Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem

This article addresses a Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem, an NP-hard combinatorial optimization problem. The problem is solved by using a cooperative approach that uses a local search for exploring a series of neighbourhoods induced from the Lagrangian relaxation. Each neighbourhood is submitted to an optimization process using two alternative strategies: reducing and moving strategies. The reducing strategy serves to reduce the current search space whereas the moving strategy explores the new search space. The performance of the proposed approach is evaluated on benchmark instances taken from the literature. Its obtained results are compared with those reached by some recent methods available in the literature. New solutions have been obtained for almost 80% of the instances tested.     

Design of a decentralized framework for collaborative product design using memetic algorithms

This paper proposes a generalized bi-level decentralized framework to model collaborative design problems over autonomous stakeholders with each having different objectives. At the system level, a system solution derived from the Pareto concept is created. A facilitator agent is introduced to search for Pareto optimal solutions based on a Memetic Algorithm (MA). At the design disciplinary level, design agents representing design teams are introduced to optimize their own objectives. The proposed framework will guide the collaborative designers to converge to Pareto optimal solutions given any forms of design utility functions. The only information exchanged between the two levels is numerical values instead of utility functions. Therefore sensitive (private) design information can be protected. Three comparison experiments are conducted to evaluate the solution quality and explore the applicability of the proposed framework to collaborative design problems.     

Asynchronous teams for joint lot-sizing and scheduling problem in flow shops

The integrated production scheduling and lot-sizing problem in a flow shop environment consists of establishing production lot sizes and allocating machines to process them within a planning horizon in a production line with machines arranged in series. The problem considers that demands must be met without backlogging, the capacity of the machines must be respected, and machine setups are sequence-dependent and preserved between periods of the planning horizon. The objective is to determine a production schedule to minimise the setup, production and inventory costs. A mathematical model from the literature is presented, as well as procedures for obtaining feasible solutions. However, some of the procedures have difficulty in obtaining feasible solutions for large-sized problem instances. In addition, we address the problem using different versions of the Asynchronous Team (A-Team) approach. The procedures were compared with literature heuristics based on Mixed Integer Programming. The proposed A-Team procedures outperformed the literature heuristics, especially for large instances. The developed methodologies and the results obtained are presented.     

On the optimal design of water distribution networks: a practical MINLP approach

We propose a practical solution method for real-world instances of a water-network optimization problem with fixed topology using a nonconvex continuous NLP (NonLinear Programming) relaxation and a MINLP (Mixed Integer NonLinear Programming) search. Our approach employs a relatively simple and accurate model that pays some attention to the requirements of the solvers that we employ. Our view is that in doing so, with the goal of calculating only good feasible solutions, complicated algorithmics can be confined to the MINLP solver. We report successful computational experience using available open-source MINLP software on problems from the literature and on difficult real-world instances. An important contribution of this paper is that the solutions obtained, besides being low cost, are immediately usable in practice because they are characterized by an allocation of diameters to pipes that leads to a correct hydraulic operation of the network. This is not the case for most of the other methods presented in the literature.     

Modelling and a tabu search solution for the slab reallocation problem in the steel industry

This paper considers a slab reallocation problem arising from operations planning in the steel industry. The problem involves reallocating steel slabs to customer orders to improve the utilisation of slabs and the level of customer satisfaction. It can be viewed as an extension of a multiple knapsack problem. We firstly formulate the problem as an integer nonlinear programming (INLP) model. With variable replacement, the INLP model is then transformed into a mixed integer linear programming (MILP) model, which can be solved to optimality by MILP optimisers for very small instances. To obtain satisfactory solutions efficiently for practical-sized instances, a heuristic algorithm based on tabu search (TS) is proposed. The algorithm employs multiple neighbourhoods including swap, insertion and ejection chain in local search, and adopts solution space decomposition to speed up computation. In the ejection chain neighbourhood, a new and more effective search method is also proposed to take advantage of the structural properties of the problem. Computational experiments on real data from an advanced iron and steel company in China show that the algorithm generates very good results within a short time. Based on the model and solution approach, a decision support system has been developed and implemented in the company.     

A (μ, λ)-coordination mechanism for agent-based multi-project scheduling

A new generic negotiation-based mechanism to coordinate project planning software agents to share resources among projects is described. The mechanism, which takes into account asymmetric information and opportunistic behavior, is concretized for the decentralized resource constrained multi-project scheduling problem, and evaluated on 80 benchmark instances taken from the literature and 60 newly generated instances. Computational tests show that the proposed mechanism comes close to results obtained by central solution methods. For twelve benchmark instances new best solutions could be computed.     

