Efficient solution of the 3G network planning problem

The 3G universal mobile telecommunications system (UMTS) planning problem is combinatorially explosive and difficult to solve optimally, though solution methods exist for its three main subproblems (cell, access network, and core network planning). We previously formulated the entire problem as a single integrated mixed-integer linear program (MIP) and showed that only small instances of this global planning problem can be solved to optimality by a commercial MIP solver within a reasonable amount of time (St-Hilaire, Chamberland, & Pierre, 2006). Heuristic methods are needed for larger instances. This paper provides the first complete formulation for the heuristic sequential method (St-Hilaire, Chamberland, & Pierre, 2005) that re-partitions the global formulation into the three conventional subproblems and solves them in sequence using a MIP solver. This greatly improves the solution time, but at the expense of solution quality. We also develop a new hybrid heuristic that uses the results of the sequential method to generate constraints that provide tighter bounds for the global planning problem with the goal of reaching the provable optimum solution much more quickly. We empirically evaluate the speed and solution accuracy of four solution methods: (i) the direct MIP solution of the global planning problem, (ii) a local search heuristic applied to the global planning problem, (iii) the sequential method and (iv) the new hybrid method. The results show that the sequential method provides very good results in a fraction of the time needed for the direct MIP solution of the global problem, and that optimum results can be provided by the hybrid heuristic in greatly reduced time.     

An adaptive large neighborhood search heuristic for the share-a-ride problem

The Share-a-Ride Problem (SARP) aims at maximizing the profit of serving a set of passengers and parcels using a set of homogeneous vehicles. We propose an adaptive large neighborhood search (ALNS) heuristic to address the SARP. Furthermore, we study the problem of determining the time slack in a SARP schedule. Our proposed solution approach is tested on three sets of realistic instances. The performance of our heuristic is benchmarked against a mixed integer programming (MIP) solver and the Dial-a-Ride Problem (DARP) test instances. Compared to the MIP solver, our heuristic is superior in both the solution times and the quality of the obtained solutions if the CPU time is limited. We also report new best results for two out of twenty benchmark DARP instances.     

A new approach to solve the multi-product multi-period inventory lot sizing with supplier selection problem

This research work deals with the multi-product multi-period inventory lot sizing with supplier selection problem. Formerly, this kind of problem was formulated and solved using an exhaustive enumeration algorithm and a heuristic algorithm. In this paper, a new algorithm based on a reduce and optimize approach and a new valid inequality is proposed to solve the multi-product multi-period inventory lot sizing with supplier selection problem. Numerical experiments ratify the success of the proposed heuristic algorithm. For the set of 150 benchmark instances, including 75 small-sized instances, 30 medium-sized instances, and 45 large-sized instances, the algorithm always obtained better solutions compared with those previously published. Furthermore, according to the computational results, the developed heuristic algorithm outperforms the CPLEX MIP solver in both solution quality and computational time.     

Tight bounds from a path based formulation for the tree of hub location problem

This paper considers the tree of hub location problem. We propose a four index formulation which yields much tighter LP bounds than previously proposed formulations, although at a considerable increase of the computational burden when obtained with a commercial solver. For this reason we propose a Lagrangean relaxation, based on the four index formulation, that exploits the structure of the problem by decomposing it into independent subproblems which can be solved quite efficiently. We also obtain upper bounds by means of a simple heuristic that is applied at the inner iterations of the method that solves the Lagrangean dual. As a consequence, the proposed Lagrangean relaxation produces tight upper and lower bounds and enable us to address instances up to 100 nodes, which are notably larger than the ones previously considered in the literature, with sizes up to 20 nodes. Computational experiments have been performed with benchmark instances from the literature. The obtained results are remarkable. For most of the tested instances we obtain or improve the best known solution and for all tested instances the deviation between our upper and lower bounds, never exceeds 10%.     

A tabu search algorithm for the global planning problem of third generation mobile networks

In this paper, we propose a tabu search (TS) algorithm for the global planning problem of third generation (3G) universal mobile telecommunications system (UMTS) networks. This problem is composed of three NP-hard subproblems: the cell, the access network and the core network planning subproblems. Therefore, the global planning problem consists in selecting the number, the location and the type of network nodes (including the base stations, the radio network controllers, the mobile switching centers and the serving GPRS (General Packet Radio Service) support nodes) as well as the interconnections between them. After describing our metaheuristic, a systematic set of experiments is designed to assess its performance. The results show that quasi-optimal solutions can be obtained with the proposed approach.     

