旅游线路优化设计探讨

本文主要探讨最佳旅游线路的设计问题，在满足相关约束条件的情况下，用最少的天数游览尽可能多的景点是我们追求的目标。本文以运筹学中最优化理论和图论的相关知识为基础，对河南省旅游线路设计的问题加以分析。     

多目标决策

目标决策又称“矢量优化”，“多目标规划”，“多准则决策”等，它是系统科学和管理科学的重要研究分支，这里的“多目标”是指有多个需要的优质的目标函数，且这些目标函数是矛盾的和不可公度的，数学规划中的线性规则，非线性规则，动态规划，整数规划等都是以追求单个目标的最优化为特征的，与多目标决策不同，在多目标决策中，常常会出现使某一个或者某些目标函数达不到最优的情况，这种目标函数之间的矛盾性决定了多目标决策问题一般不存在能使所有的目标函数同时达到最优的绝对最优解，而只存在非劣解和满意解的概念。     

在数学教学中充分运用多媒体和网络教学的策略

课堂教学的最优化是指教学过程中各要素功能的优化以及通过要素间的协同作用,提高教学效率,实现学习目标。因此,课堂教学的最优化要求教师要善于选择实现既定学习目标,最恰当的方法和手段,使学生能够深刻地、自觉地、积极地、独立地去学习。巴班斯基指出：“最优化向教师指出了费力较少,而又能达到较高教育效果的捷径,它使教师从许多习以为常,但效益很少的行动中解放出来。     

职高学生美术学习有效性评价探索

做好职高学生美术学习有效性评价,首要的是要正视当前职高学生美术评价中存在的一些问题。在此基础上,在评价中要做到评价的最优化,提倡多主体、多方法的评价,注重评价与学习结果的并重等评价方式上采取一些积极的措施。     

商业银行集团客户统一授信额度的优化配置研究

企业集团是商业银行重要的贷款客户,商业银行面临企业集团的授信业务风险尤为突出。在结构化模型的框架下,考虑统一授信额度的约束,基于对违约风险控制和贷款收益管理的多目标决策,构建了企业集团成员企业授信额度优化配置模型。示例分析表明,在考虑不同目标重要性的前提下,使用如遗传算法等最优化求解方法,可得到对成员企业授信额度的优化配置方案,从而有助于商业银行积极主动的防范集团客户的信贷风险。     

对方案有偏好的区间数多属性灰色关联决策模型

针对属性值以区间数形式给出并且已知方案偏好信息的多属性决策问题,提出了一种灰色关联分析的决策方法。该方法依据一般的灰色关联分析方法的基本思路,给出了该问题的计算步骤,其核心是通过构建并求解一个单目标最优化模型,得到属性权重信息,从而计算出每个方案客观偏好值与主观偏好值的灰色关联系数,进而得到每个方案客观偏好与主观偏好的关联度,根据关联度对所有方案进行排序。最后给出了一个数值例子,结果表明方法简单,有效和易于计算。     

一种信息安全投资的智能化决策方法研究

当组织的信息系统因为漏洞而受到的威胁时,组织必须进行信息安全投资决策以减少损失.信息安全投资决策是一个多目标决策和NP难题.为精确解决组织的信息安全投资决策问题,本文提出一种改进的二进制的粒子群优化算法(PSO),帮助组织最优化的投资和实现最大化的弥补漏洞.为加快收敛速度,在传统的离散PSO中移植了一种记忆机制.经过实验,改进的算法具有更好的搜索效率和稳定性.为企业提供了一种简单有效的决策支持工具.     

基于经济资本的商业银行授信审批体系设计研究

在快速变化的市场条件以及较强的监管资本约束下,商业银行无法单纯依靠规模扩张实现价值最大化目标,需要建立以经济资本为基础的授信审批体系,实现资本资源的有效利用和科学的绩效评价。本文基于经济资本分别研究了单笔业务和多笔业务等情景下的授信审批机制设计,构建了贷款决策的最优化模型,为商业银行进一步完善授信审批体系提供参考。     

略谈英语教学的最优化

著名教育家巴班斯基认为,实现教学最优化有两个标准:一是师生消耗的时间要尽可能少一些;二是要使学生的知识、能力、品德获得最大可能的发展。一句话就是要以最少的时间获得最佳的结果。对英语教学而言,就是对英语教学做系统分析,选择可能适应教学过程的最佳方案,各种因素优化组合,使外语教学在条件许可的范围内具有最适合的目标功能——学生的英语听说能力和运用英语交际的能力得到一定的提高。如何实现英语教学的最优化呢?一、英语教学最优化的关键——教师教育观念的转变实现英语教学最优化,涉及教学过程的各个方面,但首先是教师观念的转…     

