Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem

The unconstrained binary quadratic programming problem (BQP) is known to be NP-hard and has many practical applications. This paper presents a simulated annealing (SA)-based heuristic for the BQP. The new SA heuristic for the BQP is based on a simple (1-opt) local search heuristic and designed with a simple cooling schedule, but the multiple annealing processes are adopted. To show practical performances of the SA, we test on publicly available benchmark instances of large size ranging from 500 to 2500 variables and compare them with other heuristics such as multi-start local search, the previous SA, tabu search, and genetic algorithm incorporating the 1-opt local search. Computational results indicate that our SA leads to high-quality solutions with short times and is more effective than the competitors particularly for the largest benchmark set. Furthermore, the values of new best-known solutions found by the SA for several large instances are also reported.     

An evolutionary heuristic for quadratic 0–1 programming

In this paper we present a heuristic algorithm for the well-known Unconstrained Quadratic 0–1 Programming Problem. The approach is based on combining solutions in a genetic paradigm and incorporates intensification algorithms used to improve solutions and speed up the method. Extensive computational experiments on instances with up to 500 variables are presented and we compare our approach both with powerful heuristic and exact algorithms from the literature establishing the effectiveness of the method in terms of solutions quality and computing time.     

A variable neighborhood search based matheuristic for nurse rostering problems

A practical nurse rostering problem, which arises at a ward of an Italian private hospital, is considered. In this problem, it is required each month to assign shifts to the nursing staff subject to various requirements. A matheuristic approach is introduced, based on a set of neighborhoods iteratively searched by a commercial integer programming solver within a defined global time limit, relying on a starting solution generated by the solver running on the general integer programming formulation of the problem. Generally speaking, a matheuristic algorithm is a heuristic algorithm that uses non trivial optimization and mathematical programming tools to explore the solutions space with the aim of analyzing large scale neighborhoods. Randomly generated instances, based on the considered nurse rostering problem, were solved and solutions computed by the proposed procedure are compared to the solutions achieved by pure solvers within the same time limit. The results show that the proposed solution approach outperforms the solvers in terms of solution quality. The proposed approach has also been tested on the well known Nurse Rostering Competition instances where several new best results were reached.     

A simple and effective metaheuristic for the Minimum Latency Problem

The Minimum Latency Problem (MLP) is a variant of the Traveling Salesman Problem which aims to minimize the sum of arrival times at vertices. The problem arises in a number of practical applications such as logistics for relief supply, scheduling and data retrieval in computer networks. This paper introduces a simple metaheuristic for the MLP, based on a greedy randomized approach for solution construction and iterated variable neighborhood descent with random neighborhood ordering for solution improvement. Extensive computational experiments on nine sets of benchmark instances involving up to 1000 customers demonstrate the good performance of the method, which yields solutions of higher quality in less computational time when compared to the current best approaches from the literature. Optimal solutions, known for problems with up to 50 customers, are also systematically obtained in a fraction of seconds.     

A hybrid simulated annealing and column generation approach for capacitated multicommodity network design

This paper presents a hybrid simulated annealing (SA) and column generation (CG) algorithm for the path-based formulation of the capacitated multicommodity network design (PCMND) problem. In the proposed method, the SA metaheuristic algorithm manages open and closed arcs. Several strategies for adding and dropping arcs are suggested and evaluated. For a given design vector in the proposed hybrid approach, the PCMND problem becomes a capacitated multicommodity minimum cost flow (CMCF) problem. The exact evaluation of the CMCF problem is performed using the CG algorithm. The parameter tuning is done by means of design of experiments approach. The performance of the proposed algorithm is evaluated by solving several benchmark instances. The results of the proposed algorithm are compared with the solutions of CPLEX solver and the best-known method in the literature under different time limits. Statistical analysis proves that the proposed algorithm is able to obtain better solutions.     

Transgenetic algorithm for the Traveling Purchaser Problem

In this paper an evolutionary algorithm is presented for the Traveling Purchaser Problem, an important variation of the Traveling Salesman Problem. The evolutionary approach proposed in this paper is called transgenetic algorithm. It is inspired on two significant evolutionary driving forces: horizontal gene transfer and endosymbiosis. The performance of the algorithm proposed for the investigated problem is compared with other recent works presented in the literature. Computational experiments show that the proposed approach is very effective for the investigated problem with 17 and 9 new best solutions reported for capacitated and uncapacitated instances, respectively.     

An adaptive memory methodology for the vehicle routing problem with simultaneous pick-ups and deliveries

This paper deals with a routing problem variant which considers customers to simultaneously require delivery and pick-up services. The examined problem is referred to as the Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries (VRPSPD). VRPSPD is an NP-hard combinatorial optimization problem, practical large-scale instances of which cannot be solved by exact solution methodologies within acceptable computational times. Our interest was therefore focused on metaheuristic solution approaches. In specific, we introduce an Adaptive Memory (AM) algorithmic framework which collects and combines promising solution features to generate high-quality solutions. The proposed strategy employs an innovative memory mechanism to systematically maximize the amount of routing information extracted from the AM, in order to drive the search towards diverse regions of the solution space. Our metaheuristic development was tested on numerous VRPSPD instances involving from 50 to 400 customers. It proved to be rather effective and efficient, as it produced high-quality solutions, requiring limited computational effort. Furthermore, it managed to produce several new best solutions.     

