Heuristic Solution Approach Research Articles

Heuristic solution approaches for the maximum minsum dispersion problem

The Maximum Minsum Dispersion Problem (Max-Minsum DP) is a strongly NP-Hard problem that belongs to the family of equitable dispersion problems. When dealing with dispersion, the operations research literature has focused on optimizing efficiency-based objectives while neglecting, for the most part, measures of equity. The most common efficiency-based functions are the sum of the inter-element distances or the minimum inter-element distance. Equitable dispersion problems, on the other hand, attempt to address the balance between efficiency and equity when selecting a subset of elements from a larger set. The objective of the Max-Minsum DP is to maximize the minimum aggregate dispersion among the chosen elements. We develop tabu search and GRASP solution procedures for this problem and compare them against the best in the literature. We also apply LocalSolver, a commercially available black-box optimizer, to compare our results. Our computational experiments show that we are able to establish new benchmarks in the solution of the Max-Minsum DP.

The Hybrid Electric Vehicle – Traveling Salesman Problem

The reduction in carbon dioxide levels by using hybrid electric vehicles is a currently ongoing endeavor. Although this development is quite advanced for hybrid electric passenger cars, small transporters and trucks are far behind. We try to address this challenge by introducing a new optimization problem that describes the delivery of goods with a hybrid electric vehicle to a set of customer locations. The Hybrid Electric Vehicle – Traveling Salesman Problem extends the well-known Traveling Salesman Problem by adding different modes of operation for the vehicle, causing different costs and driving times for each arc within a delivery network.As the use of different modes of operation immensely increases the complexity of the problem, we present a heuristic solution approach, based mainly on a Tabu Search, to solve this optimization problem. Additionally, we provide a set of realistic benchmark instances based on real-world delivery tours to test and evaluate our solution approach. We also implemented a mathematical problem formulation and are able to solve small instances with the IBM ILOG CPLEX Optimization Studio, which allows us to prove the quality of the solutions, provided by our heuristic.

An Industrially Validated CMM Inspection Process with Sequence Constraints

An efficient CMM inspection process implemented in industry gives significant productivity improvements. A key part of this improvement is the optimization of the inspection sequences. To ensure quality of the inspection the sequences are often constrained with respect to the order of the measurements. This gives rise to so called precedence constraints when modelling the inspection sequence as a variation of the travelling salesperson problem (TSP). Two heuristic solution approaches and a generic optimizing algorithm are considered. A generation based stochastic algorithm is found to reduce cycle time by as much as 12% in comparison to the currently used algorithm.

Designing Response Supply Chain against Bioattacks

Bioattacks, i.e., the intentional release of pathogens or biotoxins against humans to cause serious illness and death, pose a significant threat to public health and safety due to the availability of pathogens worldwide, scale of impact, and short treatment time window. In this paper, we focus on the problem of prepositioning inventory of medical countermeasures (MCM) to defend against such bioattacks. We introduce a two-stage robust optimization model that considers the policymaker’s static inventory decision, attacker’s move, and policymaker’s adjustable shipment decision, so as to minimize inventory and life loss costs, subject to population survivability targets. We consider a heuristic solution approach that limits the adjustable decisions to be affine, which allows us to cast the problem as a tractable linear optimization problem. We prove that, under mild assumptions, the heuristic is in fact optimal. Experimental evidence suggests that the heuristic’s performance remains near-optimal for general settings as well. We illustrate how our model can serve as a decision support tool for policy making. In particular, we perform a thorough case study on how to preposition MCM inventory in the United States to guard against anthrax attacks. We calibrate our model using data from multiple sources, including publications of the National Academies of Sciences and the U.S. Census. We find that, for example, if U.S. policymakers want to ensure a 95% survivability target for anthrax attacks that simultaneously affect at most two cities (in the same or different states), the minimum annual inventory budget required is approximately $330 million. We also discuss how our model can be applied in other contexts as well, e.g., to analyze safety-stock placement in supply-chain networks to hedge against disruptions.

