Heuristic Solution Methods Research Articles

The Weighted Fair Sequences Problem

Scheduling problems on which constraints are imposed with regard to the temporal distances between successive executions of the same task have numerous applications, ranging from task scheduling in real-time systems to automobile production on a mixed-model assembly line. This paper introduces a new NP-hard optimization problem belonging to this class of problems, namely the Weighted Fair Sequences Problem (WFSP). We present a mathematical formulation for the WFSP based on mixed-integer linear programming (MILP) as well as a series of cuts to improve its resolution via exact methods. Finally, we propose a heuristic solution method that works with much less variables of the WFSP formulation. The reported computational experiments show that, for a given time horizon, the proposed MILP-based heuristic increases the size of WFSP instances that can be tackled in practice. Moreover, its results should be considered as optimal whether a presented conjecture on the WFSP problem is proved true in the future.

On the resource renting problem with overtime

In this paper the Resource Renting Problem with Overtime (RRP/overtime) is presented. The RRP/overtime is a new problem in which the assumptions of the basic RRP are combined with the possibility to schedule (parts of) activities during overtime. The addition of this extension increases the applicability of the RRP to real world problems. This paper also presents a solution technique for this extension of the resource renting problem. The solution procedure uses a scatter search heuristic to optimize a priority list, which is then in turn used by a schedule generation scheme (PatSGS). A variation on this schedule generation scheme is also used in dedicated local search procedures. The third contribution of this research is a new lower bound for the RRP/overtime problem, which is used to evaluate the results of the proposed heuristic solution method.

Improving regional road network resilience by optimised traffic guidance

ABSTRACTIn this paper, a new approach for improving the traffic performance of regional road networks during the recovery period following a disaster life cycle is presented. Regional road networks are often uncongested and have sparse and long-spanning link densities. Consequently, they are more impacted by natural disasters and thereby by potential road closures that may be imposed afterwards. Information about road closures after disruptive events can be transmitted through roadside information dissemination methods such as variable message signs, Cooperative-Intelligent Transport Systems or highway advisory radio. This paper proposes an optimisation model to find optimal location of roadside guidance devices across a regional road network for improving total travel time (TTT) within the network. To achieve this, firstly, a network design model is formulated using a bi-level framework and implemented to find the optimal locations of roadside guidance devices that lead to reducing the TTT of a disrupted network. Secondly, two methods for solving the formulated problem are presented, an exact solution method called SO-relaxation that cuts the solution space using system optimum traffic assignment. The other method is a hybrid-GA that is a heuristic solution method. Results show that locating guidance devices optimally in a disrupted network leads to a more resilient road network in which the post-disaster TTT of the network during recovery phase is less than when no action is taken. It is also shown that the improvement achieved by roadside guidance is a function of available resources and the road users willingness to obey the guidance provided.

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.

A decomposition algorithm to solve the multi-hop Peer-to-Peer ride-matching problem

In this paper, we mathematically model the multi-hop Peer-to-Peer (P2P) ride-matching problem as a binary program. We formulate this problem as a many-to-many problem in which a rider can travel my transferring between multiple drivers, and a driver can carry multiple riders. We propose a pre-processing procedure to reduce the size of the problem, and devise a decomposition algorithm to solve the original ride-matching problem to optimality by means of solving multiple smaller problems. We conduct extensive numerical experiments to demonstrate the computational efficiency of the proposed algorithm and show its practical applicability to reasonably-sized dynamic ride-matching contexts. Finally, in the interest of even lower solution times, we propose heuristic solution methods, and investigate the trade-offs between solution time and accuracy.

A heuristic solution method for disassemble-to-order problems with binomial disassembly yields

In disassemble-to-order problems, where a specific amount of several components must be obtained from the disassembly of several types of returned products, random disassembly yields create a formidable challenge for appropriate planning. In this context, it is typically assumed that yields from disassembly are either stochastically proportional or follow a binomial process. In the case of yield process misspecification, it has been shown (see Inderfurth et al. (2015)) that assuming binomial yields usually results in a lower penalty than assuming stochastically proportional yields. While there have been heuristics developed for the disassemble-to-order problem with stochastically proportional yields, a suitable, powerful heuristic for binomial yields is needed in order to facilitate solving problems with complex real-world product structures. We present a heuristic approach that is based on a decomposition procedure for the underlying non-linear stochastic optimization problem and that can be applied to problems of arbitrary size. A comprehensive numerical performance study using both randomly generated instances as well as a full factorial experimental design and, additionally, the data of a practical case example reveals that this heuristic delivers close-to-optimal results.

