjective problems (MOPs).     

An MO‐GVNS algorithm for solving a multiobjective hybrid flow shop scheduling problem

This paper addresses the multiobjective hybrid flow shop (MOHFS) scheduling problem. In the MOHFS problem considered here, we have a set of jobs that must be performed in a set of stages. At each stage, we have a set of unrelated parallel machines. Some jobs may skip stages. The evaluation criteria are the minimizations of makespan, the weighted sum of the tardiness, and the weighted sum of the earliness. For solving it, an algorithm based on the multiobjective general variable neighborhood search (MO‐GVNS) metaheuristic, named adapted MO‐GVNS, is proposed. This work also presents and compares the results obtained by the adapted MO‐GVNS with those of four other algorithms: multiobjective reduced variable neighborhood search, nondominated sorting genetic algorithm II (NSGA‐II), and NSGA‐III, and another MO‐GVNS from the literature. The results were evaluated based on the Hypervolume, Epsilon, and Spacing metrics, and statistically validated by the Levene test and confidence interval charts. The results showed the efficiency of the proposed algorithm for solving the MOHFS problem.     

Adaptive weighted-sum method for bi-objective optimization: Pareto front generation

This paper presents a new method that effectively determines a Pareto front for bi-objective optimization with potential application to multiple objectives. A traditional method for multiobjective optimization is the weighted-sum method, which seeks Pareto optimal solutions one by one by systematically changing the weights among the objective functions. Previous research has shown that this method often produces poorly distributed solutions along a Pareto front, and that it does not find Pareto optimal solutions in non-convex regions. The proposed adaptive weighted sum method focuses on unexplored regions by changing the weights adaptively rather than by using a priori weight selections and by specifying additional inequality constraints. It is demonstrated that the adaptive weighted sum method produces well-distributed solutions, finds Pareto optimal solutions in non-convex regions, and neglects non-Pareto optimal solutions. This last point can be a potential liability of Normal Boundary Intersection, an otherwise successful multiobjective method, which is mainly caused by its reliance on equality constraints. The promise of this robust algorithm is demonstrated with two numerical examples and a simple structural optimization problem.     

基于分解和多策略变异的多目标差分进化算法*

差分进化是一种有效的优化技术,已成功用于多目标优化问题。但也存在Pareto最优集合的收敛慢和多样性差等问题。针对上述不足,本文提出了一种基于分解和多策略变异的多目标差分进化算法(MODE/DMSM)。该算法利用基于分解的方法将多目标优化问题分解为多个单目标优化问题;通过高效的非支配排序方法选择具有良好收敛性和多样性的解来指导差分进化过程;采用了多策略变异方法来平衡进化过程中收敛性和多样性。在ZDT和DTLZ的10个测试函数上的仿真结果表明,本文算法在Parato最优集合的收敛性和多样性优于其他六种代表性多目标优化算法。     

Multiobjective optimization–based fault‐tolerant flight control system design

The loss of measurements used for controller scheduling or envelope protection in modern flight control systems due to sensor failures leads to a challenging fault‐tolerant control law design problem. In this article, an approach to design such a robust fault‐tolerant control system, including full envelope protections using multiobjective optimization techniques, is proposed. The generic controller design and controller verification problems are derived and solved using novel multiobjective hybrid genetic optimization algorithms. These algorithms combine the multiobjective genetic search strategy with local, single‐objective optimization to improve convergence speed. The proposed strategies are applied to the design of a fault‐tolerant flight control system for a modern civil aircraft. The results of an industrial controller verification and validation campaign using an industrial benchmark simulator are reported.     

