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.     

Combining different prioritization methods in the analytic hierarchy process synthesis

A multicriteria approach for combining prioritization methods within the analytic hierarchy process (AHP) is proposed. The leading assumption is that for each particular decision problem and related hierarchy, AHP must not necessarily employ only one prioritization method (e.g. eigenvector method). If more available methods are used to identify the best estimates of local priorities for each comparison matrix in the hierarchy, then the estimate of final alternatives’ priorities should also be the best possible, which is in natural concordance with an additive compensatory structure of the AHP synthesis. The most popular methods for deriving priorities from comparison matrices are identified as candidates (alternatives) to participate in AHP synthesis: additive normalization, eigenvector, weighted least-squares, logarithmic least-squares, logarithmic goal programming and fuzzy preference programming. Which method will be used depends on the result of multicriteria evaluation of their priority vectors’ performance with regard to suggested deviation and rank reversal measures. Two hierarchies with matrices of size 3–6 are used to illustrate an approach.     

Neural networks for solving multicriteria solid transportation problem

In this paper, we present neural networks for solving multicriteria solid transportation problems. The original problem is transformed into an equivalent continuous problem from the continuous-time dynamic system and its optimal solution can be got. The procedure and efficiency of this approach are shown with numerical simulations.     

Forming management decisions in organizational systems on the basis of simulation of their activity

The methodological problems of designing a decision making system based on the discrete model of collective, purposeful, and regulated activity are considered, the information and functional models are presented, and the principles of formation of the hierarchy of objective functions (criterions) are described, the general algorithm for solving the problem, possible methods of multicriteria optimization and parametric synthesis in a complex organizational system are given, the design of a simulation model of the system and its computer implementation is presented.     

Multi-criteria analysis for a maintenance management problem in an engine factory: rational choice

The industrial organization needs to develop better methods for evaluating the performance of its projects. We are interested in the problems related to pieces with differing degrees of dirt. In this direction, we propose and evaluate a maintenance decision problem of maintenance in an engine factory that is specialized in the production, sale and maintenance of medium and slow speed four stroke engines. The main purpose of this paper is to study the problem by means of the analytic hierarchy process to obtain the weights of criteria, and the TOPSIS method as multicriteria decision making to obtain the ranking of alternatives, when the information was given in linguistic terms.     

多指标动态规划的人机交互式满意权衡法

1984年,Nakayama和Sawaragi提出了一种求解静态多目标决策问题的人机交互式满 意权衡方法.本文结合动态规划的结构特点,进一步发展了Nakayama方法的基本思想,表明 该方法可以推广到用来求解多指标动态规划问题,而且通过对原方法的改进,消除了其存在的 一些不足之处.本文所提方法,在较弱的限制条件下,针对一类普遍使用的多指标动态规划模 型,可以获得决策者充分满意的解.     

Multicriteria programming in medical diagnosis and treatments

This paper deals with a special case of multicriteria optimization problems. The problems studied come from the medical domain and are of a very important practical relevance. One of the problems refers to the ranking of treatments for the Trigeminal Neuralgia. The second problem refers to a hierarchy of risk factors for Bronchial Asthma. The most common way to deal with a multiobjective optimization problem is to apply Pareto dominance relationship between solutions. But in the cases studied here, a decision cannot be made just by using Pareto dominance. In one of the experiments, all the potential solutions are nondominated (and we need to clearly find a hierarchy of these solutions) and in the second experiment most of the solutions are nondominated between them. We propose a novel multiple criteria procedure and then an evolutionary scheme is applied for solving the problems. Results obtained by the proposed approach in a very simple way are same as the results (or even better) obtained by applying weighted-sum method. The advantage of the proposed technique is that it does not require any additional information about the problem (like weights for each criteria in the case of weighted-sumapproach).     

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.     

Lossless convexification of a class of optimal control problems with non-convex control constraints

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lossless convexification of the optimal control problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non-convex optimal control problem. The solution approach is demonstrated on a number of planetary soft landing optimal control problems.     

Dynamic multi-objective evolutionary algorithms for single-objective optimization

This paper proposes a new method for handling the difficulty of multi-modality for the single-objective optimization problem (SOP). The method converts a SOP to an equivalent dynamic multi-objective optimization problem (DMOP). A new dynamic multi-objective evolutionary algorithm (DMOEA) is implemented to solve the DMOP. The DMOP has two objectives: the original objective and a niche-count objective. The second objective aims to maintain the population diversity for handling the multi-modality difficulty during the search process. Experimental results show that the performance of the proposed algorithm is significantly better than the state-of-the-art competitors on a set of benchmark problems and real world antenna array problems.     

多指标动态规划的交互式满意置换率法

提出了一种新的求解多指标动态规划问题的算法,它是由多目标静态规划的交互式满意 置换率法[1]推广得到的.通过增加附加状态变量进行数学模型转换,将单指标动态规划问题 转化为静态规划问题,再进行迭代.这样既减少了计算量,又使各指标间的置换关系易于求 得.所提方法在人机交互过程中对决策者的要求不高,对于一类常见的多指标动态规划问题, 可以迅速获得满意的解.     

Design of retarded fractional delay differential systems using the method of inequalities

Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems （RFDDSs） by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian＇s original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.     

A hierarchical approach for planning a multisensor multizone search for a moving target

This paper deals with a well-known problem in the general area of search theory: optimize the search resources sharing so as to maximize the probability of detection of a (moving) target. However, the problem we consider here considerably differs from the classical one. First, there is a bilevel search planning and we have to consider jointly discrete and continuous optimization problems. To this perspective original methods are proposed within a common framework. Furthermore, this framework is sufficiently general and versatile so as to be easily and successfully extended to the difficult problem of the multizone multisensor search planning for a Markovian target.     

