Parallel matheuristics for the discrete unit commitment problem with min‐stop ramping constraints

The discrete unit commitment problem with min‐stop ramping constraints optimizes the daily production of thermal power plants, subject to an operational reactivity of thermal units in a 30‐minute delay. Previously, mixed integer programming (MIP) formulations aimed at an exact optimization approach. This paper derives matheuristics to face the short time limit imposed by the operational constraints. Continuous relaxations guide the search for feasible solutions exploiting tailored variable fixing strategies. Parallel matheuristics are derived considering complementary strategies in parallel. Tests were performed on more than 600 real‐life instances. Our parallel matheuristic provides high‐quality solutions and outperforms the MIP approach in the time limits imposed by the industrial application. This paper illustrates a special interest for matheuristics in industrial highly constrained problems: many tailored neighborhood searches can be derived from an MIP formulation, and their combination in a parallel scheme improves the solution quality as well as the consistency of the heuristic.     

Heuristic algorithms for the general nonlinear separable knapsack problem

We consider the nonlinear knapsack problem with separable nonconvex functions. Depending on the assumption on the integrality of the variables, this problem can be modeled as a nonlinear programming or as a (mixed) integer nonlinear programming problem. In both cases, this class of problems is very difficult to solve, both from a theoretical and a practical viewpoint. We propose a fast heuristic algorithm, and a local search post-optimization procedure. A series of computational comparisons with a heuristic method for general nonconvex mixed integer nonlinear programming and with global optimization methods shows that the proposed algorithms provide high-quality solutions within very short computing times.     

An improved binary particle swarm optimization for unit commitment problem

This paper proposes a new improved binary PSO (IBPSO) method to solve the unit commitment (UC) problem, which is integrated binary particle swarm optimization (BPSO) with lambda-iteration method. The IBPSO is improved by priority list based on the unit characteristics and heuristic search strategies to repair the spinning reserve and minimum up/down time constraints. To verify the advantages of the IBPSO method, the IBPSO is tested and compared to the other methods on the systems with the number of units in the range of 10–100. Numerical results demonstrate that the IBPSO is superior to other methods reported in the literature in terms of lower production cost and shorter computational time.     

A hybrid neural network and simulated annealing approach to the unit commitment problem

In this paper, the authors present an approach combining the feedforward neural network and the simulated annealing method to solve unit commitment, a mixed integer combinatorial optimisation problem in power system. The artificial neural network is used to determine the discrete variables corresponding to the state of each unit at each time interval. The simulated annealing method is used to generate the continuous variables corresponding to the power output of each unit and the production cost. The type of neural network used in this method is a multi-layer perceptron trained by the back-propagation algorithm. A set of load profiles as inputs and the corresponding unit commitment schedules as outputs (satisfying the minimum up–down, spinning reserve and crew constraints) are utilized to train the network. A method to generate the training patterns is also presented. The experimental result demonstrates that the proposed approach can solve unit commitment in a reduced computational time with an optimum generation schedule.     

Using tabu search with ranking candidate list to solve production planning problems with setups

This study considers production planning problems involving multiple products, multiple resources, multiple periods, setup times, and setup costs. It can be formulated as a mixed integer program (MIP). Solving a realistic MIP production planning problem is NP-hard; therefore, we use tabu search methods to solve such a difficult problem. Furthermore, we improve tabu search by a new candidate list strategy, which sorts the neighbor solutions using post-optimization information provided by the final tableau of the linear programming simplex algorithm. A neighbor solution with higher priority in the ranking sequence has a higher probability of being the best neighbor solution of a current solution. According to our experiments, the proposed candidate list strategy tabu search produces a good solution faster than the traditional simple tabu search. This study also suggests that if the evaluation of the entire neighborhood space in a tabu search algorithm takes too much computation and if an efficient and effective heuristic to rank the neighbor solutions can be developed, the speed of tabu search algorithm could be significantly increased by using the proposed candidate list strategy.     

An application of genetic and evolutive algorithms to unit commitment problem

 Here is introduced an application of the Genetic and Evolutive Algorithms to the Unit Commitment Problem. It is a mixed integer problem of constrained non linear combinatorial optimization. The many constraints make the problem very complex. Three cases of study on the problem have been faced, characterized by crescent grades of completeness/ difficulties in order to understand which are the advantages and the difficulties which arise from the evolutive approach. In the cases of study have been faced dimensions of the problem significant in practice: from 10 up to 1000 generators.     