Using interactive multiobjective methods to solve DEA problems with value judgements

Data envelopment analysis (DEA) is a performance measurement tool that was initially developed without consideration of the decision maker (DM)'s preference structures. Ever since, there has been a wide literature incorporating DEA with value judgements such as the goal and target setting models. However, most of these models require prior judgements on target or weight setting. This paper will establish an equivalence model between DEA and multiple objective linear programming (MOLP) and show how a DEA problem can be solved interactively without any prior judgements by transforming it into an MOLP formulation. Various interactive multiobjective models would be used to solve DEA problems with the aid of PROMOIN, an interactive multiobjective programming software tool. The DM can then search along the efficient frontier to locate the most preferred solution where resource allocation and target levels based on the DM's value judgements can be set. An application on the efficiency analysis of retail banks in the UK is examined. Comparisons of the results among the interactive MOLP methods are investigated and recommendations on which method may best fit the data set and the DM's preferences will be made.     

镁砂熔炼过程全厂电能分配实时多目标优化方法研究

镁砂熔炼过程具有多工况、群炉并行生产、高能耗等特点.在全厂供电容量约束下,为了最大化能源使用效率,需要根据全厂每台炉子的工况变化实时分配电能,实现全厂镁砂单位能耗与平均品位的多目标优化. 本文基于最小二乘支持向量机技术建立了镁砂熔炼过程全厂电能分配优化模型.根据不同工况下降低镁炉供电量对镁砂熔炼过程的影响程度,提出了基于工况优先级的电能分配策略.根据主熔工况下镁砂产量与品位指标函数的特性分析,推导出 主熔工况下电能分配模型决策变量维数缩减的条件. 为了提高多目标优化算法的运行效率,设计了一种快速非支配解集构造方法,用来提高传统多目标粒子群优化算法的寻优效率. 基于标准测试问题与现场实际例子对所提出的方法进行了检验.基于现场例子的实验结果证明所提出的方法能够避免工厂出现的用电超容量情况,并且提高了全厂用电效率.     

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

The conventional unconstrained binary quadratic programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQP instances with two and three objectives.     

求解多目标问题的Memetic免疫优化算法

将基于Pareto支配关系的局部下山算子和差分算子引入免疫多目标优化算法之中,提出了一种求解多目标问题的Memetic免疫优化算法(Memetic immune algorithm for multiobjective optimization,简称MIAMO).该算法利用种群中抗体在决策空间上的位置关系设计了两种有效的启发式局部搜索策略,提高了免疫多目标优化算法的求解效率.仿真实验结果表明,MIAMO与其他4种有效的多目标优化算法相比,不仅在求得Pareto最优解集的逼近性、均匀性和宽广性上有明显优势,而且算法的收敛速度与免疫多目标优化算法相比明显加快.     

Nonlinear multiobjective model-predictive control scheme for wastewater treatment process

A nonlinear multiobjective model-predictive control (NMMPC) scheme, consisting of self-organizing radial basis function (SORBF) neural network prediction and multiobjective gradient optimization, is proposed for wastewater treatment process (WWTP) in this paper. The proposed NMMPC comprises a SORBF neural network identifier and a multiple objectives controller via the multi-gradient method (MGM). The SORBF neural network with concurrent structure and parameter learning is developed as a model identifier for approximating on-line the states of WWTP. Then, this NMMPC optimizes the multiple objectives under different operating functions, where all the objectives are minimized simultaneously. The solution of optimal control is based on the MGM which can shorten the solution time. Moreover, the stability and control performance of the closed-loop control system are well studied. Numerical simulations reveal that the proposed control strategy gives satisfactory tracking and disturbance rejection performance for WWTP. Experimental results show the efficacy of the proposed method.     

Taylor series approach to fuzzy multiobjective linear fractional programming

This paper presents the use of a Taylor series for fuzzy multiobjective linear fractional programming problems (FMOLFP). The Taylor series is a series expansion that a representation of a function. In the proposed approach, membership functions associated with each objective of fuzzy multiobjective linear fractional programming problem transformed by using a Taylor series are unified. Thus, the problem is reduced to a single objective. Practical applications and numerical examples are used in order to show the efficiency and superiority of the proposed approach.