A Relationship between optimality and efficiency in multicriteria 0–1 programming problems

An efficient or nondominated solution to a multicriteria minimization problem is a feasible solution for which a decrease in the value of any criterion can only be obtained if the value of at least one other criterion is increased. Interest in the conditions under which solutions to multicriteria programming problems can be shown to be efficient has grown enormously in recent years, not least of all due to the awareness that significant planning problems can only be meaningfully modelled if multiple measures of effectiveness are considered. However, the broad class of multicriteria 0–1 programming problems, which are of great practical importance, has received only limited attention in the literature. We establish the identity of the set of efficient solutions with respect to such multicriteria programming problems with any criteria and any constraint set and the set of optimal solutions to a parametrized unicriterion problem incorporating these criteria. Illustrative numerical examples are provided.     

A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm

Genetic algorithms (GAs), which are directed stochastic hill climbing algorithms, are a commonly used optimization technique and are generally applied to single criterion optimization problems with fairly complex solution landscapes. There has been some attempts to apply GA to multicriteria optimization problems. The GA selection mechanism is typically dependent on a single-valued objective function and so no general methods to solve multicriteria optimization problems have been developed so far. In this paper, a new method of transformation of the multiple criteria problem into a single-criterion problem is presented. The problem of transformation brings about the need for the introduction of thePareto set estimation method to perform the multicriteria optimization using GAs. From a given solution set, which is the population of a certain generation of the GA, the Pareto set is found. The fitness of population members in the next GA generation is calculated by a distance metric with a reference to the Pareto set of the previous generation. As we are unable to combine the objectives in some way, we resort to this distance metric in the positive Pareto space of the previous solutions, as the fitness of the current solutions. This new GA-based multicriteria optimization method is proposed here, and it is capable of handling any generally formulated multicriteria optimization problem. The main idea of the method is described in detail in this paper along with a detailed numerical example. Preliminary computer generated results show that our approach produces better, and far more Pareto solutions, than plain stochastic optimization methods.     

A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

New challenges in engineering design lead to multiobjective (multicriteria) problems. In this context, the Pareto front supplies a set of solutions where the designer (decision-maker) has to look for the best choice according to his preferences. Visualization techniques often play a key role in helping decision-makers, but they have important restrictions for more than two-dimensional Pareto fronts. In this work, a new graphical representation, called Level Diagrams, for n-dimensional Pareto front analysis is proposed. Level Diagrams consists of representing each objective and design parameter on separate diagrams. This new technique is based on two key points: classification of Pareto front points according to their proximity to ideal points measured with a specific norm of normalized objectives (several norms can be used); and synchronization of objective and parameter diagrams. Some of the new possibilities for analyzing Pareto fronts are shown. Additionally, in order to introduce designer preferences, Level Diagrams can be coloured, so establishing a visual representation of preferences that can help the decision-maker. Finally, an example of a robust control design is presented - a benchmark proposed at the American Control Conference. This design is set as a six-dimensional multiobjective problem.     

Decision making with multiple objectives using GAI networks

This paper deals with preference representation on combinatorial domains and preference-based recommendation in the context of multicriteria or multiagent decision making. The alternatives of the decision problem are seen as elements of a product set of attributes and preferences over solutions are represented by generalized additive decomposable (GAI) utility functions modeling individual preferences or criteria. Thanks to decomposability, utility vectors attached to solutions can be compiled into a graphical structure closely related to junction trees, the so-called GAI network. Using this structure, we present preference-based search algorithms for multicriteria or multiagent decision making. Although such models are often non-decomposable over attributes, we actually show that GAI networks are still useful to determine the most preferred alternatives provided preferences are compatible with Pareto dominance. We first present two algorithms for the determination of Pareto-optimal elements. Then the second of these algorithms is adapted so as to directly focus on the preferred solutions. We also provide results of numerical tests showing the practical efficiency of our procedures in various contexts such as compromise search and fair optimization in multicriteria or multiagent problems.     

