An iterated local search algorithm for the vehicle routing problem with convex time penalty functions

We propose an iterated local search algorithm for the vehicle routing problem with time window constraints. We treat the time window constraint for each customer as a penalty function, and assume that it is convex and piecewise linear. Given an order of customers each vehicle to visit, dynamic programming (DP) is used to determine the optimal start time to serve the customers so that the total time penalty is minimized. This DP algorithm is then incorporated in the iterated local search algorithm to efficiently evaluate solutions in various neighborhoods. The amortized time complexity of evaluating a solution in the neighborhoods is a logarithmic order of the input size (i.e., the total number of linear pieces that define the penalty functions). Computational comparisons on benchmark instances with up to 1000 customers show that the proposed method is quite effective, especially for large instances.     

The vehicle routing problem with flexible time windows and traveling times

We generalize the standard vehicle routing problem by allowing soft time window and soft traveling time constraints, where both constraints are treated as cost functions. With the proposed generalization, the problem becomes very general. In our algorithm, we use local search to determine the routes of vehicles. After fixing the route of each vehicle, we must determine the optimal start times of services at visited customers. We show that this subproblem is NP-hard when cost functions are general, but can be efficiently solved with dynamic programming when traveling time cost functions are convex even if time window cost functions are non-convex. We deal with the latter situation in the developed iterated local search algorithm. Finally we report computational results on benchmark instances, and confirm the benefits of the proposed generalization.     

Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand

We examine neighborhood structures for heuristic search applicable to a general class of vehicle routing problems (VRPs). Our methodology utilizes a cyclic-order solution encoding, which maps a permutation of the customer set to a collection of many possible VRP solutions. We identify the best VRP solution in this collection via a polynomial-time algorithm from the literature. We design neighborhoods to search the space of cyclic orders. Utilizing a simulated annealing framework, we demonstrate the potential of cyclic-order neighborhoods to facilitate the discovery of high quality a priori solutions for the vehicle routing problem with stochastic demand (VRPSD). Without tailoring our solution procedure to this specific routing problem, we are able to match 16 of 19 known optimal VRPSD solutions. We also propose an updating procedure to evaluate the neighbors of a current solution and demonstrate its ability to reduce the computational expense of our approach.     

A composite-neighborhood tabu search approach to the traveling tournament problem

The Traveling Tournament Problem (TTP) is a combinatorial problem that combines features from the traveling salesman problem and the tournament scheduling problem. We propose a family of tabu search solvers for the solution of TTP that make use of complex combination of many neighborhood structures. The different neighborhoods have been thoroughly analyzed and experimentally compared. We evaluate the solvers on three sets of publicly available benchmarks and we show a comparison of their outcomes with previous results presented in the literature. The results show that our algorithm is competitive with those in the literature.     

A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce \({\mathcal O}(1)\) evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.     

A Constraint Programming Framework for Local Search Methods

We propose in this paper a novel integration of local search algorithms within a constraint programming framework for combinatorial optimization problems, in an attempt to gain both the efficiency of local search methods and the flexibility of constraint programming while maintaining a clear separation between the constraints of the problem and the actual search procedure. Each neighborhood exploration is performed by branch-and-bound search, whose potential pruning capabilities open the door to more elaborate local moves, which could lead to even better approximate results. Two illustrations of this framework are provided, including computational results for the traveling salesman problem with time windows. These results indicate that it is one order of magnitude faster than the customary constraint programming approach to local search and that it is competitive with a specialized local search algorithm.     

Local search heuristics for multi-index assignment problems with decomposable costs

The multi-index assignment problem (MIAP) with decomposable costs is a natural generalization of the well-known assignment problem. Applications of the MIAP arise, for instance, in the field of multi-target multi-sensor tracking. We describe an (exponentially sized) neighbourhood for a solution of the MIAP with decomposable costs, and show that one can find a best solution in this neighbourhood in polynomial time. Based on this neighbourhood, we propose a local search algorithm. We empirically test the performance of published constructive heuristics and the local search algorithm on random instances; a straightforward iterated local search algorithm is also tested. Finally, we compute lower bounds to our problem, which enable us to assess the quality of the solutions found.     

Restricted dynamic programming based neighborhoods for the hop-constrained minimum spanning tree problem

In this paper we develop, study and test new neighborhood structures for the Hop-constrained Minimum Spanning Tree Problem (HMSTP). These neighborhoods are defined by restricted versions of a new dynamic programming formulation for the problem and provide a systematic way of searching neighborhood structures based on node-level exchanges. We have also developed several local search methods that are based on the new neighborhoods. Computational experiments for a set of benchmark instances with up to 80 nodes show that the more elaborate methods produce in a quite fast way, heuristic solutions that are, for all cases, within 2% of the optimum.     

A parallel competitive colonial algorithm for JIT flowshop scheduling

This paper proposes two parallel algorithms which are improved by heuristics for a bi-objective flowshop scheduling problem with sequence-dependent setup times in a just-in-time environment. In the proposed algorithms, the population will be decomposed into the several sub-populations in parallel. Multiple objectives are combined with min–max method then each sub-population evolves separately in order to obtain a good approximation of the Pareto-front. After unifying the obtained results, we propose a variable neighborhood algorithm and a hybrid variable neighborhood search/tabu search algorithm to improve the Pareto-front. The non-dominated sets obtained from our proposed algorithms, a genetic local search and restarted iterated Pareto greedy algorithm are compared. It is found that most of the solutions in the net non-dominated front are yielded by our proposed algorithms.     

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.