The dynamic vehicle rescheduling problem

The pre-planned schedules of a transportation company are often disrupted by unforeseen events. As a result of a disruption, a new schedule has to be produced as soon as possible. This process is called the vehicle rescheduling problem, which aims to solve a single disruption and restore the order of transportation. However, there are multiple disruptions happening over a “planning unit” (usually a day), and all of them have to be addressed to achieve a final feasible schedule. From an operations management point of view the quality of the final solution has to be measured by the combined quality of every change over the horizon of the “planning unit”, not by evaluating the solution of each disruption as a separate problem. The problem of finding an optimal solution where all disruptions of a “planning unit” are addressed will be introduced as the dynamic vehicle rescheduling problem (DVRSP). The disruptions of the DVRSP arrive in an online manner, but giving an optimal final schedule for the “planning unit” would mean knowing all information in advance. This is not possible in a real-life scenario, which means that heuristic solution methods have to be considered. In this paper, we present a recursive and a local search algorithm to solve the DVRSP. In order to measure the quality of the solutions given by the heuristics, we introduce the so-called quasi-static DVRSP, a theoretical problem where all the disruptions are known in advance. We give two mathematical models for this quasi-static problem, and use their optimal solutions to evaluate the quality of our heuristic results. The heuristic methods for the dynamic problem are tested on different random instances.     

Minimising the number of gap-zeros in binary matrices

We study a problem of minimising the total number of zeros in the gaps between blocks of consecutive ones in the columns of a binary matrix by permuting its rows. The problem is referred to as the Consecutive Ones Matrix Augmentation Problem, and is known to be NP-hard. An analysis of the structure of an optimal solution allows us to focus on a restricted solution space, and to use an implicit representation for searching the space. We develop an exact solution algorithm, which is linear-time in the number of rows if the number of columns is constant, and two constructive heuristics to tackle instances with an arbitrary number of columns. The heuristics use a novel solution representation based upon row sequencing. In our computational study, all heuristic solutions are either optimal or close to an optimum. One of the heuristics is particularly effective, especially for problems with a large number of rows.     

An improved heuristic for the far from most strings problem

The Far From Most Strings Problem (FFMSP) asks for a string that is far from as many as possible of a given set of strings. All the input and the output strings are of the same length, and two strings are far if their Hamming distance is greater than or equal to a given threshold. FFMSP belongs to the class of sequence consensus problems which have applications in molecular biology, amongst others. FFMSP is NP-hard. It does not admit a constant-ratio approximation either, unless P=NP. In the last few years, heuristic and metaheuristic algorithms have been proposed for the problem, which use local search and require a heuristic, also called an evaluation function, to evaluate candidate solutions during local search. The heuristic function used, for this purpose, in these algorithms is the problem’s objective function. However, since many candidate solutions can be of the same objective value, the resulting search landscape includes many points which correspond to local maxima. In this paper, we devise a new heuristic function to evaluate candidate solutions. We then incorporate the proposed heuristic function within a Greedy Randomized Adaptive Search Procedure (GRASP), a metaheuristic originally proposed for the problem by Festa. The resulting algorithm outperforms state-of-the-art with respect to solution quality, in some cases by orders of magnitude, on both random and real data in our experiments. The results indicate that the number of local optima is considerably reduced using the proposed heuristic.     

An integrated approach to dynamic plant location and capacity planning

We consider a dynamic capacitated plant location problem in which capacities of opened plants are determined by acquisition and/or disposal of multiple types of facilities. We determine the opening schedule of plants, allocations of customers' demands and plans for acquisition and/or disposal of plant capacities that minimise the sum of discounted fixed costs for opening plants, delivery costs of products, and acquisition and operation costs of facilities. The dynamic capacitated plant location problem is formulated as a mixed integer linear program and solved by a heuristic algorithm based on Lagrangian relaxation and a cut and branch algorithm which uses Gomory cuts. Several solution properties of the relaxed problem are found and used to develop efficient solution procedures for the relaxed problem. A subgradient optimisation method is employed to obtain better lower bounds. The heuristic algorithm is tested on randomly generated test problems and results show that the algorithm finds good solutions in a reasonable amount of computation time.     

A large neighbourhood search heuristic for the aircraft and passenger recovery problem

This paper introduces a large neighbourhood search heuristic for an airline recovery problem combining fleet assignment, aircraft routing and passenger assignment. Given an initial schedule, a list of disruptions, and a recovery period, the problem consists in constructing aircraft routes and passenger itineraries for the recovery period that allow the resumption of regular operations and minimize operating costs and impacts on passengers. The heuristic alternates between construction, repair and improvement phases, which iteratively destroy and repair parts of the solution. The aim of the first two phases is to produce an initial solution that satisfies a set of operational and functional constraints. The third phase then attempts to identify an improved solution by considering large schedule changes while retaining feasibility. The whole process is iterated by including some randomness in the construction phase so as to diversify the search. This work was initiated in the context of the 2009 ROADEF Challenge, a competition organized jointly by the French Operational Research and Decision Analysis Society and the Spanish firm Amadeus S.A.S., in which our team won the first prize.     