Fleet routing and scheduling in bushfire emergency evacuation: A regional case study of the Black Saturday bushfires in Australia

Evacuation planning provides evidence base for effective decision-making in various aspects of disaster response, such as the selection of safe shelters, dynamic assignment of rescue vehicles, and the identification of safest routes and vehicle scheduling. However, an efficient emergency service response to a short-notice bushfire evacuation is a complicated procedure. Any failure to response promptly to short notice evacuation can adversely affect the effectiveness of operations and hence potentially contribute to increased fatalities. This study develops a Vehicle Routing Problem (VRP) model to enhance the efficiency and effectiveness of short-notice emergency response and rescue operations. This model computes the required number of vehicles and identifies the safest routes and schedules for late evacuees under various time windows and road disruption risk. A heuristic solution method is developed to tackle this highly complex nature of VRP due to operational interdependencies. The model parameters are realistically derived from the 2009 Black Saturday bushfires in Victoria, Australia. The results indicate the feasibility of evacuating 1100 late evacuees via low risk routes within the available resources of four shelters and seven rescue vehicles. However, the evacuation of late evacuees from the bushfire affected areas to safe shelters could be potentially affected when the hard constraints such as the time-window are changed. Nevertheless, the model outputs are useful in the development of emergency evacuation plans to mitigate the potential risk of fatality or injury during a bushfire.

Alternative Mathematical Models and Solution Approaches for Lot-Sizing and Scheduling Problems in the Brewery Industry: Analyzing Two Different Situations

This research proposes new approaches to deal with the production planning and scheduling problem in brewery facilities. Two real situations found in factories are addressed, which differ by considering (or not) the setup operations in tanks that provide liquid for bottling lines. Depending on the technology involved in the production process, the number of tank swaps is relevant (Case A) or it can be neglected (Case B). For both scenarios, new MIP (Mixed Integer Programming) formulations and heuristic solution methods based on these formulations are proposed. In order to evaluate the approach for Case A, we compare the results of a previous study with the results obtained in this paper. For the solution methods and the result analysis of Case B, we propose adaptations of Case A approaches yielding an alternative MIP formulation to represent it. Therefore, the main contributions of this article are twofold: (i) to propose alternative MIP models and solution methods for the problem in Case A, providing better results than previously reported, and (ii) to propose new MIP models and solution methods for Case B, analyzing and comparing the results and benefits for Case B considering the technology investment required.

Scheduling in-house transport vehicles to feed parts to automotive assembly lines

Due to exorbitant product variety, very limited space, and other factors, organizing efficient and timely deliveries of parts and subassemblies to final assembly within the factory is one of the most pressing problems of modern mixed-model assembly production. Many automobile producers have implemented the so-called “supermarket” concept to transfer material to the assembly line frequently and in small lots. Supermarkets are decentralized logistics areas on the shop floor where parts are intermediately stored for nearby assembly cells, to be ferried there by small transport vehicles (called tow trains or tuggers). This paper tackles the operational problem of drawing up schedules for these tow trains, such that the assembly line never starves for parts while also minimizing in-process inventory, thus satisfying just-in-time goals. We prove strong NP-completeness of the problem and present exact and heuristic solution methods. In a computational study, the procedures are shown to perform very well, solving realistic instances to (near-)optimality in a matter of minutes, clearly outperforming the simple cyclic schedules commonly used in industrial practice. We also provide some managerial insight into the right degree of automation for such a part feeding system.

A branch-and-bound approach for robust railway timetabling

This paper studies the robust cyclic timetabling problem. The goal is to modify a given reference timetable to enhance its robustness against small stochastic disturbances. The robustness is measured by the expected total delay of the realised timetable. Kroon et al. (Transp Res Part B 42(6):553–570, 2008) propose a stochastic programming approach and implement it for Netherlands Railways (NS). While the model’s outcome is accepted by practitioners, relevant planning problems are rendered intractable by computation times of up to several days. In this paper we describe a Branch-and-Bound algorithm for solving the stochastic program of Kroon et al. (Transp Res Part B 42(6):553–570, 2008). We propose specific node selection rules, variable selection rules, constructive heuristics and lower bounds. We carry out computational tests on large real-life problem instances. The results confirm that our algorithm is able to considerably improve the robustness of the reference solutions. This is achieved with computation times of a few minutes. However, the weak lower bounds we use leave a considerable optimality gap. Therefore, our algorithm is best described as a heuristic solution method.

