On decomposition methods in interactive user-preference based optimization

Evolutionary multi-objective optimization (EMO) methodologies have been widely applied to find a well-distributed trade-off solutions approximating to the Pareto-optimal front in the past decades. However, integrating the user-preference into the optimization to find the region of interest (ROI) [1] or preferred Pareto-optimal solutions could be more efficient and effective for the decision maker (DM) straightforwardly. In this paper, we propose several methods by combining preference-based strategy (like the reference points) with the decomposition-based multi-objective evolutionary algorithm (MOEA/D) [2], and demonstrate how preferred sets or ROIs near the different reference points specified by the DM can be found simultaneously and interactively. The study is based on the experiments conducted on a set of test problems with objectives ranging from two to fifteen objectives. Experiments have proved that the proposed approaches are more efficient and effective especially on many-objective problems to provide a set of solutions to the DM's preference, so that a better and a more reliable decision can be made.     

An interactive method using genetic algorithm for multi-objective optimization problems modeled in fuzzy environment

In this paper, an interactive approach based method is proposed for solving multi-objective optimization problems. The proposed method can be used to obtain those Pareto-optimal solutions of the mathematical models of linear as well as nonlinear multi-objective optimization problems modeled in fuzzy or crisp environment which reasonably meet users aspirations. In the proposed method the objectives are treated as fuzzy goals and the satisfaction of constraints is considered at different α-level sets of the fuzzy parameter used. Product operator is used to aggregate the membership functions of the objectives. To initiate the algorithm, the decision maker has to specify his(er) preferences for the desired values of the objectives in the form of reference levels in the membership space. In each iterative phase, a single objective nonlinear (usually nonconvex) optimization problem has to be solved. It is solved using real coded genetic algorithm, MI-LXPM. Based on its outcomes, the decision maker has the option to modify, if felt necessary, some or all of the reference levels in the membership function space before initiating the next iterative phase. The algorithm is stopped where user’s aspirations are reasonably met.     

Introducing robustness in multi-objective optimization

In optimization studies including multi-objective optimization, the main focus is placed on finding the global optimum or global Pareto-optimal solutions, representing the best possible objective values. However, in practice, users may not always be interested in finding the so-called global best solutions, particularly when these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the robust solutions which are less sensitive to small perturbations in variables. Although robust optimization is dealt with in detail in single-objective evolutionary optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find a robust frontier, instead of the global Pareto-optimal frontier in a problem. The first procedure is a straightforward extension of a technique used for single-objective optimization and the second procedure is a more practical approach enabling a user to set the extent of robustness desired in a problem. To demonstrate the differences between global and robust multi-objective optimization principles and the differences between the two robust optimization procedures suggested here, we develop a number of constrained and unconstrained test problems having two and three objectives and show simulation results using an evolutionary multi-objective optimization (EMO) algorithm. Finally, we also apply both robust optimization methodologies to an engineering design problem.     

Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm

Selection of optimum machining parameters is vital to the machining processes in order to ensure the quality of the product, reduce the machining cost, increasing the productivity and conserve resources for sustainability. Hence, in this work a posteriori multi-objective optimization algorithm named as Non-dominated Sorting Teaching–Learning-Based Optimization (NSTLBO) is applied to solve the multi-objective optimization problems of three machining processes namely, turning, wire-electric-discharge machining and laser cutting process and two micro-machining processes namely, focused ion beam micro-milling and micro wire-electric-discharge machining. The NSTLBO algorithm is incorporated with non-dominated sorting approach and crowding distance computation mechanism to maintain a diverse set of solutions in order to provide a Pareto-optimal set of solutions in a single simulation run. The results of the NSTLBO algorithm are compared with the results obtained using GA, NSGA-II, PSO, iterative search method and MOTLBO and are found to be competitive. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal set of solutions will help the decision maker in volatile scenarios and are useful for real production systems.     

Preference representation using Gaussian functions on a hyperplane in evolutionary multi-objective optimization

Many-objective optimization has attracted much attention in evolutionary multi-objective optimization (EMO). This is because EMO algorithms developed so far often degrade their search ability for optimization problems with four or more objectives, which are frequently referred to as many-objective problems. One of promising approaches to handle many objectives is to incorporate the preference of a decision maker (DM) into EMO algorithms. With the preference, EMO algorithms can focus the search on regions preferred by the DM, resulting in solutions close to the Pareto front around the preferred regions. Although a number of preference-based EMO algorithms have been proposed, it is not trivial for the DM to reflect his/her actual preference in the search. We previously proposed to represent the preference of the DM using Gaussian functions on a hyperplane. The DM specifies the center and spread vectors of the Gaussian functions so as to represent his/her preference. The preference handling is integrated into the framework of NSGA-II. This paper extends our previous work so that obtained solutions follow the distribution of Gaussian functions specified. The performance of our proposed method is demonstrated mainly for benchmark problems and real-world applications with a few objectives in this paper. We also show the applicability of our method to many-objective problems.     

