Solutions For Large Instances Research Articles

Heuristics and Learning Models for Dubins MinMax Traveling Salesman Problem.

This paper addresses a MinMax variant of the Dubins multiple traveling salesman problem (mTSP). This routing problem arises naturally in mission planning applications involving fixed-wing unmanned vehicles and ground robots. We first formulate the routing problem, referred to as the one-in-a-set Dubins mTSP problem (MD-GmTSP), as a mixed-integer linear program (MILP). We then develop heuristic-based search methods for the MD-GmTSP using tour construction algorithms to generate initial feasible solutions relatively fast and then improve on these solutions using variants of the variable neighborhood search (VNS) metaheuristic. Finally, we also explore a graph neural network to implicitly learn policies for the MD-GmTSP using a learning-based approach; specifically, we employ an S-sample batch reinforcement learning method on a shared graph neural network architecture and distributed policy networks to solve the MD-GMTSP. All the proposed algorithms are implemented on modified TSPLIB instances, and the performance of all the proposed algorithms is corroborated. The results show that learning based approaches work well for smaller sized instances, while the VNS based heuristics find the best solutions for larger instances.

Optimization of the integrated problem of employee timetabling and job shop scheduling

This paper deals with a real manufacturing scheduling problem that is particularly encountered in the tannery industries. This problem often integrates employee timetabling and production scheduling. The employee timetabling problem is addressed in the context of skill requirements and under availability and legislative constraints. The production scheduling is considered as a re-entrant hybrid job-shop problem with time lags and sequence dependent setup times, under machine availability constraints. The objective is to minimize the labor cost, while respecting a maximum makespan and a maximum tardiness constraints. Two different models and exact resolution methods are proposed, using Mixed Integer Linear Programming (MILP) and Constraint Programming (CP). Numerical experimentations are conducted to compare and evaluate their performances, based on randomly generated instances. The results show that the CP model is slower than the MILP model in terms of finding optimal solutions forlarge instances, but is more efficient in generating feasible solutions. Thus, providing a feasible initial solution to the MILP model using the CP model is a promising hybrid approach to reduce the computational time.

Mathematical optimization approach for facility layout on several rows

The facility layout problem is concerned with finding an arrangement of non-overlapping indivisible departments within a facility so as to minimize the total expected flow cost. In this paper we consider the special case of multi-row layout in which all the departments are to be placed in three or more rows, and our focus is on, for the first time, solutions for large instances. We first propose a new mixed integer linear programming formulation that uses continuous variables to represent the departments’ location in both x and y coordinates, where x represents the position of a department within a row and y represents the row assigned to the department. We prove that this formulation always achieves an optimal solution with integer values of y, but it is limited to solving instances with up to 13 departments. This limitation motivates the application of a two-stage optimization algorithm that combines two mathematical optimization models by taking the output of the first-stage model as the input of the second-stage model. This algorithm is, to the best of our knowledge, the first one in the literature reporting solutions for instances with up to 100 departments.

Efficient decomposition-based algorithm to solve long-term pipeline scheduling problem

This paper addresses the scheduling and inventory management of a straight pipeline system connecting a single refinery to multiple distribution centers. By increasing the number of batches and time periods, maintaining the model resolution by using linear programming-based methods and commercial solvers would be very time-consuming. In this paper, we make an attempt to utilize the problem structure and develop a decomposition-based algorithm capable of finding near-optimal solutions for large instances in a reasonable time. The algorithm starts with a relaxed version of the model and adds a family of cuts on the fly, so that a near-optimal solution is obtained within a few iterations. The idea behind the cut generation is based on the knowledge of the underlying problem structure. Computational experiments on a real-world data case and some randomly generated instances confirm the efficiency of the proposed algorithm in terms of the solution quality and time.

Facility Location with Tree Topology and Radial Distance Constraints

Let Gd = (V, Ed) be an input disk graph with a set of facility nodes V and a set of edges Ed connecting facilities in V. In this paper, we minimize the total connection cost distances between a set of customers and a subset of facility nodes S⊆V and among facilities in S, subject to the condition that nodes in S simultaneously form a spanning tree and an independent set according to graphs and Gd, respectively, where is the complement of Gd. Four compact polynomial formulations are proposed based on classical and set covering p‐Median formulations. However, the tree to be formed with S is modelled with Miller–Tucker–Zemlin (MTZ) and path orienteering constraints. Example domains where the proposed models can be applied include complex wireless and wired network communications, warehouse facility location, electrical power systems, water supply networks, and transportation networks, to name a few. The proposed models are further strengthened with clique valid inequalities which can be obtained in polynomial time for disk graphs. Finally, we propose Kruskal‐based heuristics and metaheuristics based on guided local search and simulated annealing strategies. Our numerical results indicate that only the MTZ constrained models allow obtaining optimal solutions for instances with up to 200 nodes and 1000 users. In particular, tight lower bounds are obtained with all linear relaxations, e.g., less than 6% for most of the instances compared to the optimal solutions. In general, the MTZ constrained models outperform path orienteering ones. However, the proposed heuristics and metaheuristics allow obtaining near‐optimal solutions in significantly short CPU time and tight feasible solutions for large instances of the problem.

