A Self-Adjusting Algorithm for Driver Scheduling

Public transport driver scheduling is a world wide problem, which is NP-hard. Although some mathematically based methods are being used in the transport industry, there is still much scope for improvements. This paper presents a novel evolutionary approach that simulates the self-adjusting process on a single schedule. Five factors characterized by fuzzy membership functions are first aggregated to evaluate the shift structure. This evaluating function is incorporated into a constructing heuristic to make shift selection. A self-adjusting algorithm is then designed to guide the constructing heuristic to improve a given initial schedule iteratively. In each generation an unfit portion of the working schedule is removed. Broken schedules are repaired by the constructing heuristic until stopping condition is met. Experimental results on real-world driver scheduling problems has demonstrated the success of the proposed approach.     

模糊多目标半定规划

This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.     

A fuzzy greedy heuristic for permutation flow-shop scheduling

This paper describes a polynomial-time heuristic for the permutation flow-shop scheduling problem with the makespan criterion. The proposed method consists of two phases: arranging the jobs in priority order and then constructing a sequence. A fuzzy greedy evaluation function is employed to prioritize the jobs for incorporating into the construction phase of the heuristic. Computational experiments using standard benchmark problems indicate an improvement of the new heuristic over the well-known Nawaz, Enscore and Ham (NEH) heuristic. It will be seen that the NEH heuristic is a special case of our more general heuristic.     

Monomial geometric programming with fuzzy relation equation constraints

Monomials are widely used. They are basic structural units of geometric programming. In the process of optimization, many objective functions can be denoted by monomials. We can often see them in resource allocation and structure optimization and technology management, etc. Fuzzy relation equations are important elements of fuzzy mathematics, and they have recently been widely applied in fuzzy comprehensive evaluation and cybernetics. In view of the importance of monomial functions and fuzzy relation equations, we present a fuzzy relation geometric programming model with a monomial objective function subject to the fuzzy relation equation constraints, and develop an algorithm to find an optimal solution based on the structure of the solution set of fuzzy relation equations. Two numerical examples are given to verify the developed algorithm. Our numerical results show that the algorithm is feasible and effective.     

A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size

We consider a two-dimensional cutting stock problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as its subproblem the solution of a two-dimensional knapsack problem with two-staged guillotines cuts. A further contribution of the paper consists in the definition of a mixed integer linear programming model for the solution of this knapsack problem, as well as a heuristic procedure based on dynamic programming. Computational experiments show the effectiveness of the proposed approach, which obtains very small optimality gaps and outperforms the heuristic algorithm proposed by Cintra et al. [3].     

A Constraint-Based Method for Project Scheduling with Time Windows

This paper presents a heuristic algorithm for solving RCPSP/max, the resource constrained project scheduling problem with generalized precedence relations. The algorithm relies, at its core, on a constraint satisfaction problem solving (CSP) search procedure, which generates a consistent set of activity start times by incrementally removing resource conflicts from an otherwise temporally feasible solution. Key to the effectiveness of the CSP search procedure is its heuristic strategy for conflict selection. A conflict sampling method biased toward selection of minimal conflict sets that involve activities with higher-capacity requests is introduced, and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This CSP search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically on a large set of previously studied RCPSP/max benchmark problems.     

Synthesis of distillation trains with heat integration by a combined fuzzy and graphical approach

After passing some results of fuzzy synthesis of heat exchanger networks in review the application of this approach to the synthesis of distillation trains for the separation of multicomponent mixtures is demonstrated. The available heuristic rules are transformed into fuzzy implications dependent on different criteria and that competing rule, which is to be applied, is selected by the fuzzy algorithm.The theoretically possible amount of heat recovery within the networks generated in this way is estimated by a graphical method and included in the final cost evaluation. Regarding operating parameters like column pressure and reflux ratio, according to the mathematical effort at least qualitative statements can be made in result of the estimation of possible heat recovery.As already in the case of heat exchanger networks a following learning algorithm can serve to overcome the disadvantages of this sequential approach, representing at the same time the first step of a further evolutionary improvement of the initial distillation train.     

Two-stage fuzzy production planning expected value model and its approximation method

This work develops a novel two-stage fuzzy optimization method for solving the multi-product multi-period (MPMP) production planning problem, in which the market demands and some of the inventory costs are assumed to be uncertainty and characterized by fuzzy variables with known possibility distributions. Some basic properties about the MPMP production planning problem are discussed. Since the fuzzy market demands and inventory costs usually have infinite supports, the proposed two-stage fuzzy MPMP production planning problem is an infinite-dimensional optimization problem that cannot be solved directly by conventional numerical solution methods. To overcome this difficulty, this paper adopts an approximation method (AM) to turn the original two-stage fuzzy MPMP production planning problem into a finite-dimensional optimization problem. The convergence about the AM is discussed to ensure the solution quality. After that, we design a heuristic algorithm, which combines the AM and simulated annealing (SA) algorithm, to solve the proposed two-stage fuzzy MPMP production planning problem. Finally, one real case study about a furniture manufacturing company is presented to illustrate the effectiveness and feasibility of the proposed modeling idea and designed algorithm.     

