预测复合材料开裂方向的比应变能密度准则

本文提出预测复合材料中裂纹方向的比应变能密度准则,并将Tsai-Hill与Norris准则扩展来预测复合材料中的开裂方向.用这三个准则预测了具有各种不同纤维方向的单向纤维复合材料的裂纹扩展方向,预测结果与现有的比正应力准则和应变能密度准则进行了对比.     

Optimality conditions in set optimization employing higher-order radial derivatives

There are two approaches of defining the solutions of a set-valued optimization problem:vector criterion and set criterion.This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives.In the case of vector criterion,some optimality conditions are derived for isolated (weak) minimizers.With set criterion,necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.     

Preemptive Scheduling with Two Minimax Criteria

Two preemptive single-machine bicriteria scheduling problems with release dates and deadlines are considered in this paper. Each criterion is formulated as a maximum cost. In the first problem the cost of both criteria depends on the completion time of the tasks. This problem can be solved by enumerating all the Pareto optimal points with an approach proposed by Hoogeveen (1996) for the nonpreemptive problem without release dates. In the second problem, the costs of one criterion are dependent on the completion times of the tasks and the costs of the other criterion are dependent on the start times. This problem is more difficult but an efficient algorithm is proposed for a sub-problem with heads, tails, release dates and deadlines that appears in the job-shop scheduling problem.     

Four types of nonlinear scalarizations and some applications in set optimization

There are two types of criteria of solutions for the set-valued optimization problem, the vectorial criterion and set optimization criterion. The first criterion consists of looking for efficient points of set valued map and is called set-valued vector optimization problem. On the other hand, Kuroiwa–Tanaka–Ha started developing a new approach to set-valued optimization which is based on comparison among values of the set-valued map. In this paper, we treat the second type criterion and call set optimization problem. The aim of this paper is to investigate four types of nonlinear scalarizing functions for set valued maps and their relationships. These scalarizing functions are generalization of Tammer–Weidner’s scalarizing functions for vectors. As applications of the scalarizing functions for sets, we present nonconvex separation type theorems, Gordan’s type alternative theorems for set-valued map, optimality conditions for set optimization problem and Takahashi’s minimization theorems for set-valued map.     

Local decision making and decision fusion in hierarchical levels

Hierarchical problem solving is preferred when the problem is overwhelmingly complicated. In such a case, the problem should better be analyzed in hierarchical levels. At each level, some temporary solutions are obtained; then a suitable decision fusion technique is used to merge the temporary solutions for the next level. The hierarchical framework proposed in this study depends on reutilization or elimination of previous level local agents that together perform the decisions due to a decision-fusion technique: a performance criterion is set for local agents. The criterion checks the success of agents in their local regions. An agent satisfying this criterion is reutilized in the next level, whereas an agent not successful enough is removed from the agent pool in the next level. In place of a removed agent, a number of new local agents are developed. This framework is applied on a fault detection problem.      

Comparison of tests for non-parametric hypotheses

1. Summary The main object of this paper is to find a criterion for comparison of two tests for non-parametric hypotheses, taking advantage of the qualitative information that may exist. After a detailed analysis of the problem and some earlier suggestins for its solution (sections 2–4), a criterion is suggested in section 5. In order to apply it to a concrete case, a location problem is specified in section 6. The rank tests to be compared are analyzed in section 7, and the comparison by way of the criterion is carried out in section 8. It turns out that sign tests, sometimes slightly modified, are very often optimal according to the criterion used.     

A characterization of multipliers in the Hedberg-Netrusov spaces

We expose a criterion of the membership of a function in the space of pointwise multipliers between the Hedberg-Netrusov spaces. The criterion is stated in terms of a pair of discrete weighted inequalities. Connections of the criterion with the problem of rectifiability of Lipschitz surfaces are established.     

Methods of the Convex Cone Theory in the Feasibility Problem of Multicommodity Flow

The feasibility problem of multicommodity flow is reduced to finding out if a multidimensional vector determined by the network parameters belongs to a convex polyhedral cone determined by the set of paths in the network. It is shown that this representation of the feasibility problem makes it possible to formulate the feasibility criterion described in [1] in a different form. It is proved that this criterion is sufficient. The concepts of reference vectors and networks are defined, and they are used to describe a method for solving the feasibility problem for an arbitrary network represented by a complete graph.     

主次指标为最小化总完工时间和存储费用的带有准备时间的单机分批排序问题

In this paper, the single machine scheduling problem with release dates and two hierarchical criteria is discussed. The first criterion is to minimize makespan, and the second criterion is to minimize stocking cost. We show that this problem is strongly NP-hard. We also give an O(n2) time algorithm for the special case that all stocking costs of jobs in unit time are 1.     