A Heuristic Optimisation Approach for the Scheduling of Integrated Manufacturing and Distribution Systems

The scheduling and control of production processes have great influence on the performance of manufacturing systems. The increasing customi- sation of products requires that these systems handle higher numbers of product variants along with decreasing lot sizes, so that manufacturing systems become more and more complex. Therefore, the efficient management of these systems requires reliable optimization methods for the scheduling and control of all processes and for the allocation of resources related to the system. An important aspect of production scheduling is the interface to subsequent processes, such as the distribution of goods to customers. This paper explains the so called integrated production and distribution scheduling problem and analyses numerically the performance of the integrated approach in comparison to a separated, sequential production and distribution scheduling. Due to the high computational complexity of the problem a heuristic solution approach is presented, in order to provide solutions for larger problem instances than the currently available exact optimisation software. Finally, an outline of possible further improvements regarding scheduling heuristics, combining evolutionary algorithms and linear program (LP) solvers is given.

Food Rescue and Delivery

This paper addresses a special case of periodic vehicle routing problem in which each node has a nonnegative supply or demand of a single product that is unpaired. The product collected from a pickup node can be delivered to any one node or multiple delivery nodes, and the demand of a delivery node can be met by the product collected from any one node or multiple pickup nodes. This periodic unpaired pickup and delivery vehicle-routing problem is a novel variant of the periodic vehicle routing problem. The objective of the problem was to design the pickup and delivery vehicle routes to meet required service levels of delivery nodes, minimizing the total transportation cost while satisfying certain operational constraints. This problem was driven by food relief operations in Sydney, Australia. The logistics aspect of the approach was to design and execute a vehicle routing problem for a food rescue and delivery network. The specific goals were to develop an integrated linear programming model for this new variant of the periodic vehicle routing problem and to propose an integer programming–based heuristic solution approach to solve the problem introduced in the paper. The heuristic algorithm was tested with small instances created from Cordeau's benchmark instances, and the solution approach was validated against optimal solutions obtained through the exact method before implementation on a food rescue and delivery network. The heuristic approach was found to be comparable with the optimal solution and can solve the real-world scenarios with significantly fewer resources than are used in practice.

Flexible feeder transit route design to enhance service accessibility in urban area

SummaryTo improve the accessibility of transit system in urban areas, this paper presents a flexible feeder transit routing model that can serve irregular‐shaped networks. By integrating the cost efficiency of fixed‐route transit system and the flexibility of demand responsive transit system, the proposed model is capable of letting operating feeder busses temporarily deviate from their current route so as to serve the reported demand locations. With an objective of minimizing total bus travel time, a new operational mode is then proposed to allow busses to serve passengers on both street sides. In addition, when multiple feeder busses are operating in the target service area, the proposed model can provide an optimal plan to locate the nearest one to response to the demands. A three‐stage solution algorithm is also developed to yield meta‐optimal solutions to the problem in a reasonable amount of time by transforming the problem into a traveling salesman problem. Numerical studies have demonstrated the effectiveness of the proposed model as well as the heuristic solution approach. Copyright © 2015 John Wiley & Sons, Ltd.

A comprehensive mathematical model for dynamic cellular manufacturing system design and Linear Programming embedded hybrid solution techniques

Considering the ever changing market conditions, it is essential to design responsive and flexible manufacturing systems. This study addresses the multi-period Dynamic Cellular Manufacturing System (DCMS) design problem and introduces a new mathematical model. The objective function of the mathematical model considers inter-cell and intra-cell material handling, machine purchasing, layout reconfiguration, variable and constant machine costs. Machine duplication, machine capacities, operation sequences, alternative processing routes of the products, varying demands of products and lot splitting are among the most important issues addressed by the mathematical model. It makes decisions on many system related issues, including cell formation, inter- and intra-cell layout, product routing and product flow between machines. Due to the complexity of the problem, we suggest two heuristic solution approaches that combine Simulated Annealing (SA) with Linear Programming and Genetic Algorithm (GA) with Linear Programming. The developed approaches were tested using a data set from the literature. In addition, randomly generated test problems were also used to investigate the performance of the hybrid heuristic approaches. A problem specific lower bound mathematical model was also proposed to observe the solution quality of the developed approaches. The suggested approaches outperformed the previous study in terms of both computational time and the solution quality by reducing the overall system cost.

An MINLP Model for Scheduling and Placement of Quantum Circuits with a Heuristic Solution Approach

Recent works on quantum physical design have pushed the scheduling and placement of quantum circuit into their prominent positions. In this article, a mixed integer nonlinear programming model is proposed for the placement and scheduling of quantum circuits in such a way that latency is minimized. The proposed model determines locations of gates and the sequence of operations. The proposed model is proved reducible to a quadratic assignment problem which is a well-known NP-complete combinatorial optimization problem. Since it is impossible to find the optimal solution of this NP-complete problem for large quantum circuits within a reasonable amount of time, a metaheuristic solution method is developed for the proposed model. Some experiments are conducted to evaluate the performance of the developed solution approach. Experimental results show that the proposed approach improves average latency by about 24.09% for the attempted benchmarks.