An Augmented Lagrangian Algorithm for Large Scale Multicommodity Routing

The linear multicommodity network flow (MCNF) problem has many applications in the areas of transportation and telecommunications. It has therefore received much attention, and many algorithms that exploit the problem structure have been suggested and implemented. The practical difficulty of solving MCNF models increases fast with respect to the problem size, and especially with respect to the number of commodities. Applications in telecommunications typically lead to instances with huge numbers of commodities, and tackling such instances computationally is challenging.In this paper, we describe and evaluate a fast and convergent lower-bounding procedure which is based on an augmented Lagrangian reformulation of MCNF, that is, a combined Lagrangian relaxation and penalty approach. The algorithm is specially designed for solving very large scale MCNF instances. Compared to a standard Lagrangian relaxation approach, it has more favorable convergence characteristics. To solve the nonlinear augmented Lagrangian subproblem, we apply a disaggregate simplicial decomposition scheme, which fully exploits the structure of the subproblem and has good reoptimization capabilities. Finally, the augmented Lagrangian algorithm can also be used to provide heuristic upper bounds.The efficiency of the augmented Lagrangian method is demonstrated through computational experiments on large scale instances. In particular, it provides near-optimal solutions to instances with over 3,600 nodes, 14,000 arcs and 80,000 commodities within reasonable computing time.     

A comparison of problem decomposition techniques for the FAP

This paper proposes a problem decomposition approach to solve hard Frequency Assignment Problem instances with standard meta-heuristics. The proposed technique aims to divide the initial problem into a number of easier subproblems, solve them and then recompose the partial solutions into one of the original problem. We consider the COST-259 MI-FAP instances and other Cardiff University test problems in order to simulate larger and more realistic networks. For both benchmarks the standard implementations of meta-heuristics do not generally produce a satisfactory performance within reasonable times of execution. However, the decomposed assignment approach can improve their results, both in terms of solution quality and runtime.     

Proximity Benders: a decomposition heuristic for stochastic programs

In this paper we present a heuristic approach to two-stage mixed-integer linear stochastic programming models with continuous second stage variables. A common solution approach for these models is Benders decomposition, in which a sequence of (possibly infeasible) solutions is generated, until an optimal solution is eventually found and the method terminates. As convergence may require a large amount of computing time for hard instances, the method may be unsatisfactory from a heuristic point of view. Proximity search is a recently-proposed heuristic paradigm in which the problem at hand is modified and iteratively solved with the aim of producing a sequence of improving feasible solutions. As such, proximity search and Benders decomposition naturally complement each other, in particular when the emphasis is on seeking high-quality, but not necessarily optimal, solutions. In this paper, we investigate the use of proximity search as a tactical tool to drive Benders decomposition, and computationally evaluate its performance as a heuristic on instances of different stochastic programming problems.     

Locating leak detecting sensors in a water distribution network by solving prize-collecting Steiner arborescence problems

We consider the problem of optimizing a novel acoustic leakage detection system for urban water distribution networks. The system is composed of a number of detectors and transponders to be placed in a choice of hydrants such as to provide a desired coverage under given budget restrictions. The problem is modeled as a particular Prize-Collecting Steiner Arborescence Problem. We present a branch-and-cut-and-bound approach taking advantage of the special structure at hand which performs well when compared to other approaches. Furthermore, using a suitable stopping criterion, we obtain approximations of provably excellent quality (in most cases actually optimal solutions). The test bed includes the real water distribution network from the Lausanne region, as well as carefully randomly generated realistic instances.     

Tabu Search for Frequency Assignment in Mobile Radio Networks

The main goal of the Frequency Assignment Problem in mobile radio networks consists of assigning a limited number of frequencies to each radio cell in a cellular network while minimizing electromagnetic interference due to the reuse of frequencies. This problem, known to be NP-hard, is of great importance in practice since better solutions will allow a telecommunications operator to manage larger cellular networks. This paper presents a new Tabu Search algorithm for this application. The algorithm is tested on realistic and large problem instances and compared with other methods based on simulated annealing, constraint programming and graph coloring algorithms. Empirical evidence shows that the Tabu algorithm is very competitive by giving the best solutions to the tested instances.     

Exact and heuristic methods for placing ships in locks

The ship placement problem constitutes a daily challenge for planners in tide river harbours. In essence, it entails positioning a set of ships into as few lock chambers as possible while satisfying a number of general and specific placement constraints. These constraints make the ship placement problem different from traditional 2D bin packing. A mathematical formulation for the problem is presented. In addition, a decomposition model is developed which allows for computing optimal solutions in a reasonable time. A multi-order best fit heuristic for the ship placement problem is introduced, and its performance is compared with that of the left-right-left-back heuristic. Experiments on simulated and real-life instances show that the multi-order best fit heuristic beats the other heuristics by a landslide, while maintaining comparable calculation times. Finally, the new heuristic’s optimality gap is small, while it clearly outperforms the exact approach with respect to calculation time.     