Minimizing maximum tardiness and delivery costs in a batched delivery system

High delivery costs usually urge manufacturers to dispatch their jobs in batches. However, dispatching the jobs in batches can have profound negative effects on important scheduling objective functions such as minimizing maximum tardiness. This paper considers a single machine scheduling problem with the aim of minimizing the maximum tardiness and delivery costs in a single-machine scheduling problem with batched delivery system. A mathematical model is developed for this problem which can serve to solve it with the help of a commercial solver. However, due to the fact that this model happens to be a mixed integer nonlinear programming model the solver cannot guarantee to reach the global solution. For this reason, a branch and bound algorithm (B&B) is presented to obtain the global solution. Besides, a heuristic algorithm for calculation of the initial upper bound is introduced. Computational results show that the algorithm can be beneficial for solving this problem, especially for large size instances.     

Variable neighborhood search and local branching

In this paper we develop a variable neighborhood search (VNS) heuristic for solving mixed-integer programs (MIPs). It uses CPLEX, the general-purpose MIP solver, as a black-box. Neighborhoods around the incumbent solution are defined by adding constraints to the original problem, as suggested in the recent local branching (LB) method of Fischetti and Lodi (Mathematical Programming Series B 2003;98:23–47). Both LB and VNS use the same tools: CPLEX and the same definition of the neighborhoods around the incumbent. However, our VNS is simpler and more systematic in neighborhood exploration. Consequently, within the same time limit, we were able to improve 14 times the best known solution from the set of 29 hard problem instances used to test LB.     

Optimization of stowage plans for RoRo ships

International vehicle transportation is primarily conducted using Roll-on/Roll-off (RoRo) ships, which are specialized to transport cargo on wheels such as cars, farming equipment, and military equipment. RoRo ships operate by going between different regions of the world according to predefined plans. In this work we focus on operational decisions that are required when operating a fleet of RoRo ships: given a ship set to travel according to a given route, we consider decisions such as which cargoes to carry, how many vehicles to carry from each cargo, and how to stow the vehicles carried during the voyage. A mathematical model is made describing the problem, and both a standard MIP solver and a specially designed heuristic method are used to solve the problem. Computational tests are conducted to analyze the difficulty of solving several variations of the problem. For certain types of instances the MIP solver works well, while for other types the heuristic is very fast and more accurate than the MIP solver.     

A Lagrangian heuristic for sprint planning in agile software development

Agile methods for software development promote iterative design and implementation. Most of them divide a project into functionalities, called user stories; at each iteration, often called a sprint, a subset of user stories are developed. The sprint planning phase is critical to ensure the project success, but it is also a difficult problem because several factors impact on the optimality of a sprint plan, e.g., the estimated complexity, business value, and affinity of the user stories to be included in each sprint. In this paper we present an approach for sprint planning based on an integer linear programming model. Given the estimates made by the project team and a set of development constraints, the optimal solution of the model is a sprint plan that maximizes the business value perceived by users. Solving to optimality the model by a general-purpose MIP solver, such as IBM Ilog Cplex, takes time and for some instances even finding a feasible solution requires too large computing times for an operational use. For this reason we propose an effective Lagrangian heuristic based on a relaxation of the proposed model and some greedy and exchange algorithms. Computational results on both real and synthetic projects show the effectiveness of the proposed approach.     

Mixed integer programming based heuristics for the Patient Admission Scheduling problem

The Patient Admission Scheduling (PAS) problem is a combinatorial optimization problem where elective patients are automatically assigned to beds for the duration of their stay considering not only the medical necessity but also the patient preferences. Due to its combinatorial nature, solving the previously published problem instances to optimality is a difficult task. In this paper, we present two Mixed Integer Programming (MIP) based heuristics namely Fix-and-Relax (F&R) and Fix-and-Optimize (F&O) where PAS problem instances are decomposed into sub-problems and then the sub-problems are optimized. Our approach uses patient decomposition considering patient length-of-Stay (LoS), room preference, admission date, specialism choice, and age, as well as time decomposition considering different optimization window sizes. Quick solutions generated by F&R heuristic are used as an input to the F&O heuristic and are improved in an iterative nature. Main goal of the study is to provide high quality solutions in shorter run times. Computational findings show that the proposed heuristics provide promising results towards the solution of the problem in faster CPU times than the previously reported values where less than 15 percent gap from the best known solutions is achieved for most of the test instances, and as low as 5 percent gap for some of the sample data.     