基于层次分析法的课程表的模糊综合评价

建立了高校课程表的评价指标体系,在此基础上提出了基于层次分析法的课程表的模糊综合评价方法,并用方根法简化模糊评价的权重集求解过程.通过对具体课程表的模糊综合评价,验证了该方法是科学的、可行的.     

An approximation-based approach for fuzzy multi-period production planning problem with credibility objective

This paper develops a fuzzy multi-period production planning and sourcing problem with credibility objective, in which a manufacturer has a number of plants or subcontractors. According to the credibility service levels set by customers in advance, the manufacturer has to satisfy different product demands. In the proposed production problem, production cost, inventory cost and product demands are uncertain and characterized by fuzzy variables. The problem is to determine when and how many products are manufactured so as to maximize the credibility of the fuzzy costs not exceeding a given allowable invested capital, and this credibility can be regarded as the investment risk criteria in fuzzy decision systems. In the case when the fuzzy parameters are mutually independent gamma distributions, we can turn the service level constraints into their equivalent deterministic forms. However, in this situation the exact analytical expression for the credibility objective is unavailable, thus conventional optimization algorithms cannot be used to solve our production planning problems. To overcome this obstacle, we adopt an approximation scheme to compute the credibility objective, and deal with the convergence about the computational method. Furthermore, we develop two heuristic solution methods. The first is a combination of the approximation method and a particle swarm optimization (PSO) algorithm, and the second is a hybrid algorithm by integrating the approximation method, a neural network (NN), and the PSO algorithm. Finally, we consider one 6-product source, 6-period production planning problem, and compare the effectiveness of two algorithms via numerical experiments.     

模糊多目标半定规划的最优性条件

将模糊集理论应用到多目标半定规划中来,提出了有约束的模糊多目标半定规划模型,并首次给出了其最优有效解的定义.通过构造确定的隶属度函数,将以矩阵为决策变量的模糊多目标半定规划转化为一种目标函数的某些分量由约束函数决定的确定性多目标半定规划,并证明了前者最优有效解与后者有效解的一致性.在此基础之上,讨论了二者的最优性条件.     

带集货和配送的多站点VRP优化算法研究

带集货和配送的多站点车辆路线问题(M DVRPPD)是经典VRP的扩展,是多个站点和若干客户既有需求又有供给的VRP问题.研究了该问题的模型并提出了求解该问题的多阶段启发式算法,即先用临界客户的思想把多站点转换为单一站点问题,再使用基于SFC的分组方法来构造初始解,并运用3-opt算法优化回路,之后采用插入算法改善解的可行性,从而得到最终优化解.最后通过实例计算证明了该方法解决M DVRPPD问题的实用可行性和科学有效性.     

A column generation based heuristic for sensor placement,activity scheduling and data routing in wireless sensor networks

A wireless sensor network is a network consisting of distributed autonomous electronic devices called sensors. In this work, we develop a mixed-integer linear programming model to maximize the network lifetime by optimally determining locations of sensors and sinks, sensor-to-sink data flows, and activity schedules of the deployed sensors subject to coverage, flow conservation, energy consumption and budget constraints. Since solving this model is difficult except for very small instances, we propose a heuristic method which works on a reformulation of the problem. In the first phase of this heuristic, the linear programming relaxation of the reformulation is solved by column generation. The second phase consists of constructing a feasible solution for the original problem using the columns obtained in the first phase. Computational experiments conducted on a set of test instances indicate that both the accuracy and the efficiency of the proposed heuristic is quite promising.     

多因子分层模糊评价法的算法设计探讨——模糊综合评价方法在旅游资源评价中的应用

以模糊分析技术为平台,综合模糊分析、因子分析和层次分析的基本思想,建立了多因素、分层次的资源综合评价模型.试图通过构建旅游资源评价指标体系,将旅游资源评价模糊因素数量化,建立起旅游资源评价的模糊综合评价模型,并在旅游资源价值评价领域加以运用.     

