Finding non-dominated solutions in bi-objective integer network flow problems

This paper deals with an algorithm for finding all the non-dominated solutions and corresponding efficient solutions for bi-objective integer network flow problems. The algorithm solves a sequence of ?$?$-constraint problems and computes all the non-dominated solutions by decreasing order of one of the objective functions. The optimal integer solutions for the ?$?$-constraint problems are determined by exploring a branch-and-bound tree. The algorithm makes use of the network structure to perform the computations, i.e., the network structure of the problem is not destroyed with the inclusion of an ?$?$-constraint. This paper presents the main features of the algorithm, the theoretical bases of the proposed approach and some computational issues. Experiments were done and the results are also reported in the paper.     

A Dijkstra-like method computing all extreme supported non-dominated solutions of the biobjective shortest path problem

We address the problem of determining all extreme supported solutions of the biobjective shortest path problem. A novel Dijkstra-like method generalizing Dijkstra׳s algorithm to this biobjective case is proposed. The algorithm runs in O(N(m+n log n)) time to solve one-to-one and one-to-all biobjective shortest path problems determining all extreme supported non-dominated points in the outcome space and one supported efficient path associated with each one of them. Here n is the number of nodes, m is the number of arcs and N is the number of extreme supported points in outcome space for the one-to-all biobjective shortest path problem. The memory space required by the algorithm is O(n+m) for the one-to-one problem and O(N+m) for the one-to-all problem. A computational experiment comparing the performance of the proposed methods and state-of-the-art methods is included.     

An intuitionistic fuzzy goal programming approach for finding pareto-optimal solutions to multi-objective programming problems

Multi-objective optimization in the intuitionistic fuzzy environment is the process of finding a Pareto-optimal solution that simultaneously maximizes the degree of satisfaction and minimizes the degree of dissatisfaction of an intuitionistic fuzzy decision. In this paper, a new method for solving multi-objective programming problems is developed that unlike other methods in the literature, provides compromise solutions satisfying both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. This method combines the advantages of the intuitionistic fuzzy sets concept, goal programming, and interactive procedures, and supports the decision maker in the process of solving programming problems with crisp, fuzzy, or intuitionistic fuzzy objectives and constraints. A characteristic of the proposed method is that it provides a well-structured approach for determining satisfaction and the dissatisfaction degrees that efficiently uses the concepts of violation for both objective functions and constraints. Another feature of the proposed method comes from its continuous interaction with the decision maker. In this situation, through adjusting the problem's parameters, the decision maker would have the ability of revisiting the membership and non-membership functions. Therefore, despite the lack of information at the beginning of the solving process, a compromise solution that satisfies the decision maker's preferences can be obtained. A further feature of the proposed method is the introduction of a new two-step goal programming approach for determining the compromise solutions to multi-objective problems. This approach ensures that the compromise solution obtained during each iterative step satisfies both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The application of the proposed model is also discussed in this paper.     

An approach to the construction of approximate solutions of Boolean linear programming problems

Translated from Kibernetika, No. 1, pp. 40–43, January–February, 1988.     

A parametric analysis of linear integer programming problems

Parametric programming may be utilized to obtain restrictions to linear programming relaxations to linear integer programming problems. The purpose of such approaches is to reduce the size of the subproblems that appear subsequent to solving the relaxed linear programming problem. The optimal dual variables to the linear programming problem provide information regarding the difference between the continuous linear programming optimal objective function value and that of the integer linear programming objective function value.     

Measuring fidelity to extreme programming: a psychometric approach

This study assesses the Shodan survey as an instrument for measuring an individual’s or a team’s adherence to the extreme programming (XP) methodology. Specifically, we hypothesize that the adherence to the XP methodology is not a uni-dimensional construct as presented by the Shodan survey but a multidimensional one reflecting dimensions that are theoretically grounded in the XP literature. Using data from software engineers in the University of Sheffield’s Software Engineering Observatory, two different models were thus tested and compared using confirmatory factor analysis: a uni-dimensional model and a four-dimensional model. We also present an exploratory analysis of how these four dimensions affect students’ grades. The results indicate that the four-dimensional model fits the data better than the uni-dimensional one. Nevertheless, the analysis also uncovered flaws with the Shodan survey in terms of the reliability of the different dimensions. The exploratory analysis revealed that some of the XP dimensions had linear or curvilinear relationship with grades. Through validating the four-dimensional model of the Shodan survey this study highlights how psychometric techniques can be used to develop software engineering metrics of fidelity to agile or other software engineering methods.     

