Large-scale Programming Problems Research Articles

Gait optimization and energy-based stability for biped locomotion using large-scale programming

AbstractThis paper presents a gait optimization method to generate the locomotion pattern for biped and discuss its stability. The main contribution of this paper is a newly proposed energy-based stability criterion, which permits the dynamic stable walking and could be straight-forwardly generalized to different locomotion scenarios and biped robots. The gait optimization problem is formulated subject to the constraints of the whole-body dynamics and kinematics. The constraints are established based on the modelling of bipedal hybrid dynamical systems. Following the whole-body modelling, the system energy is acquired and then applied to create the stability criterion. The optimization objective is also established on the system energy. The gait optimization is solved by being converted to a large-scale programming problem, where the transcription accuracy is improved via the spectral method. To further reduce the dimensionality of the large-scale problem, the whole-body dynamics is re-constructed. The generalization of the optimized gait is improved by the design of feedback control. The optimization examples demonstrate that the stability criterion naturally leads to a cyclic biped locomotion, though the periodicity was not previously imposed. Two simulation cases, level ground walking and slope walking, verify the generalization of the stability criterion and feedback control. The stability analyses are carried out by investigating the motions of centre of gravity and centre of pressure. It is revealed that if the tracked speed is above 0.3 m/s or the biped accelerates/climbs the slope, the stability criterion accomplishes the dynamic stable walking, where zero moment point criterion is not strictly complied.

Optimal and fast sensor geometry design method for TDOA localisation systemswith placement constraints

The sensor geometry design problem of time difference of arrival (TDOA) localisation systems based on Cramer-Rao bound is studied. Sensor placement constraints are considered, which means the available placement area is limited. This makes sensor geometry design a sensor selection problem. In two-dimensional (2D) TDOA localisation or 3D TDOA localisation on the earth surface, sensor selection can be implemented through solving a fractional integer programming problem. However, traditional fractional integer programming methods are either suboptimal or too time consuming. For this reason, a new method named path-varying sphere decoding is proposed in two steps. In step one, the programming problem is relaxed into two sphere decoding (SD) subproblems. Solving these subproblems leads to the optimal solution, and the required computational complexity is much less than those of traditional optimal methods. In step two, the structure of the cost function is explored. This makes it possible to calculate the path-varying upper-bound of a quadratic function. Thus the quadratic function constraint used in one SD subproblem becomes tighter and the calculation speed is enhanced. Theory analyses and simulation results show that the proposed method is not only optimal but also much faster than traditional optimal methods when solving large-scale programming problems.

A Compromise Decision-making Model for Multi-objective Large-scale Programming Problems with a Block Angular Structure under Uncertainty

This paper proposes a compromise model, based on the technique for order preference through similarity ideal solution (TOPSIS) methodology, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. This compromise programming method is based on the assumption that the optimal alternative is closer to fuzzy positive ideal solution (FPIS) and at the same time, farther from fuzzy negative ideal solution (FNIS).An aggregating function that is developed from LP- metric is based on the particular measure of ‘‘closeness” to the ‘‘ideal” solution.An efficient distance measurement is utilized to calculate positive and negative ideal solutions. The solution process is as follows: first, the decomposition algorithm is used to divide the large-dimensional objective space into a two-dimensional space. A multi-objective identical crisp linear programming is derived from the fuzzy linear model for solving the problem. Then, a single-objective large-scale linear programming problem is solved to find the optimal solution. Finally, to illustrate the proposed method, an illustrative example is provided.

A New Compromise Decision-making Model Based on TOPSIS and VIKOR for Solving Multi-objective Large-scale Programming Problems with a Block Angular Structure under Uncertainty

This paper proposes a compromise model, based on a new method, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. In this compromise programming method, two concepts are considered simultaneously. First of them is that the optimal alternative is closer to fuzzy positive ideal solution (FPIS) and farther from fuzzy negative ideal solution (FNIS). Second of them is that the proposed method provides a maximum ‘‘group utility’’ for the ‘‘majority’’ and a minimum of an individual regret for the ‘‘opponent’’. In proposed method, the decomposition algorithm is utilized to reduce the large-dimensional objective space. A multi objective identical crisp linear programming derived from the fuzzy linear model for solving the problem. Then, a compromise solution method is applied to solve each sub problem based on TOPSIS and VIKOR simultaneously. Finally, to illustrate the proposed method, an illustrative example is provided.

