Decision methods for some optimization problems in recognition theory

By optimizing different models of recognition algorithms, a number of discrete extreme problems appear. The search for the maximum solvable subsystem of the system of linear inequalities is one of these tasks. In certain cases additional requirements on a desired solvable subsystem can be imposed. The solution methods for some types of such tasks are proposed.     

On some optimization problem for systems of linear inequalities

In recognition theory a number of optimization problems appear. The search for the maximum solvable subsystem of the system of linear inequalities is one of these tasks. Its solution methods based on examining of the special set of subsystems are known. In this work the approximation solution method for given problem is proposed. This method is principally different from those mentioned above. It is based on some reasoning of geometric nature.     

Optimal solution of linear inequalities with applications to pattern recognition

An algorithm for the optimal solution of consistent and inconsistent linear inequalities is presented, where the optimality criterion is the maximization of the number of constraints satisfied. In the terminology of pattern recognition, the algorithm finds a linear decision function which minimizes the number of patterns misclassified. The algorithm is developed as a nonenumerative search procedure based on several new results established in this paper. Bounds on the search are also developed and the method is experimentally evaluated and shown to be computationally superior to other techniques for finding minimum-error solutions.     

Decision methods for some discrete extreme problems in recognition theory

By optimizing different models of recognition algorithms, a number of discrete extreme problems appear. The search for the maximum solvable subsystem of the system of linear inequalities is one of these tasks. The solution algorithm for this problem is described. This algorithm is effective for linear systems of small ranks. Also, an approximate method that is effective for systems of large dimensionality is proposed. The text was submitted by the author in English. Natalja N. Katerinochkina. Born 1945. Graduated from the Faculty of Mechanics and Mathematics, Moscow State University, in 1967. Received candidates degree in Physics and Mathematics in 1978. The senior scientific worker at the Dorodnicyn Computing Centre, Russian Academy of Science. Scientific interests: discrete mathematics, mathematical cybernetics, pattern recognition, discrete optimization. Author of 35 publications.     

Infinite-horizon Scheduling Algorithms for Optimal Search for Hidden Objects

This paper considers discrete search problems in which a decision-maker has to find objects lost or hidden in a given set of locations so as to minimize the expected losses incurred. Given a chance to look for a hidden object in the same location infinitely many times, this type of problem, in contrast to standard scheduling problems, has an infinite sequence as its solution. Thus we are concerned to find an algorithm that yields an optimal solution, rather than the optimal sequence itself. Using combinatorial techniques, fast optimal algorithms for solving the problems are obtained, and optimality conditions are presented for search criteria, under which the local-search algorithms yield the global optimum.     

Sequence-dependent group scheduling problem on unrelated-parallel machines

In this research we address a sequence-dependent group scheduling problem on a set of unrelated-parallel machines where the run time of each job differs on different machines. To benefit both producer and customers we attempt to minimize a linear combination of total weighted completion time and total weighted tardiness. Since the problem is shown to be NP-hard, meta-heuristic algorithms based on tabu search are developed to find the optimal/near optimal solution. For some small size yet complex problems, the results from these algorithms are compared to the optimal solutions found by CPLEX. The result obtained in all of these problems is that the tabu search algorithms could find solutions at least as good as CPLEX but in drastically shorter computational time, thus signifying the high degree of efficiency and efficacy attained by the former.     

Coordination of intelligent agents in real-time search

Search is a fundamental problem-solving method in artificial intelligence. Traditional off-line search algorithms attempt to find an optimal solution whereas real-time search algorithms try to find a suboptimal solution more quickly than traditional algorithms to meet real-time constraints. In this work, a new multi-agent real-time search algorithm is developed and its effectiveness is illustrated on a sample domain, namely maze problems. Searching agents can see their environment with a specified visual depth and hence can partially observe their environment. An agent makes use of its partial observation to select a next move, instead of using only one-move-ahead information. Furthermore agents cooperate through a marking mechanism to be able to search different parts of the search space. When an agent selects its next move, it marks its direction of move before executing the move. When another agent comes to this position, it sees this mark and, if possible, moves in a different direction than the previously selected direction. In this way, marking helps agents coordinate their moves with other agents. Although coordination brings an overhead, from experiments we observe that this mechanism is effective in both search time and solution length in maze problems.     