A genetic network programming with learning approach for enhanced stock trading model

In this paper, an enhancement of stock trading model using Genetic Network Programming (GNP) with Sarsa Learning is described. There are three important points in this paper: First, we use GNP with Sarsa Learning as the basic algorithm while both Technical Indices and Candlestick Charts are introduced for efficient stock trading decision-making. In order to create more efficient judgment functions to judge the current stock price appropriately, Importance Index (IMX) has been proposed to tell GNP the timing of buying and selling stocks. Second, to improve the performance of the proposed GNP-Sarsa algorithm, we proposed a new method that can learn the appropriate function describing the relation between the value of each technical index and the value of the IMX. This is an important point that devotes to the enhancement of the GNP-Sarsa algorithm. The third point is that in order to create more efficient judgment functions, sub-nodes are introduced in each node to select appropriate stock price information depending on the situations and to determine appropriate actions (buying/selling). To confirm the effectiveness of the proposed method, we carried out the simulation and compared the results of GNP-Sarsa with other methods like GNP with Actor Critic, GNP with Candlestick Chart, GA and Buy&Hold method. The results shows that the stock trading model using GNP-Sarsa outperforms all the other methods.     

An approximate dynamic programming approach to convex quadratic knapsack problems

Quadratic knapsack problem (QKP) has a central role in integer and combinatorial optimization, while efficient algorithms to general QKPs are currently very limited. We present an approximate dynamic programming (ADP) approach for solving convex QKPs where variables may take any integer value and all coefficients are real numbers. We approximate the function value using (a) continuous quadratic programming relaxation (CQPR), and (b) the integral parts of the solutions to CQPR. We propose a new heuristic which adaptively fixes the variables according to the solution of CQPR. We report computational results for QKPs with up to 200 integer variables. Our numerical results illustrate that the new heuristic produces high-quality solutions to large-scale QKPs fast and robustly.     

0-1 Quadratic programming approach for optimum solutions of two scheduling problems

Two scheduling problems are considered: (1) scheduling n jobs non-preemptively on a single machine to minimize total weighted earliness and tardiness (WET); (2) scheduling n jobs non-preemptively on two parallel identical processors to minimize weighted mean flow time. In the second problem, a pre-ordering of the jobs is assumed that must be satisfied for any set of jobs scheduled on each specific machine. Both problems are known to be NP-complete. A 0-1 quadratic assignment formulation of the problems is presented. An equivalent 0-1 mixed integer linear programming approach for the problems are considered and a numerical example is given. The formulations presented enable one to use optimal and heuristic available algorithms of 0-1 quadratic assignment for the problems considered here.     

Parallel programming: An axiomatic approach

This paper develops some ideas expounded in [1]. It distinguishes a number of ways of using parallelism, including disjoint processes, competition, cooperation, and communication. In each case an axiomatic proof rule is given.     

An efficient approach to approximate solutions of eighth-order boundary-value problems

In this paper, the approximate solutions to the eighth-order boundary-value differential equations are solved by using the Adomian decomposition method (ADM). The numerical solutions of the problem are calculated in the form of a series with easily computable components. The numerical illustrations show that this technique is more reliable, efficient and accurate than the traditional schemes.     

一类具有精英学习能力的增强型人工免疫网络优化算法

提出了一种用于求解优化问题的具有精英学习能力的增强型人工免疫网络(Enhanced aiNet–EL)算法. 该算法集成了亲和力学习和精英学习, 改进了免疫进化的克隆、变异和抑制算子. 通过对两个经典函数的优化实验,结果表明本文提出的Enhanced aiNet–EL算法在最优解质量和收敛速度上都要优于传统aiNet和EaiNet算法. 作为应用实例, 工业PID控制器被用于测试算法的优化性能. 实验所得的阶跃响应表明, 使用Enhanced aiNet-EL得到的系统性能要优于使用其他4种方法得到的系统     

An approach to interval programming problems with left-hand-side stochastic coefficients: An application to environmental decisions analysis

An interval programming with stochastic coefficients (IPSC) model is developed for planning of regional air quality management. The IPSC model incorporates stochastic coefficients with multivariate normal distributions within an interval parameter linear programming (ILP) framework. In IPSC, system uncertainties expressed as stochastic coefficients and intervals are addressed. Since stochastic coefficients are the left-hand-side (LHS) parameters of the constraints in IPSC, a left-hand-side chance-constrained programming (LCCP) method is developed to solve the problem. The developed IPSC model is applied to a regional air quality management system. Uncertainties in both abatement efficiencies expressed as stochastic coefficients and environmental standards expressed as intervals are reflected. Interval solutions associated with different violation probability levels and/or different environmental standards have been obtained. Air quality managers can thus analyze the solutions with appropriate combinations of the uncertainties and gain insight into the tradeoffs between the abatement costs and the risks of violating different environmental standards.     

An approach to the numerical verification of solutions for obstacle problems

In this paper, we consider numerical techniques which enable us to verify the existence of solutions for a general obstacle problem using computers. We describe the numerical verification algorithm for solving a two dimensional obstacle problem and report a numerical result.     

Integer programming problems with inexact data: Exact and approximate solutions

The study was partially supported by the Joint Foundation of the Government of Ukraine and International Scientific Foundation (grant No. K4C100).