Automatic instantiation of a Variable Neighborhood Descent from a Mixed Integer Programming model

A cutting plane algorithm for the site layout planning problem with travel barriers

In this paper, a problem arising in the planning of specialized diagnostic services in a segmented public healthcare system is addressed. The problem consists of deciding which hospitals will provide the service and their capacity levels, the allocation of demand in each institution, and the reallocation of uncovered demand to other institutions or private providers, while minimizing the total equivalent annual cost of investment and operating cost required to satisfy all the demand. An associated mixed-integer linear programming model can be solved by conventional branch and bound for relatively small instances; however, for larger instances the problem becomes intractable. To effectively address larger instances, a hybrid metaheuristic framework combining iterated greedy (IGA) and variable neighborhood descent (VND) components for this problem is proposed. Two greedy construction heuristics are developed, one starting with an infeasible solution and iteratively adding capacity and the other starting with a feasible, but expensive, solution and iteratively decrease capacity. The iterated greedy algorithm includes destruction and reconstruction procedures. Four different neighborhood structures are designed and tested within a VND procedure. In addition, the computation of local search components benefit from an intelligent exploitation of problem structure since, when the first-level location variables (hospital location and capacity) are fixed, the remaining subproblem can be solved efficiently as it is very close to a transshipment problem. All components and different strategies were empirically assessed both individually and within the IGA-VND framework. The resulting metaheuristic is able to obtain near optimal solutions, within 3% of optimality, when tested over a data base of 60- to 300-hospital instances.

Using a variable neighborhood search to solve a bi-objective identical parallel machine scheduling problem

In this paper, we propose a mixed integer programming (MIP) model for the Chicken Flock Sizing, Allocation and Scheduling Problem (CFSASP), which is an important planning problem in the broiler production supply chain. To solve the CFSASP efficiently, two variants of rolling horizon heuristics (RHHs) have been developed and applied on the case of a Norwegian broiler production company. Computational results show that the RHHs successfully obtain high-quality solutions within a reasonable time. The value of optimisation is verified through comparison with the case company's plans, where the solutions from optimisation outperforms the current solutions. Sensitivity analyses are also conducted to provide managerial insights regarding certain strategic decisions, such as how many and which days to use for hatching of chickens. Due to the promising results, the case company is now implementing an optimisation-based decision support system based on the MIP model and solution methods shown in this paper.

The generalized independent set problem (GISP) can be conceived as a relaxation of the maximum weight independent set problem. GISP has a number of practical applications, such as forest harvesting and handling geographic uncertainty in spatial information. This work presents an iterated local search (ILS) heuristic for solving GISP. The proposed heuristic relies on two new neighborhood structures, which are explored using a variable neighborhood descent procedure. Experimental results on a well-known GISP benchmark indicate our proposal outperforms the best existing heuristic for the problem. In particular, our ILS approach was able to find all known optimal solutions and to present new improved best solutions.

Modern large-scale steelmaking and continuous casting is usually composed of multiple converters, refining furnaces, continuous casting machines, multi-stage refining and reentrant line, which leads to the difficult scheduling. A mixed integer programming model is established to minimize the waiting time for all charges, and a variable neighborhood search algorithm is proposed to solve the problem. In order to improve the quality of the initial scheduling solution, heuristic scheduling rules are used to generate the initial solution. Six different neighborhood structures are designed and are constructed to generate the neighborhood solution to ensure the feasibility of neighborhood solution and improve search efficiency. On this basis, a scheduling method for steelmaking and continuous casting production is designed based on heuristic algorithm and variable neighborhood search algorithm. Simulation results show that the proposed method can obviously shorten the waiting time by using actual steelmaking and continuous casting production data.

A mixed integer programming model is proposed for multiple-class discriminant and classification analysis. When multiple discriminant functions, one for each class, are constructed with the mixed integer programming model, the number of misclassified observations in the sample is minimized. This model is an extension of the linear programming models for multiple-class discriminant analysis but may be considered as a generalization of mixed integer programming formulations for two-class classification analysis. Properties of the model are studied. The model is immune from any difficulties of many mathematical programming formulations for two-class classification analysis, such as nonexistence of optimal solutions, improper solutions, and instability under linear data transformation. In addition, meaningful discriminant functions can be generated under conditions where other techniques fail. Examples are provided. Results on publically accessible datasets show that this model is very effective in generating powerful discriminant functions.

A unified ant colony optimization algorithm for continuous optimization

Automated algorithm configuration methods have proven to be instrumental in deriving high-performing algorithms and such methods are increasingly often used to configure evolutionary algorithms. One major challenge in devising automatic algorithm configuration techniques is to handle the inherent stochasticity in the configuration problems. This article analyses a post-selection mechanism that can also be used for this task. The central idea of the post-selection mechanism is to generate in a first phase a set of high-quality candidate algorithm configurations and then to select in a second phase from this candidate set the (statistically) best configuration. Our analysis of this mechanism indicates its high potential and suggests that it may be helpful to improve automatic algorithm configuration methods.

A hierarchical solution evaluation method and a hybrid algorithm for the vehicle routing problem with drones and multiple visits

Minimizing total tardiness on a single machine with controllable processing times

Facility location is a critical component of strategic planning for public and private firms. Due to high cost of facility location, making decisions for such a problem has become an important issue which have gained a large deal of attention from researchers. This study examined the gradual maximal covering location problem with variable radius over multiple time periods. In gradual covering location problem, it is assumed that full coverage is replaced by a coverage function, so that increasing the distance from the facility decreases the amount of demand coverage. In variable radius covering problems, however, each facility is considered to have a fixed cost along with a variable cost which has a direct impact on the coverage radius. In real-world problems, since demand may change over time, necessitating relocation of the facilities, the problem can be formulated over multiple time periods. In this study, a mixed integer programming model was presented in which not only facility capacity was considered, but also two objectives were followed: coverage maximization and relocation cost minimization. A metaheuristic algorithm was presented to solve the maximal covering location problem. A simulated annealing algorithm was proposed, with its results presented. Computational results and comparisons demonstrated good performance of the simulated annealing algorithm.

The proper setting of algorithm parameters is a well-known issue that gave rise to recent research investigations from the (offline) automatic algorithm configuration perspective. Besides, the characteristics of the target optimization problem is also a key aspect to elicit the behavior of a dedicated algorithm, and as often considered from a landscape analysis perspective. In this paper, we show that fitness landscape analysis can open a whole set of new research opportunities for increasing the effectiveness of existing automatic algorithm configuration methods. Specifically, we show that using landscape features in iterated racing both (i) at the training phase, to compute multiple elite configurations explicitly mapped with different feature values, and (ii) at the production phase, to decide which configuration to use on a feature basis, provides significantly better results compared against the standard landscape-oblivious approach. Our first experimental investigations on NK-landscapes, considered as a benchmark family having controllable features in terms of ruggedness and neutrality, and tackled using a memetic algorithm with tunable population size and variation operators, show that a landscape-aware approach is a viable alternative to handle the heterogeneity of (black-box) combinatorial optimization problems.

A variable neighborhood descent heuristic for arc routing problems with time-dependent service costs

A Mixed-Integer-Programming-Model is presented within this paper for long-term expansion and operation planning of combined electric power and heat systems. The mathematical formulation of the monetary objective and the power and heat demand restraints is explained at first. The restraints for the long-term operation of a typical extraction-condensing power plant are shown afterwards. The application of the planning-model to a practical power and heat system is illustrated by some diagrams.