优化教学设计与提高化学课堂教学效率

课堂教学效率的关键取决于教学设计的优劣,即看教师的教学目标、教学方法和手段,教学过程中教与学的双边活动的构思和安排是否达到最优化。以我们的化学教学实践为例,谈几点体会。一、坚持教学目标多元化是前提教学目标是教学双方积极活动的准绳,     

Optimization and equilibrium problems with equilibrium constraints

This paper concerns optimization and equilibrium problems with the so-called equilibrium constraints mathematical programs with equilibrium constraint (MPEC) and equilibrium problems with equilibrium constraint (EPEC), which frequently appear in applications to operations research. These classes of problems can be naturally unified in the framework of multiobjective optimization with constraints governed by parametric variational systems (generalized equations, variational inequalities, complementarity problems, etc.). We focus on necessary conditions for optimal solutions to MPECs and EPECs under general assumptions in finite-dimensional spaces. Since such problems are intrinsically nonsmooth, we use advanced tools of generalized differentiation to study optimal solutions by methods of modern variational analysis. The general results obtained are concretized for special classes of MPECs and EPECs important in applications.     

On linear bilevel problems with multiple objectives at the lower level

Bilevel programming problems provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. This paper focuses on bilevel problems for which the lower level problem is a linear multiobjective program and constraints at both levels define polyhedra. This bilevel problem is reformulated as an optimization problem over a nonconvex region given by a union of faces of the polyhedron defined by all constraints. This reformulation is obtained when dealing with efficient solutions as well as weakly efficient solutions for the lower level problem. Assuming that the upper level objective function is quasiconcave, then an extreme point exists which solves the problem. An exact and a metaheuristic algorithm are developed and their performance is analyzed and compared.     

Concepts,Theory, and Techniques PRINCIPLES OF MULTIOBJECTIVE OPTIMIZATION*

This paper attempts to isolate and analyze the principal ideas of multiobjective optimization. We do this without casting aspersions on single-objective optimization or championing any one multiobjective technique. We examine each fundamental idea for strengths and weaknesses and subject two—efficiency and utility—to extended consideration. Some general recommendations are made in light of this analysis. Besides the simple advice to retain single-objective optimization as a possible approach, we suggest that three broad classes of multiobjective techniques are very promising in terms of reliably, and believably, achieving a most preferred solution. These are: (1) partial generation of the efficient set, a rubric we use to unify a wide spectrum of both interactive and analytic methods; (2) explicit utility maximization, a much-overlooked approach combining multiattribute decision theory and mathematical programming; and (3) interactive implicit utility maximization, the popular class of methods introduced by Geoffrion, Dyer, and Feinberg [24] and extended significantly by others.     

An Interactive Framework for Multi-Person,Multiobjective Decisions

Group decision making in the presence of multiple conflicting objectives is complex and difficult. This paper describes and evaluates an iterative technique to facilitate multiple objective decision making by multiple decision makers. The proposed method augments an interactive multiobjective optimization procedure with a preference ranking tool and a consensus ranking heuristic. Two multiple objective linear programming (MOLP) solution approaches, the SIMOLP method of Reeves and Franz [39] and the interactive weighted Tchebycheff procedure of Steuer and Choo [49], are recommended optimization strategies to be used independently or in concert. Computational experience suggests that the proposed framework is an effective decision-making tool. The procedure quickly located excellent compromise solutions in a series of test problems with hypothetical decision makers. In addition, human decision makers gave positive evaluations of the procedure and the production plans the procedure provided for a resource allocation case problem.     

Impact of Number of Interactions,Different Interaction Patterns,and Human Inconsistencies on Some Hybrid Evolutionary Multiobjective Optimization Algorithms*

We investigate the impact of the number of human–computer interactions, different interaction patterns, and human inconsistencies in decision maker responses on the convergence of an interactive, evolutionary multiobjective algorithm recently developed by the authors. In our context “an interaction” means choosing the best and worst solutions among a sample of six solutions. By interaction patterns we refer to whether preference questioning is more front‐, center‐, rear‐, or edge‐loaded. As test problems we use two‐ to four‐objective knapsack problems, multicriteria scheduling problems, and multiobjective facility location problems. In the tests, two different preference functions are used to represent actual decision maker preferences, linear and Chebyshev. The results indicate that it is possible to obtain solutions that are very good or even nearly optimal with a reasonable number of interactions. The results also indicate that the algorithm is robust to minor inconsistencies in decision maker responses. There is also surprising robustness toward different patterns of interaction with the decision maker. The results are of interest to the evolutionary multiobjective (EMO) community actively developing hybrid interactive EMO approaches.     