Production planning with price-dependent supply capacity

ABSTRACTWe consider a production planning problem in which a producer procures an input component for production by offering a price to suppliers. The available supply quantity for the production input depends on the price the producer offers, and this supply level constrains production output. The producer seeks to meet a set of demands over a finite horizon at a minimum cost, including component procurement costs. We model the problem as a discrete-time production and component supply–pricing planning problem with nonstationary costs, demands, and component supply levels. This leads to a two-level lot-sizing problem with an objective function that is neither concave nor convex. Although the most general version of the problem is -hard, we provide polynomial-time algorithms for two special cases of the model under particular assumptions on the cost structure. We then apply the resulting algorithms heuristically to the more general problem version and provide computational results that demonstrate the high performance quality of the resulting heuristic solution methods.

Optimizing emergency preparedness and resource utilization in mass-casualty incidents

This paper presents a response model for the aftermath of a Mass-Casualty Incident (MCI) that can be used to provide operational guidance for regional emergency planning as well as to evaluate strategic preparedness plans. A mixed integer programming (MIP) formulation is proposed for the combined ambulance dispatching, patient-to-hospital assignment, and treatment ordering problem. The goal is to allocate effectively the limited resources during the response so as to improve patient outcomes, while the objectives are to minimize the overall response time and the total flow time required to treat all patients, in a hierarchical fashion. The model is solved via exact and MIP-based heuristic solution methods. The applicability of the model and the performance of the new methods are challenged on realistic MCI scenarios. We consider the hypothetical case of a terror attack at the New York Stock Exchange in Lower Manhattan with up to 150 trauma patients. We quantify the impact of capacity-based bottlenecks for both ambulances and available hospital beds. We also explore the trade-off between accessing remote hospitals for demand smoothing versus reduced ambulance transportation times.

Robust flows with losses and improvability in evacuation planning

We consider a network flow problem, where the outgoing flow is reduced by a certain percentage in each node. Given a maximum amount of flow that can leave the source node, the aim is to find a solution that maximizes the amount of flow which arrives at the sink. Starting from this basic model, we include two new, additional aspects: On the one hand, we are able to reduce the loss at some of the nodes; on the other hand, the exact loss values are not known, but may come from a discrete uncertainty set of exponential size. Applications for problems of this type can be found in evacuation planning, where one would like to improve the safety of nodes such that the number of evacuees reaching safety is maximized. We formulate the resulting robust flow problem with losses and improvability as a two-stage mixed-integer program with uncertain recourse for finitely many scenarios and present an iterative scenario-generation procedure that avoids the inclusion of all scenarios from the beginning as well as several heuristic solution methods. In a computational study using both randomly generated instances and realistic data based on the city of Nice, France, we compare our solution algorithms.

Heuristic Search in Dual Space for Constrained Stochastic Shortest Path Problems

We consider the problem of generating optimal stochastic policies for Constrained Stochastic Shortest Path problems, which are a natural model for planning under uncertainty for resource-bounded agents with multiple competing objectives. While unconstrained SSPs enjoy a multitude of efficient heuristic search solution methods with the ability to focus on promising areas reachable from the initial state, the state of the art for constrained SSPs revolves around linear and dynamic programming algorithms which explore the entire state space. In this paper, we present i-dual, which, to the best of our knowledge, is the first heuristic search algorithm for constrained SSPs. To concisely represent constraints and efficiently decide their violation, i-dual operates in the space of dual variables describing the policy occupation measures. It does so while retaining the ability to use standard value function heuristics computed by well-known methods. Our experiments on a suite of PPDDL problems augmented with constraints show that these features enable i-dual to achieve up to two orders of magnitude improvement in run-time and memory over linear programming algorithms.

Objective Function Development Based on the Parameters of a Regional Terminal Network

The article is devoted to the development of the objective function for calculating the parameters of a terminal network in a region. The key parameters of a terminal network, as logistic system, are described. The factors influencing the parameters of a terminal network are analyzed, and the objective function, concerning the value and qualitative aspects for determining the transport and spatial/quantitative parameters proposed. The level of service quality for the clients is also taken into account. The heuristic solution method, and the results of the approach are demonstrated with the help of an application example concerning different combinations of distribution.