Refined Inequalities for Stable Marriage

We consider two approaches to the stable marriage problem: proposal algorithms and describing the stable matching polytope using linear inequalities. We illuminate the relationship between the two approaches. Beginning with a set of linear inequalities that describe the stable matching polytope, we describe a process of refining the set of linear inequalities by eliminating redundant constraints and pruning the preference lists to eliminate unattainable assignments. We show that it is trivial to use the pruned preference lists to find the firm-optimal and worker-optimal stable matchings. We then describe a new procedure that combines a proposal algorithm and our refining process to find a stable matching that does not favor one group over the other. Finally, we apply our refining process to problems in which couples submit preferences over pairs of positions.     

An improved Opposition-Based Sine Cosine Algorithm for global optimization

Real life optimization problems require techniques that properly explore the search spaces to obtain the best solutions. In this sense, it is common that traditional optimization algorithms fail in local optimal values. The Sine Cosine Algorithms (SCA) has been recently proposed; it is a global optimization approach based on two trigonometric functions. SCA uses the sine and cosine functions to modify a set of candidate solutions; such operators create a balance between exploration and exploitation of the search space. However, like other similar approaches, SCA tends to be stuck into sub-optimal regions that it is reflected in the computational effort required to find the best values. This situation occurs due that the operators used for exploration do not work well to analyze the search space. This paper presents an improved version of SCA that considers the opposition based learning (OBL) as a mechanism for a better exploration of the search space generating more accurate solutions. OBL is a machine learning strategy commonly used to increase the performance of metaheuristic algorithms. OBL considers the opposite position of a solution in the search space. Based on the objective function value, the OBL selects the best element between the original solution and its opposite position; this task increases the accuracy of the optimization process. The hybridization of concepts from different fields is crucial in intelligent and expert systems; it helps to combine the advantages of algorithms to generate more efficient approaches. The proposed method is an example of this combination; it has been tested over several benchmark functions and engineering problems. Such results support the efficacy of the proposed approach to find the optimal solutions in complex search spaces.     

多因素制约的迷宫问题最优解的求解算法

介绍迷宫问题及其最优解,引入多因素制约的迷宫问题。重点讨论多因素制约迷宫问题最优解的含义及基于广度优先搜索的求解算法,并通过两个实例分析如何基于广度优先搜索算法求解这类迷宫问题的最优解,并给出算法的伪代码。最后,进一步讨论和总结这类迷宫问题最优解的求解算法。     

Multiple shooting algorithms for jump-discontinuous problem inoptimal control and estimation

Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved     

The fixed set search applied to the power dominating set problem

In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.     

Parameterized Polyhedra and Their Vertices

Algorithms specified for parametrically sized problems are more general purpose and more reusable than algorithms for fixed sized problems. For this reason, there is a need for representing and symbolically analyzing linearly parameterized algorithms. An important class of parallel algorithms can be described as systems of parameterized affine recurrence equations (PARE). In this representation, linearly parameterized polyhedra are used to describe the domains of variables. This paper describes an algorithm which computes the set of parameterized vertices of a polyhedron, given its representation as a system of parameterized inequalities. This provides an important tool for the symbolic analysis of the parameterized domains used to define variables and computation domains in PAREs. A library of operations on parameterized polyhedra based on the Polyhedral Library has been written in C and is freely distributed.     

On cone-invariant linear matrix inequalities

An exact solution for a special class of cone-preserving linear matrix inequalities (LMIs) is developed. By using a generalized version of the classical Perron-Frobenius theorem, the optimal value is shown to be equal to the spectral radius of an associated linear operator. This allows for a much more efficient computation of the optimal solution using, for instance, power iteration-type algorithms. This particular LMI class appears in the computation of upper bounds for some generalizations of the structured singular value μ (spherical μ) and in a class of rank minimization problems previously studied. Examples and comparisons with existing techniques are provided     

具有轮盘反转算子的多Agent算法用于线性系统逼近

针对John Holland的反转算子在数值优化中的不合理性, 提出了一种轮盘反转算子来克服这种不合理性,并结合该算子提出了一种多Agent进化算(RAER), 证明了算法的全局收敛性. 无约束优化仿真实验表明, 该算法性能好于其他算法. 在求解线性系统逼近工程优化问题时, 无论在固定区域还是动态扩展区域搜索, 算法都能得到更好的模型, 较其他算法能够对搜索区域进行更为充分的探索和求精. RAER算法是实际有效的.     