An interactive evolutionary multi-objective optimization and decision making procedure

With the advent of efficient techniques for multi-objective evolutionary optimization (EMO), real-world search and optimization problems are being increasingly solved for multiple conflicting objectives. During the past decade of research and application, most emphasis has been spent on finding the complete Pareto-optimal set, although EMO researchers were always aware of the importance of procedures which would help choose one particular solution from the Pareto-optimal set for implementation. This is also one of the main issues on which the classical and EMO philosophies are divided on. In this paper, we address this long-standing issue and suggest an interactive EMO procedure which will involve a decision-maker in the evolutionary optimization process and help choose a single solution at the end. This study uses many year’s of research on EMO and would hopefully encourage both practitioners and researchers to pay more attention in viewing the multi-objective optimization as a aggregate task of optimization and decision-making.     

A preference multi-objective optimization based on adaptive rank clone and differential evolution

Evolutionary multi-objective optimization (EMO) algorithms have been used in various real-world applications. However, most of the Pareto domination based multi-objective optimization evolutionary algorithms are not suitable for many-objective optimization. Recently, EMO algorithm incorporated decision maker’s preferences became a new trend for solving many-objective problems and showed a good performance. In this paper, we first use a new selection scheme and an adaptive rank based clone scheme to exploit the dynamic information of the online antibody population. Moreover, a special differential evolution (DE) scheme is combined with directional information by selecting parents for the DE calculation according to the ranks of individuals within a population. So the dominated solutions can learn the information of the non-dominated ones by using directional information. The proposed method has been extensively compared with two-archive algorithm, light beam search non-dominated sorting genetic algorithm II and preference rank immune memory clone selection algorithm over several benchmark multi-objective optimization problems with from two to ten objectives. The experimental results indicate that the proposed algorithm achieves competitive results.     

基于模糊QoS和偏好权重的Web服务组合方法研究

为了充分体现服务质量(QoS)的不确定性和用户偏好的模糊性,本文将模糊集理论引入基于QoS的Web服务组合中,将不适合精确表示的QoS属性和用户偏好等信息用三角模糊数表示.然后基于权重和法计算模糊总目标,通过设计新的模糊数比较方法,改写Pareto支配关系,将基于模糊数比较的单目标优化问题转化为多目标优化问题,并设计模糊多目标遗传算法(FMOGA)求得Pareto最优解集.该方法不仅能够得到更加贴近实际情况的优化解,同时也解决了多属性决策方法无法对大量候选服务进行全局优化的问题.最后通过实验验证了该算法的有效性和优越性.     

An integrated multi-objective immune algorithm for optimizing the wire bonding process of integrated circuits

Optimization of the wire bonding process of an integrated circuit (IC) is a multi-objective optimization problem (MOOP). In this research, an integrated multi-objective immune algorithm (MOIA) that combines an artificial immune algorithm (IA) with an artificial neural network (ANN) and a generalized Pareto-based scale-independent fitness function (GPSIFF) is developed to find the optimal process parameters for the first bond of an IC wire bonding. The back-propagation ANN is used to establish the nonlinear multivariate relationships between the wire boning parameters and the multi-responses, and is applied to generate the multiple response values for each antibody generated by the IA. The GPSIFF is then used to evaluate the affinity for each antibody and to find the non-dominated solutions. The “Error Ratio” is then applied to measure the convergence of the integrated approach. The “Spread Metric” is used to measure the diversity of the proposed approach. Implementation results show that the integrated MOIA approach does generate the Pareto-optimal solutions for the decision maker, and the Pareto-optimal solutions have good convergence and diversity performance.     

A non dominated ranking Multi Objective Genetic Algorithm and electre method for unequal area facility layout problems

The unequal area facility layout problem (UA-FLP) comprises a class of extremely difficult and widely applicable optimization problems arising in diverse areas and meeting the requirements for real-world applications. Genetic Algorithms (GAs) have recently proven their effectiveness in finding (sub) optimal solutions to many NP-hard problems such as UA-FLP. A main issue in such approach is related to the genetic encoding and to the evolutionary mechanism implemented, which must allow the efficient exploration of a wide solution space, preserving the feasibility of the solutions and ensuring the convergence towards the optimum. In addition, in realistic situations where several design issues must be taken into account, the layout problem falls in the broader framework of multi-objective optimization problems. To date, there are only a few multi-objective FLP approaches, and most of them employ over-simplified optimization techniques which eventually influence the quality of the solutions obtained and the performance of the optimization procedure. In this paper, this difficulty is overcome by approaching the problem in two subsequent steps: in the first step, the Pareto-optimal solutions are determined by employing Multi Objective Genetic Algorithm (MOGA) implementing four separate fitness functions within a Pareto evolutionary procedure, following the general structure of Non-dominated Ranking Genetic Algorithm (NRGA) and the subsequent selection of the optimal solution is carried out by means of the multi-criteria decision-making procedure Electre. This procedure allows the decision maker to express his preferences on the basis of the knowledge of candidate solution set. Quantitative and qualitative objectives are considered referring to the slicing-tree layout representation scheme. The numerical results obtained outperform previous referenced approaches, thus confirming the effectiveness of the procedure proposed.     