Steiner tree packing revisited

The Steiner tree packing problem (STPP) in graphs is a long studied problem in combinatorial optimization. In contrast to many other problems, where there have been tremendous advances in practical problem solving, STPP remains very difficult. Most heuristics schemes are ineffective and even finding feasible solutions is already NP-hard. What makes this problem special is that in order to reach the overall optimal solution non-optimal solutions to the underlying NP-hard Steiner tree problems must be used. Any non-global approach to the STPP is likely to fail. Integer programming is currently the best approach for computing optimal solutions. In this paper we review some ??classical?? STPP instances which model the underlying real world application only in a reduced form. Through improved modelling, including some new cutting planes, and by employing recent advances in solver technology we are for the first time able to solve those instances in the original 3D grid graphs to optimimality.     

A reduction approach for solving the rectangle packing area minimization problem

In the rectangle packing area minimization problem (RPAMP) we are given a set of rectangles with known dimensions. We have to determine an arrangement of all rectangles, without overlapping, inside an enveloping rectangle of minimum area. The paper presents a generic approach for solving the RPAMP that is based on two algorithms, one for the 2D Knapsack Problem (KP), and the other for the 2D Strip Packing Problem (SPP). In this way, solving an instance of the RPAMP is reduced to solving multiple SPP and KP instances. A fast constructive heuristic is used as SPP algorithm while the KP algorithm is instantiated by a tree search method and a genetic algorithm alternatively. All these SPP and KP methods have been published previously. Finally, the best variants of the resulting RPAMP heuristics are combined within one procedure. The guillotine cutting condition is always observed as an additional constraint. The approach was tested on 15 well-known RPAMP instances (above all MCNC and GSRC instances) and new best solutions were obtained for 10 instances. The computational effort remains acceptable. Moreover, 24 new benchmark instances are introduced and promising results are reported.     

Competitive Memetic Algorithms for Arc Routing Problems

The Capacitated Arc Routing Problem or CARP arises in applications like waste collection or winter gritting. Metaheuristics are tools of choice for solving large instances of this NP-hard problem. The paper presents basic components that can be combined into powerful memetic algorithms (MAs) for solving an extended version of the CARP (ECARP). The best resulting MA outperforms all known heuristics on three sets of benchmark files containing in total 81 instances with up to 140 nodes and 190 edges. In particular, one open instance is broken by reaching a tight lower bound designed by Belenguer and Benavent, 26 best-known solutions are improved, and all other best-known solutions are retrieved.     

The track formulation for the Train Dispatching problem

With few exceptions, train movements are still controlled by human operators, the dispatchers. They establish routes and precedence between trains in real-time in order to cope with normal operations but also to recover from deviations from the timetable, and minimize overall delays. Implicitly they tackle and solve repeatedly a hard optimization problem, the Train Dispatching Problem. We recently developed a decomposition approach which allowed us to solve real-life instances to optimality or near optimality in times acceptable for dispatchers. We present here some new ideas which appear to significantly reduce computational times while solving to optimality even large instances.     

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses’ preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.     

Minimizing the completion time of a project under resource constraints and feeding precedence relations: a Lagrangian relaxation based lower bound

In this paper we study the Resource Constrained Project Scheduling Problem (RCPSP) with “Feeding Precedence” (FP) constraints and minimum makespan objective. This problem typically arises in production planning environment, like make-to-order manufacturing, where the effort associated with the execution of an activity is not univocally related to its duration percentage and the traditional finish-to-start precedence constraints or the generalized precedence relations cannot completely represent the overlapping among activities. In this context, we need to introduce in the RCPSP the FP constraints. For this problem we propose a new mathematical formulation and define a lower bound based on the Lagrangian relaxation of the resource constraints. A computational experimentation on randomly generated instances of sizes of up to 100 activities shows a better performance of this lower bound when compared to other lower bounds. Moreover, for the optimally solved instances, its value is very close to the optimal one. Furthermore, in order to show the effectiveness of the proposed lower bound on large instances for which the optimal solution is known, we adapted our approach to solve the benchmarks of the basic RCPSP from the PSLIB with 120 activities.     

Application of the out-of-kilter algorithm to the asymmetric traveling salesman problem

This paper presents a heuristic method that finds optimum or near-optimum solutions to the asymmetric traveling salesman problem. The method uses the out-of-kilter algorithm to search for a neighbourhood. When subtours are produced by a flow-augmenting path of the out-of-kilter algorithm, it patches them into a Hamiltonian cycle. It extends the neighbourhood space by exchanging an even number of arcs, and it also exchanges arcs by a non-sequential primary change. Instances from real applications were used to test the algorithm, along with randomly generated problems. The new heuristic algorithm produced optimum solutions for 16 out of 28 real-world instances from TSPLIB and other sources. Also, compared with four efficient heuristics, it produced the best solutions for all except six instances. It also produced relatively good solutions in reasonable times for 216 randomly generated instances from nine instance generators.