Supply chain optimisation with both production and transportation integration: multiple vehicles for a single perishable product

This paper deals with an extension of the integrated production and transportation scheduling problem (PTSP) by considering multiple vehicles (PTSPm) for optimisation of supply chains. The problem reflects a real concern for industry since production and transportation subproblems are commonly addressed independently or sequentially, which leads to sub-optimal solutions. The problem includes specific capacity constraints, the short lifespan of products and the special case of the single vehicle that has already been studied in the literature. A greedy randomised adaptive search procedure (GRASP) with an evolutionary local search (ELS) is proposed to solve the instances with a single vehicle as a special case. The method has been proven to be more effective than those published and provides shorter computational times with new best solutions for the single vehicle case. A new set of instances with multiple vehicles is introduced to favour equitable future research. Our study extends previous research using an indirect resolution approach and provides an algorithm to solve a wide range of one-machine scheduling problems with the proper coordination of single or multiple vehicles.     

Multiple machine JIT scheduling: a tabu search approach

This paper presents an approach to solving the multiple machine, non-preemptive, earliness-tardiness scheduling problem with unequal due dates in a flow shop with machine tiers (FMT). In this variant of the flow shop problem, machines are arranged in tiers or groups, and the jobs must visit one machine in each tier. The processing times, machine assignments, and due dates are deterministic and known in advance. The objective is to find a permutation schedule that minimizes the total deviation of each job from its due date. A tabu search (TS) meta-heuristic combined with an LP evaluation function is applied to solve this problem and results are compared to optimal permutation solutions for small problems and the earliest due date schedule for large problems. Several neighborhood generation methods and two diversification strategies are examined to determine their effect on solution quality. Results show that the TS method works well for this problem. TS found the optimal solution in all but one of the small problem instances and improved the earliest due date solutions for larger instances where no optimal solutions could be found.     

Models and algorithms for the heterogeneous dial-a-ride problem with driver-related constraints

This paper introduces models and algorithms for a static dial-a-ride problem arising in the transportation of patients by non-profit organizations such as the Austrian Red Cross. This problem is characterized by the presence of heterogeneous vehicles and patients. In our problem, two types of vehicles are used, each providing a different capacity for four different modes of transportation. Patients may request to be transported either seated, on a stretcher or in a wheelchair. In addition, some may require accompanying persons. The problem is to construct a minimum-cost routing plan satisfying service-related criteria, expressed in terms of time windows, as well as driver-related constraints expressed in terms of maximum route duration limits and mandatory lunch breaks. We introduce both a three-index and a set-partitioning formulation of the problem. The linear programming relaxation of the latter is solved by a column generation algorithm. We also propose a variable neighborhood search heuristic. Finally, we integrate the heuristic and the column generation approach into a collaborative framework. The column generation algorithm and the collaborative framework provide tight lower bounds on the optimal solution values for small-to-medium-sized instances. The variable neighborhood search algorithm yields high-quality solutions for realistic test instances.     

A fast branch,bound and remember algorithm for disassembly line balancing problem

In recent years, the interests of disassembly line have increased owing to economic reasons and the increase of environmental awareness. Effective line can provide many advantages in terms of economic aspect and it facilitates competition the companies with others. This study contributes to the relevant literature by a branch, bound and remember algorithm for disassembly line balancing problem with AND/OR precedence. The proposed exact solution method employs the memory-based dominance rule to eliminate the reduplicated sub-problems by storing all the searched sub-problems and to utilise cyclic best-first search strategy to obtain high-quality complete solutions fast. In this paper, minimising the number of stations is taken as the performance measure. The proposed methodology is tested on a set of 260 instances and compared with the mathematical model using CPLEX solver and five well-known metaheuristics. Computational results show that the proposed method is capable of obtaining the optimal solutions for all the tested instances with less than 0.1?seconds on average. Additionally, comparative study demonstrates that the proposed method is the state-of-the-art algorithm and outperforms the CPLEX solver and metaheuristics in terms of both solution quality and search speed aspects.     