Incorporation of implicit decision-maker preferences in multi-objective evolutionary optimization using a multi-criteria classification method

Nowadays, most Multi-Objective Evolutionary Algorithms (MOEA) concentrate mainly on searching for an approximation of the Pareto frontier to solve a multi-objective optimization problem. However, finding this set does not completely solve the problem. The decision-maker (DM) still has to choose the best compromise solution from that set. But as the number of criteria increases, several important difficulties arise in performing this task. Identifying the Region of Interest (ROI), according to the DM’s preferences, is a promising alternative that would facilitate the selection process. This paper approaches the incorporation of preferences into a MOEA in order to characterize the ROI by a multi-criteria classification method. This approach is called Hybrid Multi-Criteria Sorting Genetic Algorithm and is composed of two phases. First, a metaheuristic is used to generate a small set of solutions that are classified in ordered categories by the DM. Thus, the DM’s preferences will be reflected indirectly in this set. In the second phase, a multi-criteria sorting method is combined with an evolutionary algorithm. The first one is used to classify new solutions. Those classified as ‘satisfactory’ are used for creating a selective pressure towards the ROI. The effectiveness of our method was proved in nine instances of a public project portfolio problem. The obtained results indicate that our approach achieves a good characterization of the ROI, and outperforms the standard NSGA-II in simple and complex problems. Also, these results confirm that our approach is able to deal with many-objective problems.     

Using multi-population intelligent genetic algorithm to find the pareto-optimal parameters for a nano-particle milling process

Nano-particle materials have been widely applied in many industries and the wet-type mechanical milling process is a popular powder technology to produce the nano-particles. Since the milling process involves a number of process parameters and the multi-objective quality criteria, it is very important to set the optimal milling process parameters in order to achieve the desired multiple quality criteria. In this study, a new multi-objective evolutionary algorithm (MOEA), called the multi-population intelligent genetic algorithm (MPIGA), is proposed to find the optimal process parameters for the nano-particle milling process. In the new method, the orthogonal array (OA) experiment is first applied to obtain the analytic data of the milling process. Then the response surface method (RSM) is applied to model the nano-particle milling process and to determine the objective (fitness) value. The generalized Pareto-based scale-independent fitness function (GPSIFF) is then used to evaluate the Pareto solutions. Finally, the MPIGA is proposed to find the Pareto-optimal solutions. The results show that the integrated MPIGA approach can generate the Pareto-optimal solutions for the decision maker to determine the optimal parameters and to achieve the desired product qualities for a nano-particle milling process.     

Unsatisfying functions and multiobjective fuzzy satisfaction design using genetic algorithms

This paper describes a new fuzzy satisfaction method using genetic algorithms (GA) for multiobjective problems. First, an unsatisfying function, which has a one-to-one correspondence with the membership function, is introduced for expressing "fuzziness". Next, the multiobjective design problem is transformed into a satisfaction problem of constraints by introducing an aspiration level for each objective. Here, in order to handle the fuzziness involved in aspiration levels and constraints, the unsatisfying function is used, and the problem is formulated as a multiobjective minimization problem of unsatisfaction ratings. Then, a GA is employed to solve the problem, and a new strategy is proposed to obtain a group of Pareto-optimal solutions in which the decision maker (DM) is interested. The DM can then seek a satisfaction solution by modifying parameters interactively according to preferences.     

A multi-objective genetic algorithm approach for solving feature addition problem in feature fatigue analysis

Feature fatigue (FF) is used to represent the phenomenon of customer’s inconsistent satisfaction with products: customers prefer to choose products with more features and capabilities initially, but after having worked with a product, they become frustrated or dissatisfied with the usability problems caused by too many features. To “defeat” FF, it is essential for designers to decide what features should be added when developing a product to make the product attractive enough and not too hard to use at the same time. In this paper, a feature fatigue multi-objective genetic algorithm (FFMOGA) method is reported for solving the feature addition problem. In the proposed method, fitness functions are established based on Bayesian networks, which can represent the uncertain customer preferences and reflect the relationships among features. The computational experiments on a smart phone case show that the FFMOGA approach can find multiple solutions along the Pareto-optimal frontier for designers to select from, and these obtained solutions have good performance in convergence.     