Scheduling interfering job sets on parallel machines

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT–LPT–SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy – based on the properties of a non-dominated solution – to ensure that all parts of the non-dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs.     

A hybrid genetic algorithm for the job shop scheduling problem

This paper presents a hybrid genetic algorithm for the job shop scheduling problem. The chromosome representation of the problem is based on random keys. The schedules are constructed using a priority rule in which the priorities are defined by the genetic algorithm. Schedules are constructed using a procedure that generates parameterized active schedules. After a schedule is obtained a local search heuristic is applied to improve the solution. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.     

A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over

In this paper, the multi-item, single-level, capacitated, dynamic lot sizing problem with set-up carry-over and backlogging, abbreviated to CLSP⁺, is considered. The problem is formulated as a mixed integer programming problem. A heuristic method consisting of four elements: (1) a demand shifting rule, (2) lot size determination rules, (3) checking feasibility conditions and (4) set-up carry-over determination, provides us with an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing it by solving a minimum-cost network flow problem. Then the improved solution is used as a starting solution for a tabu search procedure, with the value of moves assessed using the same minimum-cost network problem. Computational results on randomly generated problems show that the algorithm, which is coded in C++, is able to provide optimal solutions or solutions extremely close to optimal. The computational efficiency makes it possible to solve reasonably large problem instances routinely on a personal computer.     

Algorithms for effective transfer of ballast for an oil installation

The problem considered is to transfer ballast (water) between ballast tanks in an offshore production platform in a fast and efficient way, and at the same time maintain certain criteria regarding the platform’s safety, stability and strength. In case of an emergency situation, the algorithm must return a solution in short time. Two alternative algorithms are evaluated; one mixed integer programming (MIP) model and one heuristic algorithm. It is shown that the much simpler heuristic algorithm yields satisfactory solutions in almost no time, while the MIP model takes up to several minutes to come to a solution. The heuristic algorithm is installed in control systems for a platform operating in the North Sea and the experience so far has been good.     

An effective heuristic algorithm to minimise stack shuffles in selecting steel slabs from the slab yard for heating and rolling

Steel production is a multi-stage process. A slab yard serves as a buffer between the continuous casting stage and the steel rolling stage. Steel slabs are stored in stacks in the yard. Shuffling is needed when picking up a slab for heating and rolling, if it is not in the top position of a stack. This paper studies the problem of selecting appropriate slabs in the yard for a given rolling schedule so as to minimise the total shuffling cost. The study uses the hot strip rolling mill in Shanghai Baoshan Iron and Steel Complex as an application background. We propose a new heuristic algorithm to solve the problem. This is a two-phase algorithm that first generates an initial feasible solution and then improves it using local search. The new algorithm is compared with the algorithm in use on randomly generated test problems and on real data. Experimental results show that the proposed algorithm yields significant better solutions. The average improvement over the old algorithm is 15%.     

面向靠桥率及道口冲突率的航班-机位指派问题优化模型及其启发式算法研究

在给定航班时刻表条件下,对于进出港航班的机位分配,除了必须满足航班、飞机和机位之间的技术性要求之外,还要考虑尽量提高整个机场的机位利用率,且方便旅客出入港及时、安全和便捷.文章以飞机机型、所属航空公司、客运/货运航班、国内/国际航班等匹配条件为约束条件,以航班-机位分配完成率、靠桥率、道口非冲突率为目标,建立了一个航班...     

An exact branch-and-price algorithm for scheduling rescue units during disaster response

In disaster operations management, a challenging task for rescue organizations occurs when they have to assign and schedule their rescue units to emerging incidents under time pressure in order to reduce the overall resulting harm. Of particular importance in practical scenarios is the need to consider collaboration of rescue units. This task has hardly been addressed in the literature. We contribute to both modeling and solving this problem by (1) conceptualizing the situation as a type of scheduling problem, (2) modeling it as a binary linear minimization problem, (3) suggesting a branch-and-price algorithm, which can serve as both an exact and heuristic solution procedure, and (4) conducting computational experiments – including a sensitivity analysis of the effects of exogenous model parameters on execution times and objective value improvements over a heuristic suggested in the literature – for different practical disaster scenarios. The results of our computational experiments show that most problem instances of practically feasible size can be solved to optimality within ten minutes. Furthermore, even when our algorithm is terminated once the first feasible solution has been found, this solution is in almost all cases competitive to the optimal solution and substantially better than the solution obtained by the best known algorithm from the literature. This performance of our branch-and-price algorithm enables rescue organizations to apply our procedure in practice, even when the time for decision making is limited to a few minutes. By addressing a very general type of scheduling problem, our approach applies to various scheduling situations.     