Mathematical programming-based approaches for multi-facility glass container production planning

This paper introduces a mathematical model (together with a relaxed version) and solution approaches for the multi-facility glass container production planning (MF-GCPP) problem. The glass container industry covers the production of glass packaging (bottle and jars), where a glass paste is continuously distributed to a set of parallel molding machines that shape the finished products. Each facility has a set of furnaces where the glass paste is produced in order to meet the demand. Furthermore, final product transfers between facilities are allowed to face demand. The objectives include meeting demand, minimizing inventory investment and transportation costs, as well as maximizing the utilization of the production facilities. A novel mixed integer programming formulation is introduced for MF-GCPP and solution approaches applying heuristics and meta-heuristics based on mathematical programming are developed. A multi-population genetic algorithm defines for each individual the partitions of the search space to be optimized by the MIP solver. A variant of the fix-and-optimize improvement heuristic is also introduced. The computational tests are carried on instances generated from real-world data provided by a glass container company. The results show that the proposed methods return competitive results for smaller instances, comparing to an exact solver method. In larger instances, the proposed methods are able to return high quality solutions.     

Improving the modulo simplex algorithm for large-scale periodic timetabling

The periodic event scheduling problem (PESP), in which events have to be scheduled repeatedly over a given period, is a complex and well-known discrete problem with numerous real-world applications. The most prominent of them is to find periodic timetables in public transport. Although even finding a feasible solution to the PESP is NP-hard, recent achievements demonstrate the applicability and practicability of the periodic event scheduling model. In this paper we propose different approaches to improve the modulo network simplex algorithm (Nachtigall and Opitz, 2008 [17]), which is a powerful heuristic for the PESP problem, by exploiting improved search methods in the modulo simplex tableau and larger classes of cuts to escape from the many local optima. Numerical experiments on large-scale railway instances show that our algorithms not only perform better than the original method, but even outperform a state-of-the-art commercial MIP solver.     

Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times

A scheduling problem with unrelated parallel machines, sequence and machine-dependent setup times, due dates and weighted jobs is considered in this work. A branch-and-bound algorithm (B&B) is developed and a solution provided by the metaheuristic GRASP is used as an upper bound. We also propose a set of instances for this type of problem. The results are compared to the solutions provided by two mixed integer programming models (MIP) with the solver CPLEX 9.0. We carry out computational experiments and the algorithm performs extremely well on instances with up to 30 jobs.     

A recombination‐based matheuristic for mixed integer programming problems with binary variables

This work introduces a heuristic for mixed integer programming (MIP) problems with binary variables, based on information obtained from differences between feasible solutions as well as solutions from the linear relaxation. This information is used to build a neighborhood that is explored as a sub‐MIP problem. The proposed heuristic is evaluated using 45 problems from the MIPLIB repository. Its performance, in terms of solution improvement over the results obtained after exploring 50,000 nodes of the branch‐and‐bound tree, is compared against that of Solution Polishing, which is another recombination‐based heuristic for MIP problems used within the CPLEX solver; as well as against the solution obtained by running the default CPLEX branch‐and‐cut (B&C) method under a same time limit. The computational results indicate that the proposed method is able to yield results that are significantly better than those obtained by the default CPLEX B&C approach and comparable to those of Solution Polishing in terms of the mean solution quality. This equivalence of expected solution quality, coupled with a simpler implementation, suggests the use of the proposed approach as a possible alternative for improving the quality of solutions in MIP problems.     

Hybrid column generation for large-size Covering Integer Programs: Application to transportation planning

The well-known column generation scheme is often an efficient approach for solving the linear relaxation of large-size Covering Integer Programs (CIP). In this paper, this technique is hybridized with an extension of the best-known CIP approximation heuristic, taking advantage of distinct criteria of columns selection. This extension uses fractional optimization for solving pricing subproblems. Numerical results on a real-case transportation planning problem show that the hybrid scheme accelerates the convergence of column generation both in terms of number of iterations and computational time. The integer solutions generated at the end of the process can also be improved for a significant proportion of instances, highlighting the potential of diversification of the approximation heuristic.     