A heuristic multi-start decomposition approach for optimal design of serial machining lines

We study an optimal design problem for serial machining lines. Such lines consist of a sequence of stations. At every station, the operations to manufacture a product are grouped into blocks. The operations within each block are performed simultaneously by the same spindle head and the blocks of the same station are executed sequentially. The inclusion and exclusion constraints for combining operations into blocks and stations as well as the precedence constraints on the set of operations are given. The problem is to group the operations into blocks and stations minimizing the total line cost. A feasible solution must respect the given cycle time and all given constraints. In this paper, a heuristic multi-start decomposition approach is proposed. It utilizes a decomposition of the initial problem into several sub-problems on the basis of a heuristic solution. Then each obtained sub-problem is solved by an exact algorithm. This procedure is repeated many times, each time it starts with a new heuristic solution. Computational tests show that the proposed approach outperforms simple heuristic algorithms for large-scale problems.     

Lower and upper bounding procedures for the bin packing problem with concave loading cost

We address the one-dimensional bin packing problem with concave loading cost (BPPC), which commonly arises in less-than-truckload shipping services. Our contribution is twofold. First, we propose three lower bounds for this problem. The first one is the optimal solution of the continuous relaxation of the problem for which a closed form is proposed. The second one allows the splitting of items but not the fractioning of bins. The third one is based on a large-scale set partitioning formulation of the problem. In order to circumvent the challenges posed by the non-linearity of the objective function coefficients, we considered the inner-approximation of the concave load cost and derived a relaxed formulation that is solved by column generation. In addition, we propose two subset-sum-based heuristics. The first one is a constructive heuristic while the second one is a local search heuristic that iteratively attempts to improve the current solution by selecting pairs of bins and solving the corresponding subset sum-problem. We show that the worst-case performance of any BPPC heuristic and any concave loading cost function is bounded by 2. We present the results of an extensive computational study that was carried out on large set of benchmark instances. This study provides empirical evidence that the column generation-based lower bound and the local search heuristic consistently exhibit remarkable performance.     

A Lagrangian Relaxation Heuristic for Capacitated Facility Location with Single-Source Constraints

Facility location models are applicable to problems in many diverse areas, such as distribution systems and communication networks. In capacitated facility location problems, a number of facilities with given capacities must be chosen from among a set of possible facility locations and then customers assigned to them. We describe a Lagrangian relaxation heuristic algorithm for capacitated problems in which each customer is served by a single facility. By relaxing the capacity constraints, the uncapacitated facility location problem is obtained as a subproblem and solved by the well-known dual ascent algorithm. The Lagrangian relaxations are complemented by an add heuristic, which is used to obtain an initial feasible solution. Further, a final adjustment heuristic is used to attempt to improve the best solution generated by the relaxations. Computational results are reported on examples generated from the Kuehn and Hamburger test problems.     

An effective and simple heuristic for the set covering problem

This paper investigates the development of an effective heuristic to solve the set covering problem (SCP) by applying the meta-heuristic Meta-RaPS (Meta-heuristic for Randomized Priority Search). In Meta-RaPS, a feasible solution is generated by introducing random factors into a construction method. Then the feasible solutions can be improved by an improvement heuristic. In addition to applying the basic Meta-RaPS, the heuristic developed herein integrates the elements of randomizing the selection of priority rules, penalizing the worst columns when the searching space is highly condensed, and defining the core problem to speedup the algorithm. This heuristic has been tested on 80 SCP instances from the OR-Library. The sizes of the problems are up to 1000 rows × 10,000 columns for non-unicost SCP, and 28,160 rows × 11,264 columns for the unicost SCP. This heuristic is only one of two known SCP heuristics to find all optimal/best known solutions for those non-unicost instances. In addition, this heuristic is the best for unicost problems among the heuristics in terms of solution quality. Furthermore, evolving from a simple greedy heuristic, it is simple and easy to code. This heuristic enriches the options of practitioners in the optimization area.     

求解具有max-t-norm合成算子的模糊关系不等式

研究一类具有max-t-norm合成算子的模糊关系不等式,该问题是模糊关系方程以及区间值模糊关系方程的推广.通过分析其解集的特点,提出一个基于筛选原则求解该类问题的算法,并给出数值算例说明该算法的有效性.     

On the recoverable robust traveling salesman problem

We consider an uncertain traveling salesman problem, where distances between nodes are not known exactly, but may stem from an uncertainty set of possible scenarios. This uncertainty set is given as intervals with an additional bound on the number of distances that may deviate from their expected, nominal values. A recoverable robust model is proposed, that allows a tour to change a bounded number of edges once a scenario becomes known. As the model contains an exponential number of constraints and variables, an iterative algorithm is proposed, in which tours and scenarios are computed alternately. While this approach is able to find a provably optimal solution to the robust model, it also needs to solve increasingly complex subproblems. Therefore, we also consider heuristic solution procedures based on local search moves using a heuristic estimate of the actual objective function. In computational experiments, these approaches are compared.