Joint planning of berth and yard allocation in transshipment terminals using multi-cluster stacking strategy

In this work, a joint planning problem for berth and yard allocation in transshipment terminals is addressed. Multi-cluster stacking strategy is proposed to split each transshipment flow into a number of container clusters and then stack each cluster in different yard blocks. A mixed integer quadratic programming model is formulated to minimize the total distance of exchanging containers between mother vessels and feeders, and the workload imbalance among yard blocks. A novel three-stage heuristic solution approach is developed and extensive numerical experiments are conducted to show the effectiveness of the proposed approach and the benefit of the multi-cluster strategy.

Integrated redistricting, location-allocation and service sharing with intra-district service transfer to reduce demand overload and its disparity

Service demand overload has been one of the main concerns in district-based service planning, because it strongly affects service quality. Moreover, the overload problem usually involves overload disparity among districts. The disparity often results from outdated district boundaries not reflecting up-to-date spatial demand distributions. A lack of systematic methodologies, however, has hindered solving such overload and disparity problems despite the increasing availability of information on spatial service demand and supply. This paper presents a novel mathematical programming model to address the service demand overload problem by reorganizing services in multiple spatial scales. The mathematical program optimizes simultaneously (1) redistricting service areas, (2) allocating multiple service resources into service-providing units in each district, and (3) sharing services between service-providing units within a district. Information on geographically distributed units is used as the spatial data of the model. This new model integrates districting and location-allocation problems as a combined problem. A heuristic solution approach is also presented to solve large problem instances. As a case study, a judicial service overload problem is examined for a state court system in the United States. This new integrated approach enables efficient utilization of the geographically distributed service capacity. In addition, these new features of the model allow for better utilization of spatial information for practical service planning.

Optimal dynamic expansion planning of distribution systems considering non-renewable distributed generation using a new heuristic double-stage optimization solution approach

This paper presents a dynamic (i.e., time-based) model for distribution system expansion planning (DSEP) considering distributed generation. The proposed model optimizes both investment and operation costs of distribution system. It determines the optimal location and size of distributed generators as well as the reinforcement strategy for primary (i.e., medium voltage) distribution feeders along a specified planning horizon. Besides, the dynamic feature of this model enables it to determine the time of each investment. The investment costs consist of installation cost of distributed generators and reinforcement cost of primary distribution feeders. Similarly, the operation costs comprise the cost of energy losses, operation and maintenance cost of the equipment and cost of power purchased from upstream grid (i.e., sub-transmission or transmission grid). The introduced model is solved using a combination of two efficient heuristic methods of Modified Integer-coded Harmony Search (MIHS) to find the optimal expansion scheme and Enhanced Gravitational Search Algorithm (EGSA) to optimize the operation costs. Furthermore, the suggested solution approach also incorporates an efficient mechanism for coding the candidate solutions in MIHS algorithm. The effectiveness of the proposed method and coding mechanism is extensively demonstrated by testing on two radial distribution systems and comparing the obtained results with the results of several other solution techniques.

Risk assessment for multiple automated guided vehicle manufacturing network

Automated guided vehicles (AGVs) are moving devices for material handling in a manufacturing system through a network of guide paths. The network is configured of nodes of work stations and arcs of guide paths. To obtain this more availability of the system having reliable arcs are desirable. Advanced manufacturing systems feasibility is considered via economic evaluation. Thus, this work proposes a risk based dynamic program to determine more reliable arcs for fortification purposes. With respect to the multi stage decision making process of the multiple AGVs on different arcs, we develop a dynamic program being a useful tool for multi stage decision making. To counteract the dynamism of data in different time periods, Bayesian approach is employed to determine the loss function of moving through the stages of the proposed AGV routing network. By increasing the number of nodes and AGVs the problem is considered in NP-hard class, and thus the required effort for optimization motivates to develop a heuristic solution approach.