A DSS for distributed computer system design in the presence of multiple conflicting objectives

The design of distributed computer systems (DCS) requires compromise among several desirable and conflicting objectives. Design tools for this purpose should, therefore, facilitate the process of making such tradeoffs. To this end, this paper presents a prototype Decision Support System (DSS) which uses multicriteria decisions making techniques as the underlying methodology to aid the designer in making compromises in a systematic and efficient manner.While there are several isolated subproblems of DCS design that can be modelled and solved quantitatively, there are also, many design aspects that are difficult to quantify and/or formalize. Thus the design process requires a synthesis of analytic model execution and informed judgement on the part of the designer. The DSS aids in this iterative process by executing appropriate models and generating a sequence of ‘Pareto-optimal’ or non-dominated set of solution vectors. The relatively unstructured task of making tradeoffs among the components of each vector is left in the hands of the designer. Efficiency is achieved by avoiding needles search through clearly inferior solutions and focusing on non-dominated ones only. Various details of the prototype, implemented on a UNIVAC 1100 and an IBM PC AT, are highlighted in an example session. The potential advantages of using multicriteria techniques as opposed to the widespread practice of using single criteria optimization methods are also noted in this paper.     

一种基于单接口多信道无线Mesh网路由协议改进

在无线Mesh网中,MCRP是一种单收发器多信道路由协议;通过对该协议的分析,针对协议中存在的缺陷,即在链路断开后触发链路修复或链路发现造成的较大网络开销,引入一种阀值估算算法对其进行改进,提出了一种基于链路预测的路由协议PRE-MCRP;并由NS2仿真实验证明,与标准的MCRP协议和AODV协议相比较,PRE-MCRP协议不仅有效地降低了控制开销和端到端的传输时延,而且增加了数据包的投递率,改善了网络性能。     

Neural network approach for multicriteria solid transportation problem

In this paper, we propose neural network approach for multicriteria solid transportation problems(STP). First we suggest a neural network architecture to solve single-objective STP according to augmented Lagrange multiplier method. Due to the massive computing unit-neurons and parallel mechanism of neural network approach can solve the large scale problem efficiently and optimal solution can be got. Then we transform the original multicriteria problem into a single objective problem by global criteria method and adopt the neural network approach to solve it. By this way we can get the satisfactory solution of the original problem. The procedure and efficiency of this approach are shown with numerical simulations.     

A Multicriteria Method for Identification and Forecasting

A multicriteria approach to identify and forecast mathematical models is considered. The need for such an approach arises, in particular, when it is necessary to take into account errors that cannot be reduced to one function and in the absence of specific information about the data interference class. The paper deals with a multicriteria version of the identification sets method based on approximating and visualizing the graph of the vector function of identification errors and its projections onto the space of identification parameters. The nearness function is introduced that describes the proximity of a criterion point to the set of nonimprovable (Pareto efficient) solutions of the identification problem. The efficient criteria set (Pareto frontier), the sets of efficient and subefficient parameters, and the corresponding forecast trajectory tubes are studied. To construct these objects, methods for approximating implicitly specified sets are used, in particular, methods for approximating the Edgeworth–Pareto hull and the deep holes method. The technique and examples for two criteria of identification quality are considered in detail.     

面向卷积神经网络的高并行度FPGA加速器设计

大多数基于卷积神经网络（CNN）的算法都是计算密集型和存储密集型的,很难应用于具有低功耗要求的航天、移动机器人、智能手机等嵌入式领域。针对这一问题,提出一种面向CNN的高并行度现场可编程逻辑门阵列（FPGA）加速器。首先,比较研究CNN算法中可用于FPGA加速的4类并行度;然后,提出多通道卷积旋转寄存流水（MCRP）结构,简洁有效地利用了CNN算法的卷积核内并行;最后,采用输入输出通道并行+卷积核内并行的方案提出一种基于MCRP结构的高并行度CNN加速器架构,并将其部署到XILINX的XCZU9EG芯片上,在充分利用片上数字信号处理器（DPS）资源的情况下,峰值算力达到2 304 GOPS。以SSD-300算法为测试对象,该CNN加速器的实际算力为1 830.33 GOPS,硬件利用率达79.44%。实验结果表明,MCRP结构可有效提高CNN加速器的算力,基于MCRP结构的CNN加速器可基本满足嵌入式领域大部分应用的算力需求。     

A strategy of multi-criteria decision-making task ranking in social-networks

In this paper, we formulate an interesting problem of multicriteria decision-making task ranking in social networks (MCDM-TR). MCDM-TR contains two phases: (1) finding a set of decision-making experts for tasks who not only complete the decision-making of the given task but also have the minimal communication cost among them; (2) ranking the decision-made tasks according to a certain decision standard. In this paper, we focus on these two phases and propose an efficient algorithm for multicriteria decision-making tasks in social networks. A case study of academic conferences quality evaluation system (ACQES) is also studied to illustrate our strategy.     