The intermittent travelling salesman problem

AbstractIn this paper, we introduce a new variant of the travelling salesman problem, namely the intermittent travelling salesman problem (ITSP), which is inspired by real‐world drilling/texturing applications. In this problem, each vertex can be visited more than once and there is a temperature constraint enforcing a time lapse between two consecutive visits. A branch‐and‐bound approach is proposed to solve small instances to optimality. We furthermore develop four variable neighbourhood search metaheuristics which produce high‐quality solutions for large instances. An instance library is built and made publicly available.

Scheduling electric vehicles

The vehicle scheduling problem (VSP) is a traditional problem in public transport. One of the main assumptions is that buses can be operated the whole day without any interruption for refueling etc. Recently, new technological innovations have led to the introduction of electric vehicles (EVs). For these new vehicles, we cannot ignore the need of refueling during the day, as the range of an electric bus is severely limited, because of the capacity of the batteries. In this paper, we study the electric VSP (e-VSP), where we use EVs with a limited range. During the day the batteries can be charged; in this paper we assume that a battery cannot be replaced/substituted. We present two models that differ in the level of detail resembling the actual processes. In our first model, we assume a linear charging process, work with a constant price of electricity during the day, and do not take the effect of the depth-of-discharge on the lifetime of the battery into account. Our second model resembles practice much better: we allow any type of charging process, work with the actual electricity prices, and take the depreciation cost of the battery into account. To keep this model tractable, however, we approximate the exact value of the charge by discretizing it. The refined model can be solved to optimality using integer linear programming for instances of small/medium size, and therefore, we describe two other solution methods based on column generation that find good, but not necessarily optimal, solutions for large instances. We have tested our algorithms on real-world instances.

Aggregation methodologies for perishability management in production and distribution system

An existing integrated model such as the production-inventory-routing-problem (PIDRP) can be used to generate operational decision in the planning horizon. However, for certain products, such as food, freshness of the product are also an important factor to be considered. Typically, determining the solutions for large instances of PIDRP is not possible. The contribution of this research is to propose two aggregation techniques that can manage large instances of PIDRP that consider perishability of products. The first technique is based on a clustering algorithm that considers constraints from delivery capacity. The second technique is a tailored aggregation for producing subsets of products that can be ordered jointly. Computational results show that the proposed techniques can be used to reduce problem size while maintaining good quality solution within acceptable run time. The gaps of the solutions for problem sets up to 30 retailers, 20 products and eight periods are less than 5%. [Received 8 December 2016; Revised 27 March 2017; Accepted 21 April 2017[

An Efficient Approach for the Reentrant Parallel Machines Scheduling Problem under Consumable Resources Constraints

In present manufacturing environment, the reentrant scheduling problem is one of the most important issues in the planning and operation of production systems. It has a large scope such as capacity distribution and inventory control. On the other hand, the markets are very competitive; it is a critical requirement of operational management to have effective management of resources (consumable and renewable) so as to achieve optimal production plan. This study considers a reentrant parallel machines scheduling problem with consumable resources. Each job consumes several components and must be processed more than once in a stage composed of identical parallel machines. The resources availability, jobs assignment and sequencing at each cycle and are considered and optimized simultaneously. On the basis of this representation, a MILP model is developed. Thus, that MILP model can be used for the problem in order to find the exact solution. Since, this problem is clearly NP-hard, and optimal solutions for large instances are highly intractable, a genetic algorithm is developed to obtain near-optimal solution. Then, an improvement phase based on different local search procedures are performed and examined to generate better solutions. The system performances are assessed in terms of measures such as the solution quality and the execution time. The effectiveness of the proposed metaheuristic is examined based on comparative study. The simulation results demonstrate that the presented algorithm is able to find an optimal solution for small-sized problems and can effectively find a near optimal solution for large-sized problems to minimize the makespan of the considered problem.

