一种解决GA收敛于局部最优解问题的新思路

通过分析GA早熟收敛的原因,给出了常用的解决GA早熟收敛的方法。同时,提出了一种解决GA收敛于局部最优解问题的新思路。

退化运输问题最优解求法的一个注记

通过一例退化运输问题用位势法作最优解判别的失效，指出了求其最优解的一个注记。

一种基于贪心法和穷举法的全局最优解算法--以限制条件下长方体遍历为例

以长方体遍历为例,利用一个三维矩阵模拟一个由若干小方块构成的长方体,利用了贪心算法先求出了遍历器的移动路线,再利用了穷举算法求出了遍历器可以被消除的剩余小方块,使得遍历器在限制条件下尽可能多地消除小方块。本文的算法思路在全局最优解的研究领域是大有可为的。

就背包和部件加工问题浅论贪婪算法的运用及优化方案

贪婪算法作为一种求最优解问题的方法,具有简便、迅捷的特点,然而贪婪算法因其基于局部求最优解的特点,决定了其在很大程度上无法得到问题的最优解。本文通过对[0-1背包问题]以及部件加工问题的分析,阐述了贪婪算法的应用以及贪婪算法存在的局限性,进而引出贪婪算法的优化方案——k阶优化方法,进一步对求最优解问题进行完善和归纳。

Hierarchical multicast with inter-layer random network coding

To maximize the aggregate throughput achieved in heterogeneous networks, this paper investigates inter-session network coding for the distribution of layered source data. We define inter-layer hierarchical random linear network codes （IHRLNC）, which not only take the flexibility of intersession network coding for layer mixing but also consider the strict priority inherent in the layered source data. Furthermore, we propose the inter-layer hierarchical multicast （IHM）, which performs IHRLNC in the network such that each sink can recover some source layers according to its individu- al capacity. To determine the optimal type of IHRLNC that should be performed on each edge in IHM, we formulate an optimization problem based on 0-1 integer linear programming, and propose a heuristic approach to approximate the optimal solution in polynomial time. Simulation results show that the proposed IHM can achieve throughput gains over the layered muhicast schemes.

Layout problem of multi-component systems arising for improving maintainability

To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainability was analyzed, and the layout problem for maintainability was presented. It was formulated as an optimization problem, where maintainability, layout space and distance requirement were formulated as objective functions. A multi-objective particle swarm optimization algorithm, in which the constrained-domination relationship and the update strategy of the global best were simply modified, was then used to obtain Pareto optimal solutions for the maintainability layout design problem. Finally, application in oxygen generation system of a spacecraft was studied in detail to illustrate the effectiveness and usefulness of the proposed method. The results show that the concurrent maintainability design can be carried out during the layout design process by solving the layout optimization problem for maintainability.

Improvement of Lagrangian relaxation performance for open pit mines constrained long-term production scheduling problem

Constrained long-term production scheduling problem(CLTPSP) of open pit mines has been extensively studied in the past few decades due to its wide application in mining projects and the computational challenges it poses become an NP-hard problem.This problem has major practical significance because the effectiveness of the schedules obtained has strong economical impact for any mining project.Despite of the rapid theoretical and technical advances in this field,heuristics is still the only viable approach for large scale industrial applications.This work presents an approach combining genetic algorithms(GAs) and Lagrangian relaxation(LR) to optimally determine the CLTPSP of open pit mines.GAs are stochastic,parallel search algorithms based on the natural selection and the process of evolution.LR method is known for handling large-scale separable problems; however,the convergence to the optimal solution can be slow.The proposed Lagrangian relaxation and genetic algorithms(LR-GAs) combines genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers.This approach leads to improve the performance of Lagrangian relaxation method in solving CLTPSP.Numerical results demonstrate that the LR method using GAs to improve its performance speeding up the convergence.Subsequently,highly near-optimal solution to the CLTPSP can be achieved by the LR-GAs.

Solving Hitchcock’s transportation problem by a genetic algorithm

Genetic algorithms (GAs) employ the evolutionary process of Darwin’s nature selection theory to find the solutions of optimization problems. In this paper, an implementation of genetic algorithm is put forward to solve a classical transportation problem, namely the Hitchcock’s Transportation Problem (HTP), and the GA is improved to search for all optimal solutions and identify them automatically. The algorithm is coded with C++ and validated by numerical examples. The computational results show that the algorithm is efficient for solving the Hitchcock’s transportation problem.

An Optimized Constraint Decomposition Method in Concurrent Engineering

In order to facilitate solution, a complex problem is normally decomposed into many small sub-problems during product development process. Teams are formed to resolve each sub-problem. The original problem is resolved from solutions of sub-problems. Ideally, sub-problems are not only mutually independent but also inherent parameters of original problem. Solution of original problem can be directly derived from the collection of solutions from simplified sub-problems. In practice, the degree of interdependency is indeed reduced, sub-problems are neither totally independent nor all inherent parameters of original problem. This paper discusses team coordination under this condition and design solution from each team, which not only satisfies total requirements but also is an optimal one. The suggested optimized constraint decomposition method will insure workable Pareto solution.

BILEVEL PROGRAMMING MODEL AND SOLUTION METHOD FOR MIXED TRANSPORTATION NETWORK DESIGN PROBLEM

By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem （MNDP） as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower- level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an Ml-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.

Compound Method of Solving Logistics Routes Allocation

The logistics routes allocation discusses optimal routing from origin to destination through distribution center （DC） on condition that both transport and distribution cost should be taken into account. The problem can be solved by the iterative non-linear programming （INLP）, in which the transport cost and distribution cost are assumed to be linear and non-linear, respectively. The method works well in most situations. However, when the distribution cost predominates in the total cost, the method falls, and the solution given by the method is not a global minimum but a local minimum. Further study reveals that the INLP method is still a kind of transport routing method like vehicle routing problem （VRP）, and the failure of the method must happen when the distribution cost is a major one. On such a condition, further computation on other extreme points, which physically means forcing all routes to pass through one DC one by one, should be carried out. By comparing values on these extreme points, the global optimal solution can be got. The method has both theoretical and practical meaning. In theoretical field, it might force us to seek new method; in practice, it reminds us to do such kind of check when the transport distance is short and warehousing work is major that often happens in local consolidation center or de-vanning center.