An adaptive evolutionary multi-objective approach based on simulated annealing

A multi-objective optimization problem can be solved by decomposing it into one or more single objective subproblems in some multi-objective metaheuristic algorithms. Each subproblem corresponds to one weighted aggregation function. For example, MOEA/D is an evolutionary multi-objective optimization (EMO) algorithm that attempts to optimize multiple subproblems simultaneously by evolving a population of solutions. However, the performance of MOEA/D highly depends on the initial setting and diversity of the weight vectors. In this paper, we present an improved version of MOEA/D, called EMOSA, which incorporates an advanced local search technique (simulated annealing) and adapts the search directions (weight vectors) corresponding to various subproblems. In EMOSA, the weight vector of each subproblem is adaptively modified at the lowest temperature in order to diversify the search toward the unexplored parts of the Pareto-optimal front. Our computational results show that EMOSA outperforms six other well established multi-objective metaheuristic algorithms on both the (constrained) multi-objective knapsack problem and the (unconstrained) multi-objective traveling salesman problem. Moreover, the effects of the main algorithmic components and parameter sensitivities on the search performance of EMOSA are experimentally investigated.     

基于决策者偏好区域的多目标粒子群算法研究*

多目标优化问题中,决策者往往只对目标空间的某一区域感兴趣,因此需要在这一特定的区域能够得到比较稠密的Pareto解,但传统的方法却找出全部的Pareto前沿,决策效率不高。针对该问题,给出了基于决策者偏好区域的多目标粒子群优化算法。它只求出与决策者偏好区域相关的部分Pareto最优集,从而减少了进化代数,加快收敛速度,有利于决策者进行更有效的决策。算法把解与偏好区域的距离作为影响引导者选择和剪枝策略的一个因素,运用格栅方法实现解在Pareto边界分布的均匀性。仿真结果表明该算法是有效的。     

The methodology of multiple-criteria decision making in the optimization of an urban transportation system: case study of Poznań City in Poland

The methodology of multiple-criteria decision making applied to the optimization of an urban transportation system is presented in the paper. Three mathematical models of different complexity are constructed to optimize the allocation of vehicles to certain routes in a mass transit system. All models take into account both passengers' and operator's objectives. The optimization problems are formulated in terms of multiple-objective fuzzy linear programming and multiple-objective non-linear programming. The sensitivity and precision analysis of the models is carried out. Two interactive multi-objective mathematical programming procedures are utilized to solve the problems. They generate samples of Pareto-optimal compromise solutions and provide the decision maker (DM)with an effective tool that supports him/her in the decision making process. Finally, the DM selects the solution that best fits his or her expectations.     

三种基于偏好的区间多目标进化算法及应用

区间参数多目标优化问题是普遍存在且非常重要的。目前直接求解该类问题的进化优化方法非常少,且已有方法的目的是找到收敛性好且分布均匀的Pareto最优解集。为得到符合决策者偏好的最满意解,本文综述3种基于偏好的区间多目标进化算法,并将其应用于特定环境下机器人路径规划问题,比较3种算法的性能。研究结果可丰富特定环境下机器人路径规划的求解方法,提高机器人路径优化效果。     

机组短期负荷环境／经济调度多目标混合优化

环境/经济短期负荷调度主要由调度周期内的最优机组组合和负荷环境/经济分配组成,本文将变权重多目标进化算法与混沌局部优化相结合形成混合优化算法应用到电站机组环境/经济运行多目标优化问题中,在混合多目标优化算法中采用组合结构基因,其中机组基因用于机组组合全局粗寻优,参数基因用于负荷分配局部优化,基因修正与罚函数结合解决约束问题．通过对优秀个体进行基于线性搜索的混沌局部优化,可加快收敛速度和降低计算时间．实例仿真结果说明所提出的算法能获得较好分布的Pareto优化解．     

Optimizing security and quality of service in a Real-time database system using Multi-objective genetic algorithm

Both network security and quality of service (QoS) consume computational resource of IT system and thus may evidently affect the application services. In the case of limited computational resource, it is important to model the mutual influence between network security and QoS, which can be concurrently optimized in order to provide a better performance under the available computational resource. In this paper, an evaluation model is accordingly presented to describe the mutual influence of network security and QoS, and then a multi-objective genetic algorithm NSGA-II is revised to optimize the multi-objective model. Using the intrinsic information from the target problem, a new crossover approach is designed to further enhance the optimization performance. Simulation results validate that our algorithm can find a set of Pareto-optimal security policies under different network workloads, which can be provided to the potential users as the differentiated security preferences. These obtained Pareto-optimal security policies not only meet the security requirement of the user, but also provide the optimal QoS under the available computational resource.