A new method selection approach for fuzzy group multicriteria decision making

Fuzzy multicriteria decision making (MCDM) has been widely used in ranking a finite number of decision alternatives characterized by fuzzy assessments with respect to multiple criteria. In group decision settings, different fuzzy group MCDM methods often produce inconsistent ranking outcomes for the same problem. To address the ranking inconsistency problem in fuzzy group MCDM, this paper develops a new method selection approach for selecting a fuzzy group MCDM method that produces the most preferred group ranking outcome for a given problem. Based on two group averaging methods, three aggregation procedures and three defuzzification methods, 18 fuzzy group MCDM methods are developed as an illustration to solve the general fuzzy MCDM problem that requires cardinal ranking of the decision alternatives. The approach selects the group ranking outcome of a fuzzy MCDM method which has the highest consistency degree with its corresponding ranking outcomes of individual decision makers. An empirical study on the green bus fuel technology selection problem is used to illustrate how the approach works. The approach is applicable to large-scale group multicriteria decision problems where inconsistent ranking outcomes often exist between different fuzzy MCDM methods.     

Use of parallel deterministic dynamic programming and hierarchical adaptive genetic algorithm for reservoir operation optimization

Reservoir operation optimization (ROO) is a complicated dynamically constrained nonlinear problem that is important in the context of reservoir system operation. In this study, parallel deterministic dynamic programming (PDDP) and a hierarchical adaptive genetic algorithm (HAGA) are proposed to solve the problem, which involves many conflicting objectives and constraints. In the PDDP method, multi-threads are found to exhibit better speed-up than single threads and to perform well for up to four threads. In the HAGA, an adaptive dynamic parameter control mechanism is applied to determine parameter settings, and an elite individual is preserved in the archive from the first hierarchy to the second hierarchy. Compared with other methods, the HAGA provides a better operational result with greater effectiveness and robustness because of the population diversity created by the archive operator. Comparison of the results of the HAGA and PDDP shows two contradictory objectives in the ROO problem-economy and reliability. The simulation results reveal that: compared with proposed PDDP, the proposed HAGA integrated with parallel model appears to be better in terms of power generation benefit and computational efficiency.     

Attainability of optimal solutions to a linear problem of multicriterion optimization with respect to the weighed sum of variously important and transitively subordinated criteria

This paper presents methods of finding criteria coefficients such that optimal solutions are obtained to a linear problem of multicriteria optimization with respect to the weighed sum of variously important and transitively subordinated criteria. The case of a partial transitive subordination is also considered, and a method is founded that finds coefficients such that optimal solutions to the problem of multicriteria optimization are attainable with respect to the weighed sum of variously important and partially transitively subordinated criteria. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 135–138, September–October 2008.     

Polynomial approximation technique for dynamic optimization problems

This paper considers the general dynamic optimization problem and describes a polynomial approximation technique for its solution. The proposed procedure utilizes the classical method of Ritz, where the unknown decision function is postulated to be a polynomial of degree n, the coefficients of which are solved for with optimization methods such as the sequential unconstrained minimization technique (SUMT). Thus a series of new transformed minimization problems in finite dimensions is created and solved, instead of the original problem of infinite dimensions. The proposed technique is illustrated with a practical example from the aggregate production planning area.     

非线性离散系统的近似最优跟踪控制

研究非线性离散系统的最优跟踪控制问题. 通过在由最优控制问题所导致的非线性两点边值问题中引入灵敏度参数, 并对它进行Maclaurin级数展开, 将原最优跟踪控制问题转化为一族非齐次线性两点边值问题. 得到的最优跟踪控制由解析的前馈反馈项和级数形式的补偿项组成. 解析的前馈反馈项可以由求解一个Riccati差分方程和一个矩阵差分方程得到. 级数补偿项可以由一个求解伴随向量的迭代算法近似求得. 以连续槽式反应器为例进行仿真验证了该方法的有效性．     

一种基于动态规划策略的离散动态大系统递阶优化神经网络

给出了一种具有集成化特征的、快速求解大规模系统动态规划问题的神经网络模型 (LDPNN),该神经网络将大系统的各子系统的动态方程约束嵌入局部优化子网络,使得整个 网络的结构简洁、紧凑,便于硬件实现,该神经网络计算模型克服了数值方法迭代计算的缺 陷,求解效率高,适宜于大规模动态系统实时优化应用.     

Four-layer framework for combinatorial optimization problems domain

Four-layer framework for combinatorial optimization problems/models domain is suggested for applied problems structuring and solving: (1) basic combinatorial models and multicriteria decision making problems (e.g., clustering, knapsack problem, multiple choice problem, multicriteria ranking, assignment/allocation); (2) composite models/procedures (e.g., multicriteria combinatorial problems, morphological clique problem); (3) basic (standard) solving frameworks, e.g.: (i) Hierarchical Morphological Multicriteria Design (HMMD) (ranking, combinatorial synthesis based on morphological clique problem), (ii) multi-stage design (two-level HMMD), (iii) special multi-stage composite framework (clustering, assignment/location, multiple choice problem); and (4) domain-oriented solving frameworks, e.g.: (a) design of modular software, (b) design of test inputs for multi-function system testing, (c) combinatorial planning of medical treatment, (d) design and improvement of communication network topology, (e) multi-stage framework for information retrieval, (f) combinatorial evolution and forecasting of software, devices. The multi-layer approach covers ‘decision cycle’, i.e., problem statement, models, algorithms/procedures, solving schemes, decisions, decision analysis and improvement.