A hybrid global–local approach for optimization of injection gate locations in liquid composite molding process simulations

The optimization of injection gate locations in liquid composite molding processes by trial and error based methods is time consuming and requires an elevated level of intuition, even when high fidelity physics-based numerical models are available. Optimization based on continuous sensitivity equations (CSE) and gradient search algorithms focused towards minimizing the mold infusion time gives a robust approach that will converge to local optima based on the initial solution. Optimization via genetic algorithms (GA) utilizes natural selection as a means of finding the optimal solution in the global domain; the computed solution is at best, close to the global optimum with further refinement still possible. In this paper, we present a hybrid global–local search approach that combines evolutionary GAs with gradient-based searches via the CSE. The hybrid approach provides a global search with the GA for a predetermined amount of time and is subsequently further refined with a gradient-based search via the CSE. In our hybrid method, we utilize the efficiency of gradient searches combined with the robustness of the GA. The resulting combination has been demonstrated to provide better and more physically correct results than either method alone. The hybrid method provides optimal solutions more quickly than GA alone and more robustly than CSE based searches alone. A resin infusion quality parameter that measures the deviation from a near uniform mold volume infusion rate is defined. The effectiveness of the hybrid method with a modified objective function that includes both the infusion time and the defined mold infusion quality parameter is demonstrated.     

A VNS-LP algorithm for the robust dynamic maximal covering location problem

This study introduces a robust variant of the well-known dynamic maximal covering location problem (DMCLP) and proposes an integer linear programming formulation of the robust DMCLP. A hybrid approach for solving both deterministic and robust variant of the DMCLP is developed, which is based on hybridization of a Variable neighborhood search and a linear programming technique. The main idea is to split the problem into subproblems and to combine optimal solutions of the obtained subproblems in order to construct solution of the initial problem. The results of the proposed hybrid approach on instances of the deterministic DMCLP are presented and compared with the results of the state-of-the-art approach from the literature and with the results of commercial CPLEX solver. The presented computational analysis shows that the proposed hybrid algorithm outperforms other approaches for the DMCLP. In addition, the algorithm was tested on the instances of the robust variant of DMCLP, and obtained results are discussed in detail.

     

A tabu search algorithm for solving a multicriteria flexible job shop scheduling problem

The problem that we consider in this article is a flexible job shop scheduling problem issued from the printing and boarding industry. Two criteria have to be minimised, the makespan and the maximum lateness. Two tabu search algorithms are proposed for finding a set of non-dominated solutions: the first is based on the minimisation of one criterion subject to a bound on the second criterion (ε-constraint approach) and the second is based on the minimisation of a linear combination of criteria. These algorithms are tested on benchmark instances from the literature and the results are discussed. The total tardiness is considered as a third criterion for the second tabu search and results are presented and discussed.     

GRASP with path relinking for a multiple objective sequencing problem for a mixed-model assembly line

This research presents a new application of greedy randomised adaptive search procedure (GRASP) to address a production sequencing problem for mixed-model assembly line in a just-in-time (JIT) production system in two different cases. In the former case, small size sequencing problems are considered and two objectives are presented; minimisation of setups and optimisation of stability of material usage rates. These two objectives are inversely correlated with each other, so simultaneous optimisation of both is challenging. This type of problem is NP-hard. The GRASP, with path relinking, searches for efficient frontier where simultaneous optimisation of number of setups and usage rates is desired. Several test problems are solved via GRASP and its performance is compared to solutions obtained via complete enumeration and simulated annealing (SA), tabu search (TS) and genetic algorithms (GA) approaches from the literature. Experimental results reveal that the GRASP with path relinking provides near-optimal solutions in terms of the two objectives and its ‘average inferiority%’ and ‘average percentile’ performances are superior to that of other heuristics. In the latter case, the goal is to explore varying the emphasis of these two conflicting objectives. Larger sequencing problems are considered and solved via GRASP with path relinking. Its objective function values are compared to the solutions obtained via a SA approach from the literature. Experimental results show that GRASP also provides good performance on large size problems and its percentage improvement is better than that of SA. Overall results also show, however, that the GRASP performs poorly with regard to CPU time.     

A divide and conquer-based greedy search for two-machine no-wait job shop problems with makespan minimisation

This paper addresses a two-machine no-wait job shop problem with makespan minimisation. It is well known that this problem is strongly NP-hard. A divide-and-conquer approach (DC for short) is adopted to calculate the optimal timetable of a given sequence. It decomposes the given sequences into several independent parts and conquers them separately. A timetable enhancing method is introduced to further improve the timetable obtained by DC. It constructs a set of flow shop type jobs based on the result from DC and calculates the best timetable for these newly constructed jobs by the well-known Gilmore and Gomory method (GG for short). An efficient greedy search is proposed by integrating DC with GG to search for the best sequence. Experimental results show that the proposed algorithm can find the optimal solutions for 96% of the randomly generated test instances on average.     