Route Optimization for the Distribution Network of a Confectionary Chain

This study considers the distribution network of a well-known perishable food manufacturer and its franchises in Turkey. As the countrywide number of stores is increasing fast, the company is facing problems due to its central distribution of products from a single factory. The objective is to decrease the cost of transportation while maintaining a high level of customer satisfaction. Hence, the focus is on the vehicle routing problem (VRP) of this large franchise chain within each city. The problem is defined as a rich VRP with heterogeneous fleet, site-dependent and compartmentalized vehicles, and soft/hard time windows. This NP-hard problem is modelled and tried with real data on a commercial solver. A basic heuristic procedure which can be used easily by the decision makers is also employed for obtaining quick and high-quality solutions for large instances.

Efficient metaheuristic algorithm and re-formulations for the unrelated parallel machine scheduling problem with sequence and machine-dependent setup times

In this paper, an unrelated parallel machine scheduling problem with sequence and machine-dependent setup times and makespan minimization is studied. A new makespan linearization and several mixed integer formulations are proposed for this problem. These formulations outperform the previously published formulations regarding size of instances and computational time to reach optimal solutions. Using these models, it is possible to solve instances six times larger than what was previously solved and to obtain optimal solutions on instances of the same size up to four orders of magnitude faster. A metaheuristic algorithm based on multi-start algorithm and variable neighbourhood descent metaheuristic is proposed. Composite movements were defined for the improvement phase of the proposed metaheuristic algorithm that considerably improved the performance of the algorithm providing small deviations from optimal solutions in medium-sized instances and outperforming the best known solutions for large instances.

Scheduling at coal handling facilities using Simulated Annealing

The main thrust of this study is the operational scheduling of the continuous coal handling and blending processes when considering multiple, and sometimes conflicting, objectives. A widely applicable generic goal programming model is proposed. Furthermore, assumptions regarding the certainty of demand during different periods are challenged, endeavoring to provide more robust schedules in a largely stochastic environment. As the study aims to provide scheduling solutions to any coal handling facility, the Simulated Annealing metaheuristic is proposed to ensure that acceptably good solutions for large instances of the generic model can be found in reasonable computational time. The generic approach and its suggested application will be valuable not only in the coal handling environment, but also in the continuous product manufacturing/blending or continuous material handling environment.

Multiple machine JIT scheduling: a tabu search approach

This paper presents an approach to solving the multiple machine, non-preemptive, earliness-tardiness scheduling problem with unequal due dates in a flow shop with machine tiers (FMT). In this variant of the flow shop problem, machines are arranged in tiers or groups, and the jobs must visit one machine in each tier. The processing times, machine assignments, and due dates are deterministic and known in advance. The objective is to find a permutation schedule that minimizes the total deviation of each job from its due date. A tabu search (TS) meta-heuristic combined with an LP evaluation function is applied to solve this problem and results are compared to optimal permutation solutions for small problems and the earliest due date schedule for large problems. Several neighborhood generation methods and two diversification strategies are examined to determine their effect on solution quality. Results show that the TS method works well for this problem. TS found the optimal solution in all but one of the small problem instances and improved the earliest due date solutions for larger instances where no optimal solutions could be found.

Coordination of set-ups between two stages of a supply chain using multi-objective genetic algorithms

A multi-objective genetic algorithm (MOGA) solution approach for a sequencing problem to coordinate set-ups between two successive stages of a supply chain is presented in this paper. The production batches are processed according to the same sequence in both stages. Each production batch has two distinct attributes and a set-up occurs in the upstream stage every time the first attribute of the new batch is different from the previous one. In the downstream stage, there is a set-up when the second attribute of the new batch is different from that of the previous one. Two objectives need to be considered in sequencing the production batches including minimizing total set-ups and minimizing the maximum number of set-ups between the two stages. Both problems are NP-hard so attainment of an optimal solution for large problems is prohibited. The solution approach starts with an initialization stage followed by evolution of the initial solution set over generations. The MOGA makes use of non-dominated sorting and a niche mechanism to rank individuals in the population. Selected individuals taken from a given population form the succeeding generation using four genetic operators as: reproduction, crossover, mutation and inversion. Experiments in a number of test problems show that the MOGA is capable of finding Pareto-optimal solutions for small problems and near Pareto-optimal solutions for large instances in a short CPU time.

Data-independent neighborhood functions and strict local optima

The paper proves that data-independent neighborhood functions with the smooth property (all strict local optima are global optima) for maximum 3-satisfiability (MAX 3-SAT) must contain all possible solutions for large instances. Data-independent neighborhood functions with the smooth property for 0–1 knapsack are shown to have size with the same order of magnitude as the cardinality of the solution space. Data-independent neighborhood functions with the smooth property for traveling salesman problem (TSP) are shown to have exponential size. These results also hold for certain polynomially solvable sub-problems of MAX 3-SAT, 0–1 knapsack and TSP.