A generalized constructive algorithm using insertion-based heuristics

In this paper, a generalized constructive algorithm referred to as GCA is presented which makes it possible to select a wide variety of heuristics just by the selection of its arguments values. A general framework for generating permutations of integers is presented. This framework, referred to as PERMGEN, forms a link between the numbering of permutations and steps in the insertion-based heuristics. A number of arguments controlling the operation of GCA are identified. Features and benefits of the generalized algorithm are presented through the extension of the NEH heuristic, a successful heuristic solution approach of Nawaz, Enscore, and Ham for the permutation flowshop problem (PFSP). The goal of the experimental study is to improve the performance of the NEH heuristic on the PFSP. To achieve this goal, the space of algorithmic control arguments is searched for a combination of values that define an algorithm providing lower makespan solutions than NEH, in a linear increase of CPU time. Computational experiments on a set of 120 benchmark problem instances, originally proposed by Taillard, are performed to establish a more robust version of the original NEH constructive heuristic. The proposed procedures outperform NEH, preserving its efficiency and simplicity.

Minimising total tardiness for a single machine scheduling problem with family setups and resource constraints

This paper considers a single machine scheduling problem in which each job to be scheduled belongs to a family and setups are required between jobs belonging to different families. Each job requires a certain amount of resource that is supplied through upstream processes. Therefore, schedules must be generated in such a way that the total resource demand does not exceed the resource supply up to any point in time. The goal is to find a schedule minimising total tardiness with respect to the given due dates of the jobs. A mathematical formulation and a heuristic solution approach for two variants of the problem are presented. Computational experiments show that the proposed heuristic outperforms a state-of-the-art commercial mixed integer programming solver both in terms of solution quality and computation time.

A dynamic programming approach for the aircraft landing problem with aircraft classes

Abstract The capacity of a runway system represents a bottleneck at many international airports. The current practice at airports is to land approaching aircraft on a first-come, first-served basis. An active rescheduling of aircraft landing times increases runway capacity or reduces delays. The problem of finding an optimal schedule for aircraft landings is referred to as the “aircraft landing problem”. The objective is to minimize the total delay of aircraft landings or the respective cost. The necessary separation time between two operations must be met. Due to the complexity of this scheduling problem, recent research has been focused on developing heuristic solution approaches. This article presents a new algorithm that is able to create optimal landing schedules on multiple independent runways for aircraft with positive target landing times and limited time windows. Our numerical experiments show that problems with up to 100 aircraft can be optimally solved within seconds.

The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery

Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance.

Personalized real-time traffic information provision: Agent-based optimization model and solution framework

The advancement of information and communication technology allows the use of more sophisticated information provision strategies for real-time congested traffic management in a congested network. This paper proposes an agent-based optimization modeling framework to provide personalized traffic information for heterogeneous travelers. Based on a space–time network, a time-dependent link flow based integer programming model is first formulated to optimize various information strategies, including elements of where and when to provide the information, to whom the information is given, and what alternative route information should be suggested. The analytical model can be solved efficiently using off-the-shelf commercial solvers for small-scale network. A Lagrangian Relaxation-based heuristic solution approach is developed for medium to large networks via the use of a mesoscopic dynamic traffic simulator.

Solving a large SIP model for production scheduling at a gold mine with multiple processing streams and uncertain geology

In this paper, an efficient heuristic solution approach is applied and tested to the stochastic mine production scheduling of a relatively large gold deposit containing about 120 thousand blocks and considering a set of 15 geological scenarios generated stochastically. The case study addresses multiple processing streams and a ‘grade’ stockpile, which adds flexibility to the specific operation by advancing the processing of highly valuable material. The solution approach first generates an initial feasible solution by sequentially solving the stochastic open-pit mine production scheduling (OPMPS) period by period, and then a network-flow algorithm is used to sequentially search for improvements. In this network graph, the nodes identify candidate blocks that might have their extraction postponed or advanced, aiming for new schedules with higher value and lower risks. The results show that production schedules with low deviations from production expectations can be generated in a reasonable time for an actual mining environment.

Modelling and Optimizing an Open-Pit Truck Scheduling Problem

This paper addresses a special truck scheduling problem in the open-pit mine with different transport revenue consideration. A mixed integer programming model is formulated to define the problem clearly and a few valid inequalities are deduced to strengthen the model. Some properties and two upper bounds of the problem are proposed. Based on these inequalities, properties, and upper bounds, a heuristic solution approach with two improvement strategies is proposed to resolve the problem and the numerical experiment demonstrates that the proposed solution approach is effective and efficient.