Towards combinatorial evolution of composite systems

The paper describes combinatorial evolution of composite systems. The approach consists of the following stages: (i) design of general hierarchical structure of the examined system; (ii) design of structures for several series system generations; (iii) extraction of changes between the system generations as a set of change items and their evaluation (multicriteria analysis including usage of interval multiset estimates, binary relations over the items: compatibility, complementarity, precedence); (iv) combinatorial synthesis of system forecast(s) as selection of prospective change items while taking into account total constraint(s) (multiple choice problem) or morphological design while taking into account compatibility between the selected change items; (v) aggregation of the obtained system forecast into a resultant forecast. The approach was used for modeling of combinatorial evolution in several applications: (1) DSS COMBI for multicriteria ranking, (2) electronic equipment for image processing, (3) standard for transmission of multimedia information (MPEG, MPEG 2, MPEG 4), and (4) ZigBee communication protocol for wireless sensor network. In the article, the suggested approach is illustrated by evolution of three author courses on multicriteria decision making and modular system design. The following is presented: (a) hierarchical structures of the courses, (b) change items between the courses, (c) combinatorial design of prospective forecasts, (d) aggregation of the forecast into a resultant one.     

Literature review of reuse in business process modeling

Business process models play an important role in the analysis and improvement of the performance of an enterprise. Evidently, the quality of a business process model has a direct effect on the business performance. This evidence has motivated both the academic and industrial communities to look for suitable methods for creating good quality business process models. In particular, there is a wide agreement that reuse can accelerate the design process and produce high quality solutions by adopting best practices and agreed-up-on solutions. However, faced with various types of reusable artifacts, business process designers need a set of criteria to determine which type would suit best their needs and design context. To assist designers in their choice, we first present a set of criteria influencing the design phase in terms of effort required and the quality of the resulting model. Secondly, we use this set of criteria to present a state of the art on the most significant reusable design artifacts.     

Prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to multicriteria decision-making

A trapezoidal intuitionistic fuzzy set, some operational laws, score and accuracy functions for trapezoidal intuitionistic fuzzy values are presented in this paper. Then, the trapezoidal intuitionistic fuzzy prioritized weighted averaging (TIFPWA) operator and trapezoidal intuitionistic fuzzy prioritized weighted geometric (TIFPWG) operator are proposed to aggregate the trapezoidal intuitionistic fuzzy information. Furthermore, a multicriteria decision-making method based on the TIFPWA and TIFPWG operators and the score and accuracy functions of trapezoidal intuitionistic fuzzy values is established to deal with the multicriteria decision-making problem in which the criteria are in different priority level. Finally, a practical example about software selection for considering various prioritized relationships between the criteria of decision-making is given to demonstrate its practicality and effectiveness.     

Improved method of multicriteria fuzzy decision-making based on vague sets

An improved method is presented, which provides improved score functions to measure the degree of suitability of each of a set of alternatives, with respect to a set of criteria presented with vague values. The improved algorithm for score functions is introduced by taking into account the effect of an unknown degree (hesitancy degree) of the vague values on the degree of suitability to which each alternative satisfies the decision-maker’s requirement. The meaning of the proposed function is more transparent than that of other existing functions, which are not reasonable in some cases. The proposed function illustrates that it has stronger discrimination in comparison with previous functions. The applicability of this improved multicriteria fuzzy decision-making approach is also demonstrated by means of examples. The improved method can be used to rank the decision alternatives according to the decision criteria. The functions proposed in this paper can provide a more useful technique than previous functions, in order to efficiently help the decision-maker.     

Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems

Facility layout design (FLD) has a very important effect on the performance of a manufacturing system. The concept of FLD is usually considered as a multiobjective problem. For this reason, a layout generation and its evaluation are often challenging and time consuming due to their inherent multiple objectives in nature and their data collection process. In addition, an effective facility layout evaluation procedure necessitates the consideration of qualitative criteria, e.g., flexibility in volume and variety and quality related to the product and production, as well as quantitative criteria such as material handling cost, adjacency score, shape ratio, and material handling vehicle utilization in the decision process. This paper presents a decision-making methodology based on data envelopment analysis (DEA), which uses both quantitative and qualitative criteria, for evaluating FLD. The criteria that are to be minimized are viewed as inputs whereas the criteria to be maximized are considered as outputs. A computer-aided layout-planning tool, VisFactory, is adopted to facilitate the layout alternative design process as well as to collect quantitative data by using exact and vague data by means of fuzzy set theory. Analytic hierarchy process (AHP) is then applied to collect qualitative data related to quality and flexibility. The DEA methodology is used to solve the layout design problem by simultaneously considering both the quantitative and qualitative data. The purposed integrated procedure is applied to a real data set of a case study, which consists of 19 FLDs provided of the plastic profile production system.     

