Iterated greedy local search methods for unrelated parallel machine scheduling

This work deals with the parallel machine scheduling problem which consists in the assignment of n jobs on m   parallel machines. The most general variant of this problem is when the processing time depends on the machine to which each job is assigned to. This case is known as the unrelated parallel machine problem. Similarly to most of the literature, this paper deals with the minimization of the maximum completion time of the jobs, commonly referred to as makespan (_Cmax)$(C_{\text{max}})$. Many algorithms and methods have been proposed for this hard combinatorial problem, including several highly sophisticated procedures. By contrast, in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time. Extensive computational campaigns show that these solutions are, most of the time, better than the current state-of-the-art methodologies by a statistically significant margin.     

Tabu-enhanced iterated greedy algorithm: A case study in the quadratic multiple knapsack problem

Iterated greedy search is a simple and effective metaheuristic for combinatorial problems. Its flexibility enables the incorporation of components from other metaheuristics with the aim of obtaining effective and powerful hybrid approaches. We propose a tabu-enhanced destruction mechanism for iterated greedy search that records the last removed objects and avoids removing them again in subsequent iterations. The aim is to provide a more diversified and successful search process with regards to the standard destruction mechanism, which selects the solution components for removal completely at random.     

Iterated tabu search for the car sequencing problem

This paper introduces an iterated tabu search heuristic for the daily car sequencing problem in which a set of cars must be sequenced so as to satisfy requirements from the paint shop and the assembly line. The iterated tabu search heuristic combines a classical tabu search with perturbation operators that help escape from local optima. The resulting heuristic is flexible, easy to implement, and fast. It has produced very good results on a set of test instances provided by the French car manufacturer Renault.     

New heuristics for the maximum diversity problem

The maximum diversity problem (MDP) consists of identifying, in a population, a subset of elements, characterized by a set of attributes, that present the most diverse characteristics among the elements of the subset. The identification of such solution is an NP-hard problem. Some heuristics are available to obtain approximate solutions for this problem. In this paper, we propose different GRASP heuristics for the MDP, using distinct construction procedures and including a path-relinking technique. Performance comparison among related work and the proposed heuristics is provided. Experimental results show that the new GRASP heuristics are quite robust and are able to find high-quality solutions in reasonable computational times. G.C. Silva’s work sponsored by CAPES MSc scholarship. L.S. Ochi’s work sponsored by CNPq research grants 304103/2003-9 and 550059/2005-9. S.L. Martins’s work sponsored by CNPq research grant 475124/03-0. A. Plastino’s work sponsored by CNPq research grants 300879/00-8 and 475124/03-0.     

A branch and bound algorithm for the maximum diversity problem

This article begins with a review of previously proposed integer formulations for the maximum diversity problem (MDP). This problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized. We propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial solutions to the MDP. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the medium-sized instances (with 50 elements) as well as some large-sized instances (with 100 elements). We compare our method with the best previous linear integer formulation solved with the well-known software Cplex. The comparison favors the proposed procedure.     

Iterated tabu search for the circular open dimension problem

This paper investigates the circular open dimension problem (CODP), which consists of packing a set of circles of known radii into a strip of fixed width and unlimited length without overlapping. The objective is to minimize the length of the strip. In this paper, CODP is solved by a series of sub-problems, each corresponding to a fixed strip length. For each sub-problem, an iterated tabu search approach, named ITS, is proposed. ITS starts from a randomly generated solution and attempts to gain improvements by a tabu search procedure. After that, if the obtained solution is not feasible, a perturbation operator is subsequently employed to reconstruct the incumbent solution and an acceptance criterion is implemented to determine whether or not accept the perturbed solution. As a supplementary method, the length of the strip is determined in monotonously decreasing way, with the aid of some post-processing techniques. The search terminates and returns the best found solution after the allowed computation time has been elapsed. Computational experiments based on numerous well-known benchmark instances show that ITS produces quite competitive results, with respect to the best known results, while the computational time remains reasonable for each instance.     