Solving kinematics problems by efficient interval partitioning

In this study, a generic solution methodology is presented for solving constraint satisfaction problems with smooth continuous constraint functions. We apply the proposed method in solving small scale kinematics problems with the goal of identifying all real solutions to a given problem. The developed approach assumes a collaborative methodology that integrates interval partitioning, a new interval inference method, and local search. The resulting methodology aims at reducing the search space and discarding infeasible sub-spaces effectively and reliably during the early stages of the search so that exact solutions can be identified faster by local methods.     

Cooperative parallel adaptive neighbourhood search for the disjunctively constrained knapsack problem

This article investigates the use of parallel computing for solving the disjunctively constrained knapsack problem. The proposed parallel computing model can be viewed as a cooperative algorithm based on a multi-neighbourhood search. The cooperation system is composed of a team manager and a crowd of team members. The team members aim at applying their own search strategies to explore the solution space. The team manager collects the solutions from the members and shares the best one with them. The performance of the proposed method is evaluated on a group of benchmark data sets. The results obtained are compared to those reached by the best methods from the literature. The results show that the proposed method is able to provide the best solutions in most cases. In order to highlight the robustness of the proposed parallel computing model, a new set of large-scale instances is introduced. Encouraging results have been obtained.     

An adaptive multi-population genetic algorithm for job-shop scheduling problem

Job-shop scheduling problem (JSP) is a typical NP-hard combinatorial optimization problem and has a broad background for engineering application. Nowadays, the effective approach for JSP is a hot topic in related research area of manufacturing system. However, some JSPs, even for moderate size instances, are very difficult to find an optimal solution within a reasonable time because of the process constraints and the complex large solution space. In this paper, an adaptive multi-population genetic algorithm (AMGA) has been proposed to solve this problem. Firstly, using multi-populations and adaptive crossover probability can enlarge search scope and improve search performance. Secondly, using adaptive mutation probability and elite replacing mechanism can accelerate convergence speed. The approach is tested for some classical benchmark JSPs taken from the literature and compared with some other approaches. The computational results show that the proposed AMGA can produce optimal or near-optimal values on almost all tested benchmark instances. Therefore, we can believe that AMGA can be considered as an effective method for solving JSP.     

A penalty-based scaling algorithm for the multi-period multi-product distribution planning problem

Multi-period multi-product distribution planning problems are depicted as multi-commodity network flow problems where parameters may change over time. The corresponding mathematical formulation is presented for a discrete time setting, and it can also be used as an approximation for a continuous time setting. A penalty-based method which employs a cost-scaling approach is developed to solve some auxiliary penalty problems aiming to obtain an optimal solution for the original problem. The experiments on both random instances and case study problems show that the algorithm finds good-quality solutions with reasonable computational effort.     

Dynamic mutual adjustment search for supply chain operations planning co-ordination

Operational planning is an activity carried out by all manufacturing and logistical companies. Its co-ordination with supply chain partners aims at synchronising resources utilisation in order to minimise inefficiencies, such as unnecessary inventory holding, or in order to improve revenue through better resource utilisation. It is a rather complex process as partners have different objectives and information asymmetry is part of any effort to find good co-ordination solutions. Furthermore, because supply chains evolve in a dynamic and uncertain environment, once a co-ordination of operations plans is achieved, input data, such as forecasts or resources’ status, can change and affect on hand plans. These dynamic changes not only require updating the plan that is directly affected by the changes, but it also requires the adjustment of all plans that are part of the same co-ordination solution (Stadtler, H. 2009. A framework for collaborative planning and state-of-the-art. OR Spectrum, 31 (1), 5–30). Therefore, the development of a practical co-ordination approach should be capable of dealing with these dynamic changes. This paper proposes a dynamic mutual adjustment search heuristic, which can be used to co-ordinate the operations plans of two independent supply chain partners, linked by material and non-strategic information flows. Computational analysis shows that the proposed approach produces a win-win strategy in the context of two supply chain partners, and improves the results of upstream planning in each planning cycle, and also improves the fairness of revenue sharing when compared to optimal centralised planning.