Solving the degree-concentrated fault-tolerant spanning subgraph problem by DC programming

In this paper, we consider the maximum and minimum versions of degree-concentrated fault-tolerant spanning subgraph problem which has many applications in network communications. We prove that both this two problems are NP-hard. For the maximum version, we use DC programming relaxation to propose a heuristic algorithm. Numerical tests indicate that the proposed algorithm is efficient and effective. For the minimum version, we also formulate it as a DC program, and show that the DC algorithm does not perform well for this problem.     

Linear and quadratic programming approaches for the general graph partitioning problem

The graph partitioning problem is to partition the vertex set of a graph into a number of nonempty subsets so that the total weight of edges connecting distinct subsets is minimized. Previous research requires the input of cardinalities of subsets or the number of subsets for equipartition. In this paper, the problem is formulated as a zero-one quadratic programming problem without the input of cardinalities. We also present three equivalent zero-one linear integer programming reformulations. Because of its importance in data biclustering, the bipartite graph partitioning is also studied. Several new methods to determine the number of subsets and the cardinalities are presented for practical applications. In addition, hierarchy partitioning and partitioning of bipartite graphs without reordering one vertex set, are studied.     

Stochastic and Risk Management Models and Solution Algorithm for Natural Gas Transmission Network Expansion and LNG Terminal Location Planning

Due to the increasing demands for natural gas, it is playing a more important role in the energy system, and its system expansion planning is drawing more attentions. In this paper, we propose expansion planning models which include both natural gas transmission network expansion and LNG (Liquified Natural Gas) terminals location planning. These models take into account the uncertainties of demands and supplies in the future, which make the models stochastic mixed integer programs with discrete subproblems. Also we consider risk control in our models by including probabilistic constraints, such as a limit on CVaR (Conditional Value at Risk). In order to solve large-scale problems, especially with a large number of scenarios, we propose the embedded Benders decomposition algorithm, which applies Benders cuts in both first and second stages, to tackle the discrete subproblems. Numerical results show that our algorithm is efficient for large scale stochastic natural gas transportation system expansion planning problems.     

On the optimization properties of the correntropic loss function in data analysis

Similarity measures play a critical role in the solution quality of data analysis methods. Outliers or noise often taint the solution, hence, practical data analysis calls for robust measures. The correntropic loss function is a smooth and robust measure. In this paper, we present the properties of the correntropic loss function that can be utilized in optimization based data analysis methods.     

Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems

By constructing a kind of generalized Lagrange function for a class of multiobjective fractional optimal control problems, sufficient and necessary conditions for existence of generalized weak saddle points are established. In addition, the relationship between weak efficiency and generalized weak saddle points is discussed.     

Theoretical and algorithmic advances in multi-parametric programming and control

This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system.     

Simple measure of similarity for the market graph construction

A simple measure of similarity for the construction of the market graph is proposed. The measure is based on the probability of the coincidence of the signs of the stock returns. This measure is robust, has a simple interpretation, is easy to calculate and can be used as measure of similarity between any number of random variables. For the case of pairwise similarity the connection of this measure with the sign correlation of Fechner is noted. The properties of the proposed measure of pairwise similarity in comparison with the classic Pearson correlation are studied. The simple measure of pairwise similarity is applied (in parallel with the classic correlation) for the study of Russian and Swedish market graphs. The new measure of similarity for more than two random variables is introduced and applied to the additional deeper analysis of Russian and Swedish markets. Some interesting phenomena for the cliques and independent sets of the obtained market graphs are observed.     

Algorithm robust for the bicriteria discrete optimization problem

We apply Algorithm Robust to various problems in multiple objective discrete optimization. Algorithm Robust is a general procedure that is designed to solve bicriteria optimization problems. The algorithm performs a weight space search in which the weights are utilized in min-max type subproblems. In this paper, we experiment with Algorithm Robust on the bicriteria knapsack problem, the bicriteria assignment problem, and the bicriteria minimum cost network flow problem. We look at a heuristic variation that is based on controlling the weight space search and has an indirect control on the sample of efficient solutions generated. We then study another heuristic variation which generates samples of the efficient set with quality guarantees. We report results of computational experiments.