An AHP-based decision-making tool for the solution of multiproduct batch plant design problem under imprecise demand

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessarily involves the way that equipment may be utilized, which means that plant scheduling and production must form an integral part of the design problem. This work relies on a previous study, which proposed an alternative treatment of the imprecision (demands) by introducing fuzzy concepts, embedded in a multi-objective Genetic Algorithm (GA) that takes into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The results showed that an additional interpretation step might be necessary to help the managers choosing among the non-dominated solutions provided by the GA. The analytic hierarchy process (AHP) is a strategy commonly used in Operations Research for the solution of this kind of multicriteria decision problems, allowing the apprehension of manager subjective judgments. The major aim of this study is thus to propose a software integrating the AHP theory for the analysis of the GA Pareto-optimal solutions, as an alternative decision-support tool for the batch plant design problem solution.     

A spatial temporal decision framework for adaptation to sea level rise

There is a strong link between decision making and environmental stresses. Two dilemmas confront decision makers: how and when to adapt to sea level rise, due to complexities of environmental systems and the changing nature of the decision making process. This process is inherently complex and often involves many stakeholders with conflicting views. Considering the complexity and dynamic nature of coastal systems, this paper introduces a Spatial Temporal Decision framework to assess coastal vulnerability, and the adaptation alternatives to SLR. The STD is based upon a combination of: System Dynamics modelling; Geographical Information Systems modelling; and multicriteria analyses of stakeholders' views using the Analytical Hierarchy Process. For case study analyses, the City of the Gold Coast located in Southeast Queensland, Australia has been selected. The results of the vulnerability assessment indicate that, at the end of a 100 year simulation period, approximately 6% of the landscape in the study area will be gradually inundated over time, with 0.5 cm rise per year. However, the percentage of the vulnerable area leapt to about 34% for Scenario 2, and 56% for Scenario 3, which represent 1 cm and 1.5 cm rise per year. Using the information obtained from vulnerability assessments, three stakeholder groups (Politicians, Experts and Residents) were consulted to determine the goal, criteria and adaptation alternatives for the multicriteria analyses. Analyses of survey data reveal that across the three stakeholder groups, Effectiveness and Sustainability are the criteria of highest priority.     

Stability radius of a vector integer linear programming problem: case of a regular norm in the space of criteria

A multicriteria integer linear programming problem of finding a Pareto set is considered. The set of feasible solutions is supposed to be finite. The lower and upper achievable bounds for the radius of stability are obtained using a stability criterion and the Minkowski–Mahler inequality and assuming that the norm is arbitrary in the space of solutions and is monotone in the space of criteria. Bounds for the radius of stability in spaces with the Holder metric are given in corollaries.     

Topological network design: A survey

We consider the problem of topological optimization of communication networks subject to a number of design constraints, such as maximum network diameter, maximum node degree, k-node (link) survivability, and network fault tolerance. The primary design problem can be described as follows: Given a set of network nodes, it is required to find a topology Ψ, selected from all possible topologies, so that the cost of Ψ (measured possibly in terms of the maximum diameter, maximum node degree, etc.) is less than that of any other network topology and such that Ψ satisfies some given design constraints. Fault tolerance is concerned with the ability of the network nodes to communicate in the presence of a set of faulty links and/or nodes. The network design problem considering reliability constraints is NP-hard. We classify the research efforts presented in the literature for solving the topological optimization design problem as hierarchical, enumerative, or iterative techniques. In this paper, we provide a survey of the topological network design techniques under different design constraints. Experimental results obtained by applying a number of algorithms to a set of randomly generated networks are presented and compared.     

基于Vague集模糊推理的多评价指标模糊决策方法

目前在智能领域中对Vague集的研究已越来越广泛与深入，并运用于决策问题中，有学者已把Vague集用于多评价指标的模糊决策中，但其决策方法在某些时候却难以得到目标。为此，本文提出了一个基于Vague集模糊推理的多评价指标模糊决策方法。在这个方法中，从基于Vague集的模糊推理的观点来看待模糊决策问题。将评价指标和候选方案之间的关系用一组基于Vague集的推理规则来表示，将决策者的要求用一组Vague集来表示，经过模糊推理等过程最后得到决策结果。然后还给出了一个实例说明这种多评价指标模糊决策方法。这个基于Vague集模糊推理的多评价指标模糊决策方法的提出为决策系统提供了一个有用的工具。