An LP-based hyperparameter optimization model for language modeling

In order to find hyperparameters for a machine learning model, algorithms such as grid search or random search are used over the space of possible values of the models’ hyperparameters. These search algorithms opt the solution that minimizes a specific cost function. In language models, perplexity is one of the most popular cost functions. In this study, we propose a fractional nonlinear programming model that finds the optimal perplexity value. The special structure of the model allows us to approximate it by a linear programming model that can be solved using the well-known simplex algorithm. To the best of our knowledge, this is the first attempt to use optimization techniques to find perplexity values in the language modeling literature. We apply our model to find hyperparameters of a language model and compare it to the grid search algorithm. Furthermore, we illustrate that it results in lower perplexity values. We perform this experiment on a real-world dataset from SwiftKey to validate our proposed approach.     

Mixed control design: Numerical optimization approaches

This paper presents some new approaches to mixed performance control problems of linear systems. The design techniques proposed in this paper are based on numerical search of the norm bounded stable transfer matrix Q in the and suboptimal controller parameterizations so that the additional performance specifications are satisfied. The design problems are then converted to some finite dimensional non-linear unconstrained optimization problems by explicitly parameterizing the or norm bounded stable transfer matrix Q for any fixed order. Finally, some two-stage optimization algorithms are applied to find the optimal parameters. Numerical examples have shown significant performance improvements of the proposed algorithms over those in the existing literature.     

基于仿射变换模型的图象特征点集配准方法研究

图象配准是计算机视觉中目标识别的一种基本方法,其目的是在待识别图象中寻找与模型图象的最佳匹配.目前,对于图象间的变换为相似变换的情形已有闭合公式.本文则分别运用最小二乘和矩阵伪逆两种方法,对图象间的变换为仿射变换的情形进行了研究,并给出了简单的闭合公式.实验表明这种方法精确、稳定、受噪声影响小.     

A nature-inspired multi-objective optimisation strategy based on a new reduced space searching algorithm for the design of alloy steels

In this paper, a salient search and optimisation algorithm based on a new reduced space searching strategy, is presented. This algorithm originates from an idea which relates to a simple experience when humans search for an optimal solution to a ‘real-life’ problem, i.e. when humans search for a candidate solution given a certain objective, a large area tends to be scanned first; should one succeed in finding clues in relation to the predefined objective, then the search space is greatly reduced for a more detailed search. Furthermore, this new algorithm is extended to the multi-objective optimisation case. Simulation results of optimising some challenging benchmark problems suggest that both the proposed single-objective and multi-objective optimisation algorithms outperform some of the other well-known Evolutionary Algorithms (EAs). The proposed algorithms are further applied successfully to the optimal design problem of alloy steels, which aims at determining the optimal heat treatment regime and the required weight percentages for chemical composites to obtain the desired mechanical properties of steel hence minimising production costs and achieving the overarching aim of ‘right-first-time production’ of metals.     

Non-permutation flowshop scheduling with dual resources

Typically, in order to process jobs in a flowshop both machines and labor are required. However, in traditional scheduling problems, labor is assumed to be plentiful and only machine is considered to be a constraint. This assumption could be due to the lower cost of labor compared to machines or the complexity of dual-resource constrained problems. In this paper a mathematical model is developed to minimize the work-in-process inventory while maximizing the service level in a flowshop with dual resources. The model focuses on optimizing a non-permutation flowshop. There are different skill levels considered for labor and the setup times on machines are sequence-dependent. Jobs are allowed to skip one or more stages in the flowshop. Job release and machine availability times are considered to be dynamic. The problem is solved in two layers. The outer layer is a search algorithm to find the schedule of jobs on the machine (traditional flowshop scheduling problem) and the inner layer is a three-step heuristic to find a schedule of jobs on labor in accordance to the machine schedule. Three different search algorithms are developed to solve the proposed NP-hard problem. First algorithm can solve a permutation flowshop while the other two are developed to solve a non-permutation flowshop. The comparison between the optimal solution and the search algorithms in small examples shows a good performance of the algorithms with an average deviation of only 2.00%. An experimental design analyzes the effectiveness and efficiency of the algorithms statistically. The results show that non-permutation algorithms perform better than the permutation algorithm, although the former are less efficient. The effectiveness and efficiency in all three algorithms have an inverse relation. To the best of our knowledge, this research is the first of its kind to provide a comprehensive mathematical model for dual resource flowshop scheduling problem.