Genetic algorithm with binary representation of generating unit start-up and shut-down times for the unit commitment problem

An approach for solving the unit commitment problem based on genetic algorithm with binary representation of the unit start-up and shut-down times is presented. The proposed definition of the decision variables and their binary representation reduce the solution space and computational time in comparison to the classical genetic algorithm approach to unit commitment. The method incorporates time-dependent start-up costs, demand and reserve constraints, minimum up and down time constraints and units power generation limits. Penalty functions are applied to the infeasible solutions. Test results showed an improvement in effectiveness and computational time compared to results obtained from genetic algorithm with standard binary representation of the unit states and other methods.     

Relax and fix heuristics to solve one-stage one-machine lot-scheduling models for small-scale soft drink plants

The production planning of regional small-scale soft drink plants can be modeled by mixed integer models that integrate lot sizing and scheduling decisions and consider sequence-dependent setup times and costs. These plants produce soft drinks in different flavors and sizes and they have typically only one production line. The production process is carried out basically in two main stages: liquid preparation (stage I) and bottling (stage II). However, since the production bottleneck of these plants is often in stage II, in this study we represent the problem as a one-stage one-machine lot-scheduling model that considers stage II as the bottleneck but also takes into account a capacity constraint of stage I. To solve the problem, we propose relax and fix heuristics exploring the model structure and we evaluate their computational performances solving different problem instances based on real data of a Brazilian small-scale soft drink company. The solutions obtained are compared to the company solutions and the solutions of a general-purpose optimization software.     

Genetic algorithms to solve the cover printing problem

Inspired by successful application of evolutionary algorithms to solving difficult optimization problems, we explore in this paper, the applicability of genetic algorithms (GAs) to the cover printing problem, which consists in the grouping of book covers on offset plates in order to minimize the total production cost. We combine GAs with a linear programming solver and we propose some innovative features such as the “unfixed two-point crossover operator” and the “binary stochastic sampling with replacement” for selection. Two approaches are proposed: an adapted genetic algorithm and a multiobjective genetic algorithm using the Pareto fitness genetic algorithm. The resulting solutions are compared. Some computational experiments have also been done to analyze the effects of different genetic operators on both algorithms.     

Heuristic approaches for the multiperiod location-transportation problem with reuse of vehicles in emergency logistics

The coordination among the different actors in relief chains is crucial to provide effective and efficient response in emergency logistics. By recognizing this fact, we have developed two stochastic mixed-integer programming models to integrate and coordinate facility location, transportation and fleet sizing decisions in a multi-period, multi-commodity, and multi-modal context under uncertainty. One model even considers the option of reusing vehicles to cover extra routes within the same time period in an attempt to save overall resources and improve service levels. Typical uncertainty in victims׳ needs, incoming supply, inventory conditions, and roads availability are modeled through a set of scenarios representing plausible disaster impacts. To solve instances of practical size, we have devised relax-and-fix and fix-and-optimize heuristics based on decompositions by time, scenario, and stage. The proposed instances entail characteristics of the megadisaster in the Mountain Region of Rio de Janeiro State in Brazil. The results suggest that the integration of decisions in a multiperiod context and the option of reusing vehicles reduce total costs, thus improving the overall performance of the relief operations. Also, the time-decomposition fix-and-optimize heuristic outperforms the CPLEX solver in terms of elapsed times and optimality gaps, mainly in moderate-size instances. Finally, we show the importance to explicitly consider randomness instead of using simpler worst-case scenario approaches.     

An optimization approach for the lot sizing and scheduling problem in the brewery industry

This study considers a production lot sizing and scheduling problem in the brewery industry. The underlying manufacturing process can be basically divided into two main production stages: preparing the liquids including fermentation and maturation inside the fermentation tanks; and bottling the liquids on the filling lines, making products of different liquids and sizes. This problem differs from other problems in beverage industries due to the relatively long lead times required for the fermentation and maturation processes and because the “ready” liquid can remain in the tanks for some time before being bottled. The main planning challenge is to synchronize the two stages (considering the possibility of a “ready” liquid staying in the tank until bottling), as the production bottlenecks may alternate between these stages during the planning horizon. This study presents a novel mixed integer programming model that represents the problem appropriately and integrates both stages. In order to solve real-world problem instances, MIP-based heuristics are developed, which explore the model structure. The results show that the model is able to comprise the problem requirements and the heuristics produce relatively good-quality solutions.     

Computing solutions of the paintshop–necklace problem

How to assign colors to the occurrences of cars in a car factory? How to divide fairly a necklace between thieves who have stolen it? These two questions are addressed in two combinatorial problems that have attracted attention from a theoretical point of view these last years, the first one more by people from the combinatorial optimization community, the second more from the topological combinatorics and computer science point of view.     