A divide and conquer matheuristic algorithm for the Prize-collecting Steiner Tree Problem

The Prize-collecting Steiner Tree Problem (PCSTP) is a well-known problem in graph theory and combinatorial optimization. It has been successfully applied to solve real problems such as fiber-optic and gas distribution networks design. In this work, we concentrate on its application in biology to perform a functional analysis of genes. It is common to analyze large networks in genomics to infer a hidden knowledge. Due to the NP-hard characteristics of the PCSTP, it is computationally costly, if possible, to achieve exact solutions for such huge instances. Therefore, there is a need for fast and efficient matheuristic algorithms to explore and understand the concealed information in huge biological graphs. In this study, we propose a matheuristic method based on clustering algorithm. The main target of the method is to scale up the applicability of the currently available exact methods to large graph instances, without loosing too much on solution quality. The proposed matheuristic method is composed of a preprocessing procedures, a heuristic clustering algorithm and an exact solver for the PCSTP, applied on sub-graphs. We examine the performance of the proposed method on real-world benchmark instances from biology, and compare its results with those of the exact solver alone, without the heuristic clustering. We obtain solutions in shorter execution time and with negligible optimality gaps. This enables analyzing very large biological networks with the currently available exact solvers.     

Variable neighbourhood decomposition search for 0–1 mixed integer programs

In this paper we propose a new hybrid heuristic for solving 0–1 mixed integer programs based on the principle of variable neighbourhood decomposition search. It combines variable neighbourhood search with a general-purpose CPLEX MIP solver. We perform systematic hard variable fixing (or diving) following the variable neighbourhood search rules. The variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that exploiting boundary effects in this way considerably improves solution quality. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very difficult MIP problems. Moreover, computational results show that our method outperforms the CPLEX MIP solver, as well as three other recent most successful MIP solution methods.     

A hybrid method for the Probabilistic Maximal Covering Location–Allocation Problem

This paper presents a hybrid algorithm that combines a metaheuristic and an exact method to solve the Probabilistic Maximal Covering Location–Allocation Problem. A linear programming formulation for the problem presents variables that can be partitioned into location and allocation decisions. This model is solved to optimality for small- and medium-size instances. To tackle larger instances, a flexible adaptive large neighborhood search heuristic was developed to obtain location solutions, whereas the allocation subproblems are solved to optimality. An improvement procedure based on an integer programming method is also applied. Extensive computational experiments on benchmark instances from the literature confirm the efficiency of the proposed method. The exact approach found new best solutions for 19 instances, proving the optimality for 18 of them. The hybrid method performed consistently, finding the best known solutions for 94.5% of the instances and 17 new best solutions (15 of them optimal) for a larger dataset in one-third of the time of a state-of-the-art solver.     

供应链订单分配优化模型及其模拟退火算法

受4M1E(人、机、料、法、环)因素的随机波动影响,产品的制造过程通常是不完美的,从而产生不良产品.针对已有研究多忽略不良产品的特点,建立了更加符合实际需求的订单分配多目标混合整数规划模型,其优化目标为最小化交易成本、采购成本、不良产品数量、产品延迟交付数量,以及最大化供应商信誉评价.考虑到模型求解的复杂度,设计了一种模拟退火算法,并结合启发式规则避免了大量非法初始解与邻点解的出现.实验算例表明所建立的模型能够反映订单分配过程中的产品缺陷现象,其算法能够在允许的运算时间内获得稳定的满意解,并且随着算例规模的增大,其计算时间与优化结果均优于LINGO软件.     

A hybrid VNS approach for the short-term production planning and scheduling: A case study in the pulp and paper industry

Mathematical formulations for production planning are increasing complexity, in order to improve their realism. In short-term planning, the desirable level of detail is particularly high. Exact solvers fail to generate good quality solutions for those complex models on medium- and large-sized instances within feasible time. Motivated by a real-world case study in the pulp and paper industry, this paper provides an efficient solution method to tackle the short-term production planning and scheduling in an integrated mill. Decisions on the paper machine setup pattern and on the production rate of the pulp digester (which is constrained to a maximum variation) complicate the problem. The approach is built on top of a mixed integer programming (MIP) formulation derived from the multi-stage general lotsizing and scheduling problem. It combines a Variable Neighbourhood Search procedure which manages the setup-related variables, a specific heuristic to determine the digester's production speeds and an exact method to optimize the production and flow movement decisions. Different strategies are explored to speed-up the solution procedure and alternative variants of the algorithm are tested on instances based on real data from the case study. The algorithm is benchmarked against exact procedures.