Sufficient Optimality Criterion for Linearly Constrained,Separable Concave Minimization Problems

A sufficient optimality criterion for linearly-constrained concave minimization problems is given in this paper. Our optimality criterion is based on the sensitivity analysis of the relaxed linear programming problem. The main result is similar to that of Phillips and Rosen (Ref. 1); however, our proofs are simpler and constructive.In the Phillips and Rosen paper (Ref. 1), they derived a sufficient optimality criterion for a slightly different linearly-constrained concave minimization problem using exponentially many linear programming problems. We introduce special test points and, using these for several cases, we are able to show optimality of the current basic solution.The sufficient optimality criterion described in this paper can be used as a stopping criterion for branch-and-bound algorithms developed for linearly-constrained concave minimization problems.This research was supported by a Bolyai János Research Fellowship BO/00334/00 of the Hungarian Academy of Science and by the Hungarian Scientific Research Foundation, Grant OTKA T038027.     

Ordered Flow Shop Problems with no In-Process Waiting: Further Results

The ordered flow shop sequencing problem with no in-processing waiting (OFSNW) is considered with respect to mean flow time criterion. It is shown that the sequence in which jobs are arranged according to the shortest processing time rule (SPT) represents an optimal sequence. Additional results for the makespan criterion are also discussed.     

Linearly unrelated sequences and problem of Erdös

The main result of this paper is a criterion for linearly unrelated sequences which do not tend to infinity very fast. This criterion depends on divisibility. Applications and several examples are included. A problem of Erdös concerning the irrational sequences is partially solved.     

When do several linear operators share an invariant cone?

We establish a criterion for a finite family of matrices to possess a common invariant cone. The criterion reduces the problem of existence of an invariant cone to equality of two special numbers that depend on the family. In spite of theoretical simplicity, the practical use of the criterion may be difficult. We show that the problem of existence of a common invariant cone for four matrices with integral entries is algorithmically undecidable. Corollaries of the criterion, which give sufficient and necessary conditions, are derived. Finally, we introduce a “co-directional number” of several matrices. We prove that this parameter is close to zero iff there is a small perturbation of matrices, after which they get an invariant cone. An algorithm for its computation is presented.     

Some equivalent problems in set optimization

Given a set-valued optimization problem (P), there is more than one way of defining the solutions associated with it. Depending on the decision maker’s preference, we consider the vector criterion or the set criterion. Both criteria of solution are considered together to solve problem (P) by reducing the feasible set.     

The minimal criterion for the equivalence between local and global optimal solutions in nondifferentiable optimization problem

In the paper, a necessary and sufficient criterion it provided such that any local optimal solution is also global in a not necessarily differentiable constrained optimization problem. This criterion is compared to others earlier appeared in the literature, which are sufficient but not necessary for a local optimal solution to be global. The importance of the established criterion is illustrated by suitable examples of nonconvex optimization problems presented in the paper.     

A Linear Programming Approach to the Solution of Constrained Multi-Facility Minimax Location Problems where Distances are Rectangular

The problem of locating new facilities with respect to existing facilities is stated as a linear programming problem where inter-facility distances are assumed to be rectangular. The criterion of location is the minimization of the maximum weighted rectangular distance in the system. Linear constraints which (a) limit the new facility locations and (b) enforce upper bounds on the distances between new and existing facilities and between new facilities can be included. The dual programming problem is formulated in order to provide for an efficient solution procedure. It is shown that the duLal variables provide information abouLt the complete range of new facility locations which satisfy the minimax criterion.     

Heuristics for the Phylogeny Problem

A phylogeny is a tree that relates taxonomic units, based on their similarity over a set of characters. The problem of finding a phylogeny with the minimum number of evolutionary steps (the so-called parsimony criterion) is one of the main problems in comparative biology. In this work, we study different heuristic approaches to the phylogeny problem under the parsimony criterion. New algorithms based on metaheuristics are also proposed. All heuristics are implemented and compared under the same framework, leading to consistent and thorough comparative results. Computational results are reported for benchmark instances from the literature.     

On factorization of triangular matrices of the second

The problem of factorization of the matrices of form (5) is investigated. The problem is solved by method from [GGK]. A new criterion for canonical factorization is represented. The explicit form for factors and two examples are given.     

Lattices generated by Chip Firing Game models: Criteria and recognition algorithms

It is well-known that the class of lattices generated by Chip Firing Games (CFGs) is strictly included in the class of upper locally distributive lattices (ULD). However a necessary and sufficient criterion for this class is still an open question. In this paper we settle this problem by giving such a criterion. This criterion provides a polynomial-time algorithm for constructing a CFG which generates a given lattice if such a CFG exists. Going further we solve the same problem on two other classes of lattices which are generated by CFGs on the classes of undirected graphs and directed acyclic graphs.     

The solution of the axisymmetric elastic-plastic torsion of a shaft using varational inequalities

The axisymmetric elastic-plastic torsion of a shaft subject to the von Mises yield criterion is considered. The problem is reformulated as a variational inequality and it is proved that the problem has a unique solution. Some properties of the solution are derived.