A two-phase tabu search based evolutionary algorithm for the maximum diversity problem

In this paper, we study the maximum diversity problem (MDP) which is equivalent to the quadratic unconstrained binary optimization (QUBO) problem with cardinality constraint. The MDP aims to select a subset of elements with given cardinality such that the sum of pairwise distances between any two elements in the selected subset is maximized. For solving this computationally challenging problem, we propose a two-phase tabu search based evolutionary algorithm (TPTS/EA), which integrates several distinguishing features to ensure the diversity and the quality of the evolution, such as a two-phase tabu search algorithm which consists of a dynamic candidate list (DCL) strategy-based traditional tabu search in the first phase and a solution-based tabu search procedure to refine the search in the second phase, and two path-relinking based recombination operators to generate new offspring solutions. Tested on three sets of totally 140 public instances in the literature, the study demonstrates the efficacy of the proposed TPTS/EA algorithm in terms of both solution quality and computational efficiency. Specifically, our proposed TPTS/EA algorithm is able to improve the previous best known results for 2 instances, while matching the previous best-known solutions for 130 instances. We also provide experimental evidences to highlight the beneficial effect of several important components in our TPTS/EA algorithm.     

A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem

Over the last decade, many metaheuristics have been applied to the flowshop scheduling problem, ranging from Simulated Annealing or Tabu Search to complex hybrid techniques. Some of these methods provide excellent effectiveness and efficiency at the expense of being utterly complicated. In fact, several published methods require substantial implementation efforts, exploit problem specific speed-up techniques that cannot be applied to slight variations of the original problem, and often re-implementations of these methods by other researchers produce results that are quite different from the original ones. In this work we present a new iterated greedy algorithm that applies two phases iteratively, named destruction, were some jobs are eliminated from the incumbent solution, and construction, where the eliminated jobs are reinserted into the sequence using the well known NEH construction heuristic. Optionally, a local search can be applied after the construction phase. Our iterated greedy algorithm is both very simple to implement and, as shown by experimental results, highly effective when compared to state-of-the-art methods.     

Local approximations for maximum partial subgraph problem

We deal with MAXH₀-FREE PARTIAL SUBGRAPH. We mainly prove that 3-locally optimum solutions achieve approximation ratio (δ₀+1)/(B+2+ν₀), where B=max_v∈Vd_G(v), δ₀=min_v∈V(H0)d_H0(v) and ν₀=(|V(H₀)|+1)/δ₀. Next, we show that this ratio rises up to 3/(B+1) when H₀=K₃. Finally, we provide hardness results for MAXK₃-FREE PARTIAL SUBGRAPH.     

Approximating the maximum vertex/edge weighted clique using local search

This paper extends the recently introduced Phased Local Search (PLS) algorithm to more difficult maximum clique problems and also adapts the algorithm to handle maximum vertex/edge weighted clique instances. PLS is a stochastic reactive dynamic local search algorithm that interleaves sub-algorithms which alternate between sequences of iterative improvement, during which suitable vertices are added to the current sub-graph, and plateau search, where vertices of the current sub-graph are swapped with vertices not contained in the current sub-graph. These sub-algorithms differ in firstly their vertex selection techniques in that selection can be solely based on randomly selecting a vertex, randomly selecting within highest vertex degree, or random selecting within vertex penalties that are dynamically adjusted during the search. Secondly, the perturbation mechanism used to overcome search stagnation differs between the sub-algorithms. PLS has no problem instance dependent parameters and achieves state-of-the-art performance for maximum clique and maximum vertex/edge weighted clique problems over a large range of the commonly used DIMACS benchmark instances.     

Tabu search and GRASP for the maximum diversity problem

In this paper, we develop new heuristic procedures for the maximum diversity problem (MDP). This NP-hard problem has a significant number of practical applications such as environmental balance, telecommunication services or genetic engineering. The proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement. Although proposed in seminal tabu search papers, memory-based constructions have often been implemented in naïve ways that disregard important elements of the fundamental tabu search proposals. We will compare our tabu search construction with a memory-less design and with previous algorithms recently developed for this problem. The constructive method can be coupled with a local search procedure or a short-term tabu search for improved outcomes. Extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times.     