A Decomposition Algorithm for Solving a Three Level Large Scale linear Programming Problem

This paper presents a three level large scale linear programming problem in which the objective functions at every level are to be maximized. A three level programming problem can be thought as a static version of the Stackelberg strategy. An algorithm for solving a three planner model and a solution method for treating this problem are suggested. At each level we attempt to optimize its problem separately as a large scale programming problem using Dantzig and Wolfe decomposition method. Therefore, we handle the optimization process through a series of sub problems that can be solved independently. Finally, a numerical example is given to clarify the main results developed in this paper.

A new decision-making model for solving multi-objective large-scale programming problems with a block angular structure

This paper presents a model based on a novel compromised solution method to solve the multi-objective large-scale nonlinear programming (MOLSNLP) problems with block angular structure. In this method, an aggregating function that is developed from TOPSIS and VIKOR is proposed based on the particular measure of ‘‘closeness” to the ‘‘ideal” solution. The decomposition algorithm is utilized to reduce the large-dimensional objective space into a two-dimensional space. Furthermore, two independent solution methods are proposed to solve each nonlinear sub problem respectively. In the last step of proposed method, Single objective nonlinear programming problem is solved to find the final solution. Finally, to justify the proposed method, an illustrative example is provided. Then, the sensitivity analysis is described.

A three-level optimization method for fuzzy large-scale multiobjective nonlinear programming problems

In general, mathematical models to reflect real-world complicated decision situations, are often formulated as largescale programming problems which include a large number of variables and/or constraints. Furthermore, considering the fuzziness of human's subjective judgement in real-world decision making, it is necessary to deal with the large-scale programming problems in the fuzzy environment. From such a point of view, in this paper, under the assumption that the decision maker (DM) has fuzzy goal for each of the objective functions and the corresponding membership function may be nonlinear, a 3-level optimization method is proposed for large-scale multiobjective nonlinear programming problems (LS-MONLPs) with the block angular structure to obtain the compromise solution of the DM. Based on the proposed algorithm, the computer program is developed in FORTRAN language, and applied to the numerical example to clarify the efficiency of the proposed algorithm.

Decomposition and iterative aggregation in hierarchical and decentralised planning structures

The interpretation of decomposition approaches, originally developed for the solution of large-scale programming problems, as a representation of the planning process in a divisionalised enterprise has been treated intensively in literature. In contrast, iterative aggregation and disaggregation is seldom discussed with respect to organisational or planning aspects. This paper intends to interpret iterative aggregation in an organisational (divisionalised) context and tries to compare basic decomposition approaches with basic aggregation approaches focusing on the information flow between the different organisational levels. We also present several modifications of the standard aggregation approach and interpret them in an organisational context. The standard block-angular LP-model used implies that the structure of the organisational problem is reduced to a situation in which the co-ordination between the two organisational levels is simplified mainly to a communication process of exchanging information between the different levels.

Mathematical Programming: Theory and Algorithms.

Preface Foreword Notation Fundamental Concepts Linear Programming One-dimensional Optimization Nonlinear, Unconstrained Optimization Nonlinear Optimization with Constraints Nonlinear Constrained Optimization Integer Programming Solution of Large-scale Programming Problems: Generalized Linear Programming and Decomposition Techniques Dynamic Programming Optimization in Infinite Dimension and Applications References Appendices Index.

Team dynamics and the undergraduate curriculum

The work habits of computer science students are rarely good. Most students adopt undesirably hermetic attitudes toward problem solving, despite the fact that large-scale programming problems demand cooperative efforts for their effective solution.This is not surprising. Students learn to write programs by working alone, and are rewarded for creating programs which are somehow innovative. Much of the work produced in this sort of fashionably competitive setting is poorly communicable. Students develop idiosyncratic styles of working out-and writing down-their results, and have difficulty understanding and appreciating each other's accomplishments. Indeed, it could be said that student programs are "original" largely to the extent that they are unintelligible to other students of ostensibly similar background.This paper outlines some ways in which the curriculum of undergraduate computer science courses can be designed to promote team-oriented attitudes toward problem solving. Each of the examples discussed has been used by one or more of the authors in undergraduate classes.