Nature-inspired metaheuristics for multiobjective activity crashing

Many project tasks and manufacturing processes consist of interdependent time-related activities that can be represented as networks. Deciding which of these sub-processes should receive extra resources to speed up the whole network (i.e., where activity crashing should be applied) usually involves the pursuit of multiple objectives amid a lack of a priori preference information. A common decision support approach lies in first determining efficient combinations of activity crashing measures and then pursuing an interactive exploration of this space. As it is impossible to exactly solve the underlying multiobjective combinatorial optimization problem within a reasonable computation time for real-world problems, we have developed proper solution procedures based on three major (nature-inspired) metaheuristics. This paper describes these implementations, discusses their strengths, and provides results from computational experiments.     

AN IMPLICIT/EXPLICIT APPROACH TO MULTIOBJECTIVE OPTIMIZATION WITH AN APPLICATION TO FOREST MANAGEMENT PLANNING*

Implicit utility/value maximization and explicit utility/value maximization are identified as two major classes of multiobjective optimization methods. Explicit methods have the advantage of being able to fully exploit the power of existing mathematical programming algorithms. A disadvantage is the high information burden they place on the decision maker. Implicit (i.e., interactive) methods have complementary strengths and weaknesses: they require less extensive information but do not lend themselves as easily to use with optimizing algorithms. We develop a hybrid implicit/explicit approach that attempts to combine the advantages of both by embedding within the implicit method a procedure that periodically formulates an approximate explicit representation of the multiobjective problem and then solves it optimally without user interaction. Operationally, this requires the frequent solution of two nonlinear programs. We also report on the implementation of this method in a forest management decision support system. This is a completely microcomputer-based implementation currently undergoing field testing for use in planning the timing and intensity of timber harvests on non-industrial forests in the southeastern United States. The system has been selected as a replacement for an earlier multiobjective program (Harrison and Rosenthal [28]) used by over 1,800 landowners.     

The Minimum-Covering/Shortest-Path Problem*

Due to the inherent multiobjective nature of many network design and routing problems, there has been a tremendous increase in multiobjective network modeling in recent years. In this article we introduce one such model, the minimum-covering/shortest-path (MinCSP) problem, and formulate several variations of the problem. The MinCSP problem is a two-objective path problem: minimization of the total population negatively impacted by the path and minimization of the total path length. A population is considered to be negatively impacted by the path if the path comes within some predetermined distance of the population. Consequently, the MinCSP problem extends the concept of coverage from facility location modeling to network design. Additionally, several existing solution methods for the problem are briefly discussed and potential applications presented.     

Beyond Markowitz with multiple criteria decision aiding

The paper is about portfolio selection in a non-Markowitz way, involving uncertainty modeling in terms of a series of meaningful quantiles of probabilistic distributions. Considering the quantiles as evaluation criteria of the portfolios leads to a multiobjective optimization problem which needs to be solved using a Multiple Criteria Decision Aiding (MCDA) method. The primary method we propose for solving this problem is an Interactive Multiobjective Optimization (IMO) method based on so-called Dominance-based Rough Set Approach (DRSA). IMO-DRSA is composed of two phases: computation phase, and dialogue phase. In the computation phase, a sample of feasible portfolio solutions is calculated and presented to the Decision Maker (DM). In the dialogue phase, the DM indicates portfolio solutions which are relatively attractive in a given sample; this binary classification of sample portfolios into ‘good’ and ‘others’ is an input preference information to be analyzed using DRSA; DRSA is producing decision rules relating conditions on particular quantiles with the qualification of supporting portfolios as ‘good’; a rule that best fits the current DM’s preferences is chosen to constrain the previous multiobjective optimization in order to compute a new sample in the next computation phase; in this way, the computation phase yields a new sample including better portfolios, and the procedure loops a necessary number of times to end with the most preferred portfolio. We compare IMO-DRSA with two representative MCDA methods based on traditional preference models: value function (UTA method) and outranking relation (ELECTRE IS method). The comparison, which is of methodological nature, is illustrated by a didactic example.     

A general space-time model for combinatorial optimization problems (and not only)

We consider the problem of defining a strategy consisting of a set of facilities taking into account also the location where they have to be assigned and the time in which they have to be activated. The facilities are evaluated with respect to a set of criteria. The plan has to be devised respecting some constraints related to different aspects of the problem such as precedence restrictions due to the nature of the facilities. Among the constraints, there are some related to the available budget. We consider also the uncertainty related to the performances of the facilities with respect to considered criteria and plurality of stakeholders participating to the decision. The considered problem can be seen as the combination of some prototypical operations research problems: knapsack problem, location problem and project scheduling. Indeed, the basic brick of our model is a variable x_ilt which takes value 1 if facility i is activated in location l at time t, and 0 otherwise. Due to the conjoint consideration of a location and a time in the decision variables, what we propose can be seen as a general space-time model for operations research problems. We discuss how such a model permits to handle complex problems using several methodologies including multiple attribute value theory and multiobjective optimization. With respect to the latter point, without any loss of the generality, we consider the compromise programming and an interactive methodology based on the Dominance-based Rough Set Approach. We illustrate the application of our model with a simple didactic example.