A heuristic to solve the synchronized log-truck scheduling problem

We present a synchronized routing and scheduling problem that arises in the forest industry, as a variation of the log-truck scheduling problem. It combines routing and scheduling of trucks with specific constraints related to the Canadian forestry context. This problem includes aspects such as pick-up and delivery, multiple products, inventory stock, multiple supply points and multiple demand points. We developed a decomposition approach to solve the weekly problem in two phases. In the first phase we use a MIP solver to solve a tactical model that determines the destinations of full truckloads from forest areas to woodmills. In the second phase, we make use of two different methods to route and schedule the daily transportation of logs: the first one consists in using a constraint-based local search approach while the second one is a hybrid approach involving a constraint programming based model and a constraint-based local search model. These approaches have been implemented using COMET2.0. The method, was tested on two industrial cases from forest companies in Canada.     

A dynamic programming approach to solving the assortment planning problem with multiple quality levels

While the assortment planning problem, in which a firm selects a set of products to offer, has been widely studied, several problem instances exist which have not yet been solved to optimality. In particular, we consider an assortment planning problem under a locational choice model for consumer choice with both vertical and horizontal differentiation. We present a combined dynamic programming/line search approach which finds an optimal solution when customer preference for the horizontal attributes are distributed according to a unimodal distribution. The dynamic program makes use of new analytical results, which show that high quality products will be distributed near the mode. This enables significant state reduction and therefore efficient solution times. Efficient computation times allow us to study the solution for a wide range of system parameters and thereby draw several managerial conclusions.     

A hybrid algorithm for the cyclic hoist scheduling problem with two transportation resources

In automated electroplating lines, computer-controlled hoists are used to transfer parts from a processing resource to another one. Products are mounted into carriers and immersed sequentially in a series of tanks following a given sequence.     

Memetic algorithms for the job shop scheduling problem with operators

The job-shop scheduling problem with operators (JSO) is an extension of the classic job-shop problem in which an operation must be assisted by one of a limited set of human operators, so it models many real life situations. In this paper we tackle the JSO by means of memetic algorithms with the objective of minimizing the makespan. We define and analyze a neighborhood structure which is then exploited in local search and tabu search algorithms. These algorithms are combined with a conventional genetic algorithm to improve a fraction of the chromosomes in each generation. We also consider two different schedule builders for chromosome decoding. All these elements are combined to obtain memetic algorithms which are evaluated over an extensive set of instances. The results of the experimental study show that they reach high quality solutions in very short time, comparing favorably with the state-of-the-art methods.     

Hybrid simulation and MIP based heuristic algorithm for the production and distribution planning in the soft drink industry

This study addresses the production and distribution planning problem in the soft drink industry. The problem involves the allocation of production volumes among the different production lines in the manufacturing plants, and the delivery of products to the distribution centers (DCs). A mixed integer linear programming (MILP) model is developed for the problem.     

A computational study on the quadratic knapsack problem with multiple constraints

The quadratic knapsack problem (QKP) has been the subject of considerable research in recent years. Despite notable advances in special purpose solution methodologies for QKP, this problem class remains very difficult to solve. With the exception of special cases, the state-of-the-art is limited to addressing problems of a few hundred variables and a single knapsack constraint.In this paper we provide a comparison of quadratic and linear representations of QKP based on test problems with multiple knapsack constraints and up to eight hundred variables. For the linear representations, three standard linearizations are investigated. Both the quadratic and linear models are solved by standard branch-and-cut optimizers available via CPLEX. Our results show that the linear models perform well on small problem instances but for larger problems the quadratic model outperforms the linear models tested both in terms of solution quality and solution time by a wide margin. Moreover, our results demonstrate that QKP instances larger than those previously addressed in the literature as well as instances with multiple constraints can be successfully and efficiently solved by branch and cut methodologies.     

Integrating LP-guided variable fixing with MIP heuristics in the robust design of hybrid wired-wireless FTTx access networks

This study investigates how to model and solve the problem of optimally designing FTTx telecommunications access networks integrating wired and wireless technologies, while taking into account the uncertainty of wireless signal propagation. We propose an original robust optimization model for the related robust 3-architecture Connected Facility Location problem, which includes additional variables and constraints to model wireless signal coverage represented through signal-to-interference ratios. Since the resulting robust problem can prove very challenging even for a modern state-of-the art optimization solver, we propose to solve it by an original primal heuristic that combines a probabilistic variable fixing procedure, guided by peculiar Linear Programming relaxations, with a Mixed Integer Programming heuristic, based on an exact very large neighborhood search. A numerical study carried out on a set of realistic instances show that our heuristic can find solutions of much higher quality than a state-of-the-art solver.