An iterated local search algorithm for the vehicle routing problem with backhauls

The Vehicle Routing Problem with Backhauls (VRPB) is an extension of the VRP that deals with two types of customers: the consumers (linehaul) that request goods from the depot and the suppliers (backhaul) that send goods to the depot. In this paper, we propose a simple yet effective iterated local search algorithm for the VRPB. Its main component is an oscillating local search heuristic that has two main features. First, it explores a broad neighborhood structure at each iteration. This is efficiently done using a data structure that stores information about the set of neighboring solutions. Second, the heuristic performs constant transitions between feasible and infeasible portions of the solution space. These transitions are regulated by a dynamic adjustment of the penalty applied to infeasible solutions. An extensive statistical analysis was carried out in order to identify the most important components of the algorithm and to properly tune the values of their parameters. The results of the computational experiments carried out show that this algorithm is very competitive in comparison to the best metaheuristic algorithms for the VRPB. Additionally, new best solutions have been found for two instances in one of the benchmark sets. These results show that the performance of existing metaheuristic algorithms can be considerably improved by carrying out a thorough statistical analysis of their components. In particular, it shows that by expanding the exploration area and improving the efficiency of the local search heuristic, it is possible to develop simpler and faster metaheuristic algorithms without compromising the quality of the solutions obtained.     

Test case generators and computational results for the maximum clique problem

In the last years many algorithms have been proposed for solving the maximum clique problem. Most of these algorithms have been tested on randomly generated graphs. In this paper we present different test problem generators that arise from a variety of practical applications, as well as graphs with known maximum cliques. In addition, we provide computational experience with two exact algorithms using the generated test problems.     

Average behavior of greedy algorithms for the minimization knapsack problem: General coefficient distributions

For the minimization knapsack problem with Boolean variables, primal and dual greedy algorithms are formally described. Their relations to the corresponding algorithms for the maximization knapsack problem are shown. The average behavior of primal and dual algorithms for the minimization problem is analyzed. It is assumed that the coefficients of the objective function and the constraint are independent identically distributed random variables on [0, 1] with an arbitrary distribution having a density and that the right-hand side d is deterministic and proportional to the number of variables (i.e., d = μn). A condition on μ is found under which the primal and dual greedy algorithms have an asymptotic error of t.     

Heuristics for the mirrored traveling tournament problem

Professional sports leagues are a major economic activity around the world. Teams and leagues do not want to waste their investments in players and structure in consequence of poor schedules of games. Game scheduling is a difficult task, involving several decision makers, different types of constraints, and multiple objectives to optimize. The traveling tournament problem abstracts certain types of sport timetabling issues, where the objective is to minimize the total distance traveled by the teams. In this work, we tackle the mirrored version of this problem. We first propose a fast and effective constructive algorithm. We also describe a new heuristic based on the combination of the GRASP and iterated local search metaheuristics. A strong neighborhood based on ejection chains is also proposed and leads to significant improvements in solution quality. Very good solutions are obtained for the mirrored problem, sometimes even better than those found by other approximate algorithms for the less constrained non-mirrored version. Computational results are shown for benchmark problems and for a large instance associated with the main division of the 2003 edition of the Brazilian soccer championship, involving 24 teams.     

A comparison of three metaheuristics for the workover rig routing problem

The workover rig routing problem (WRRP) is a variant of the Vehicle Routing Problem with Time Windows (VRPTW) and arises in the operations of onshore oil fields. In this problem, a set of workover rigs located at different positions must service oil wells requesting maintenance as soon as possible. When a well requires maintenance, its production is reduced or stopped for safety reasons and some workover rig must service it within a given deadline. It is therefore important to service the wells in a timely fashion in order to minimize the production loss. Whereas for classical VRPTWs the objective is to minimize route length, in the WRRP the objective is to minimize the total lost production, equal to the sum of arrival times at the wells, multiplied by production loss rates. The WRRP generalizes the Delivery Man Problem with Time Windows by considering multiple open vehicle routes and multiple depots. This paper compares three metaheuristics for the WRRP: an iterated local search, a clustering search, and an Adaptive Large Neighborhood Search (ALNS). All approaches, in particular ALNS, have yielded good solutions for instances derived from a real-life setting.     

A study of ACO capabilities for solving the maximum clique problem

This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose and compare two different instantiations of a generic ACO algorithm for this problem. Basically, the generic ACO algorithm successively generates maximal cliques through the repeated addition of vertices into partial cliques, and uses “pheromone trails” as a greedy heuristic to choose, at each step, the next vertex to enter the clique. The two instantiations differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph. We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures—the re-sampling and the dispersion ratio—for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.