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.     

Single facility scheduling with multiple job classes

This paper considers a static single facility scheduling problem where jobs are divided into several mutually exclusive classes. The jobs in a given class need not be processed together. In addition to a known processing time for each job, there is a switching time involved which depends on the class of the job immediately preceding a job. A heuristic algorithm is proposed to find a minimum mean flow time schedule. The effectiveness of the proposed heuristic algorithm is empirically evaluated and found to indicate that the solutions obtained from this heuristic algorithm are often close to optimal.     

A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems

This paper considers a transportation problem for moving empty or laden containers for a logistic company. Owing to the limited resource of its vehicles (trucks and trailers), the company often needs to sub-contract certain job orders to outsourced companies. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such as time windows and availability of trailers. To solve such a multi-objective and multi-modal combinatorial optimization problem, a hybrid multi-objective evolutionary algorithm (HMOEA) featured with specialized genetic operators, variable-length representation and local search heuristic is applied to find the Pareto optimal routing solutions for the TTVRP. Detailed analysis is performed to extract useful decision-making information from the multi-objective optimization results as well as to examine the correlations among different variables, such as the number of trucks and trailers, the trailer exchange points, and the utilization of trucks in the routing solutions. It has been shown that the HMOEA is effective in solving multi-objective combinatorial optimization problems, such as finding useful trade-off solutions for the TTVRP routing problem.     

Improvements to a large neighborhood search heuristic for an integrated aircraft and passenger recovery problem

Because most commercial passenger airlines operate on a hub-and-spoke network, small disturbances can cause major disruptions in their planned schedules and have a significant impact on their operational costs and performance. When a disturbance occurs, the airline often applies a recovery policy in order to quickly resume normal operations. We present in this paper a large neighborhood search heuristic to solve an integrated aircraft and passenger recovery problem. The problem consists of creating new aircraft routes and passenger itineraries to produce a feasible schedule during the recovery period. The method is based on an existing heuristic, developed in the context of the 2009 ROADEF Challenge, which alternates between three phases: construction, repair and improvement. We introduce a number of refinements in each phase so as to perform a more thorough search of the solution space. The resulting heuristic performs very well on the instances introduced for the challenge, obtaining the best known solution for 17 out of 22 instances within five minutes of computing time and 21 out of 22 instances within 10 minutes of computing time.     

Simulated annealing for the unconstrained quadratic pseudo-Boolean function

In this paper, we develop a simulated annealing (SA) based heuristic for the unconstrained quadratic pseudo-Boolean function. An algorithm that solves the problem in O(n²) at each temperature of the cooling schedule is given. The performance of SA based heuristic is compared with existing bounding algorithms for this problem. Computational results and comparisons on several hundred test problems demonstrate the efficiency of our heuristic in terms of solution quality and computational time. A new set of hard test problems with their best solution is provided to facilitate future comparison.     

Two-Stage,Hybrid Flowshop Scheduling Problem

This paper describes the two-stage flowshop problem when there are identical multiple machines at each stage, and shows that the problem is NP-complete. An efficient heuristic algorithm is developed for finding an approximate solution of a special case when there is only one machine at stage 2. The effectiveness of the proposed heuristic algorithm in finding a minimum makespan schedule is empirically evaluated and found to increase with the increase in the number of jobs.     

A penalty-based heuristic algorithm for the permutation flowshop scheduling problem with sequence-dependent set-up times

This paper considers the permutation flowshop scheduling problem with sequence-dependent set-up times and develops a penalty-based heuristic algorithm to find an approximately minimum makespan schedule. The proposed algorithm determines the penalty in time associated with a particular sequence and selects the sequence with the minimum time penalty as the best heuristic solution. Computational results comparing the effectiveness and efficiency of the proposed penalty-based heuristic algorithm with an existing savings index heuristic algorithm are reported and discussed.     

校车站点及线路的优化设计

以高校新校区教师校车站点及线路安排为对象,首先针对乘车站点建立了双目标非线性规划模型,其中目标函数包括乘客到达站点的距离偏差最小与所有乘客到达站点的总的距离最小两个方面;站点确定后针对车辆数最少、车辆行驶的总距离最短、各辆车的运行距离均衡及各辆车的负荷均衡这4个目标建立针对线路优化的多目标非线性规划模型,并给出了解决这类问题的启发式优化算法.与目前国内外研究相比较,该模型与算法更实际,更具体的给出了问题的解答.