An activity-based approach for optimisation of land use and transportation network development

This paper tentatively makes use of an activity-based approach to investigate the optimisation problem of land use allocation and transportation network enhancement, in which the budget for investment and some other constraints are given for the purpose of sustainable urban development. To make investigation on residential and employment development as well as road link capacity expansions for short-term strategic planning purposes, a new bi-level programming model is proposed to capture the interactions between land use and transportation network development together with their impacts on activity-travel choice behaviours. The lower level of the proposed model is used to model the choice behaviour of commuters on activity chain, departure time, path and activity scheduling duration simultaneously over the time of day, while the upper level is to maximise the population allocation and network enhancement subject to a set of given constraints. A heuristic solution method is developed to solve the proposed bi-level model. Finally, two numerical examples are presented to demonstrate the application of the proposed model and solution algorithm together with some insightful findings.

A novel metaheuristic for traveling salesman problem: blind mole-rat algorithm

Traveling Salesman Problem (TSP) is the problem of finding a minimum distance tour of cities beginning and ending at the same city and that each city are visited only once. As the number of cities increases, it is difficult to find an optimal solution by exact methods in a reasonable duration. Therefore, in recent five decades many heuristic solution methods inspired of nature and biology have been developed. In this paper, a new metaheuristic method inspired of the by-passing the obstacle strategy of blind mole rats living in their individual tunnel systems under the soil is designed for solving TSP. The method is called as Blind Mole-rat Algorithm. The proposed algorithm is tested on different size of symmetric TSP problems and the results are compared to the best known results. Initial test results are promising although proposed metaheuristic is not yet competitive enough among other algorithms in the literature. Keywords: Traveling salesman problem, Combinatorial optimization, Metaheuristic, Blind mole-Rat algorithm

Planning of complex supply chains: A performance comparison of three meta-heuristic algorithms

Businesses have more complex supply chains than ever before. Many supply chain planning efforts result in sizable and often nonlinear optimization problems that are difficult to solve using standard solution methods. Meta-heuristic and heuristic solution methods have been developed and applied to tackle such modeling complexities. This paper aims to compare and analyze the performance of three meta-heuristic algorithms in solving a nonlinear green supply chain planning problem. A tactical planning model is presented that aims to balance the economic and emissions performance of the supply chain. Utilizing data from an Australian clothing manufacturer, three meta-heuristic algorithms including Genetic Algorithm, Simulated Annealing and Cross-Entropy are adopted to find solutions to this problem. Discussions on the key characteristics of these algorithms and comparative analysis of the numerical results provide some modeling insights and practical implications. In particular, we find that (1) a Cross-Entropy method outperforms the two popular meta-heuristic algorithms in both computation time and solution quality, and (2) Simulated Annealing may produce better results in a time-restricted comparison due to its rapid initial convergence speed.

A variable neighborhood search for the multi-period collection of recyclable materials

We consider an approach for scheduling the multi-period collection of recyclable materials. Citizens can deposit glass and paper for recycling in small cubes located at several collection points. The cubes are emptied by a vehicle that carries two containers and the material is transported to two treatment facilities. We investigate how the scheduling of emptying and transportation should be done in order to minimize the operation cost, while providing a high service level and ensuring that capacity constraints are not violated. We develop a heuristic solution method for solving the daily planning problem with uncertain accretion rate for materials by considering a rolling time horizon of a few days. We apply a construction heuristic in the first period and re-optimize the solution every subsequent period with a variable neighborhood search. Computational experiments are conducted on real life data.

Heuristics for the stochastic single-machine problem with E/T costs

This paper addresses the problem of concurrent due-date assignment and sequencing of a set of jobs on a stochastic single-machine environment with distinct job earliness and tardiness penalty costs. It is assumed that the jobs processing times are statistically independent and follow a normal distribution whose mean and variance are provided. The objective is to determine the job sequence and the due dates which minimize the expected total earliness and tardiness costs. Previous theoretical results regarding normally distributed processing times and expected values of earliness and tardiness costs are reviewed. Two efficient insertion-based constructive heuristics with polynomial time complexity are proposed. It is shown that both heuristic solution methods include safety time and the obtained sequence remains the same regardless of disruptions, which means that the results are robust. A comparative study with known methods from the literature was conducted using a set of 1700 problems with up to 2000 jobs. The results indicated that the best performance was achieved by one of the developed heuristics. Furthermore, it was proven that the heuristics are asymptotically optimal. An extension of the problem with processing times modeled as lognormal random variables was also investigated and solved with good results.