Mixed-integer linear programming (MILP) for optimisation of medical equipment maintenance schedules

The paper presents highlights of a doctoral research addressed to model and solve the problem of preventive maintenance scheduling of fleets of vehicles. The problem is formulated and several Ant Colony based approaches were proposed and tested considering different instances of the maintenance scheduling problem, including applications related to the preventive maintenance of an aircraft fleet belonging to the Brazilian Air Force. The most successful approach has shown to be the one based on ACS with a specific local search procedure and inspired on the application of ACO to the timetabling problem. Details on the problem formulation, on the proposed approaches, and on the performed tests and applications are presented.KeywordsLocal SearchPreventive MaintenanceLocal Search ProcedureMaintenance ScheduleMaintenance TaskThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Optimisation of maintenance routing and scheduling for offshore wind farms

Air cargo transportation, loading, and phase-based maintenance service scheduling in demand channel routes

In this chapter, a formulation for applying Ant Colony Optimization (ACO) to power plant maintenance scheduling optimization (PPMSO) has been developed and successfully tested using four case studies (original and modified versions of two benchmark case studies from the literature). In particular, the performance of the heuristic formulation developed, the two local search algorithms introduced and the overall utility of the ACO-PPMSO formulation were investigated. The results obtained have shown that the heuristic formulation improves the performance of the ACO-PPMSO algorithm significantly when applied to the four case studies investigated. It was found that while the PPMSO-2-opt local search operator seems to work well for unconstrained problems, it is not suitable for highlyconstrained PPMSO problems. Lastly, the results obtained by ACO-PPMSO for the two original case studies were better than those obtained by other optimisation methods, such as various genetic algorithm (GAs) formulations and simulated annealing (SA). For the 21-unit and 22-unit case studies, a new optimal solution has been found by the ACO-PPMSO

Linear programming (LP) and mixed integer linear programming (MILP) problems belong among very important class of problems that find their applications in various managerial consequences. The aim of the paper is to discuss computational performance of current optimization packages for solving large scale LP and MILP optimization problems. Current market with LP and MILP solvers is quite extensive. Probably among the most powerful solvers GUROBI 6.0, IBM ILOG CPLEX 12.6.1, and XPRESS Optimizer 27.01 belong. Their attractiveness for academic research is given, except their computational performance, by their free availability for academic purposes. The solvers are tested on the set of selected problems from MIPLIB 2010 library that contains 361 test instances of different hardness (easy, hard, and not solved).

Power gating is a very effective technique to reduce the subthreshold leakage by using sleep transistors to turn off the functional blocks or cells when they are not used. When the sleep transistors are turned on, the power grid may experience a huge current surge which may violate the integrity of the power grid. This paper addresses this problem by formulating the wakeup scheduling of sleep transistors as an exact mixed integer linear program (MILP). Since the resulting MILP is hard, we propose a very efficient yet near optimal algorithm by successively relaxing the MILP to a sequence of linear program (LP) problems. The results obtained on the ISCAS benchmarks indicate that our proposed algorithm obtains a near optimal solution with a speedup of 15× on average compared to the MILP. The proposed algorithm has a runtime complexity which is linear in practice.

Supply chain network design and operation: Systematic decision-making for centralized, distributed, and mobile biofuel production using mixed integer linear programming (MILP) under uncertainty

BackgroundFlux Balance Analysis (FBA) is a genome-scale computational technique for modeling the steady-state fluxes of an organism’s reaction network. When the organism’s reaction network needs to be completed to obtain growth using FBA, without relying on the genome, the completion process is called reaction gap-filling. Currently, computational techniques used to gap-fill a reaction network compute the minimum set of reactions using Mixed-Integer Linear Programming (MILP). Depending on the number of candidate reactions used to complete the model, MILP can be computationally demanding.ResultsWe present a computational technique, called FastGapFilling, that efficiently completes a reaction network by using only Linear Programming, not MILP. FastGapFilling creates a linear program with all candidate reactions, an objective function based on their weighted fluxes, and a variable weight on the biomass reaction: no integer variable is used. A binary search is performed by modifying the weight applied to the flux of the biomass reaction, and solving each corresponding linear program, to try reducing the number of candidate reactions to add to the network to generate a working model. We show that this method has proved effective on a series of incomplete E. coli and yeast models with, in some cases, a three orders of magnitude execution speedup compared with MILP. We have implemented FastGapFilling in MetaFlux as part of Pathway Tools (version 17.5), which is freely available to academic users, and for a fee to commercial users. Download from: biocyc.org/download.shtml.ConclusionsThe computational technique presented is very efficient allowing interactive completion of reaction networks of FBA models. Computational techniques based on MILP cannot offer such fast and interactive completion.

In yard-crane scheduling problems, as loading operations take priority over unloading, the delivery sequence of unloading from the quaysides to the yard is uncertain. The delivery sequence changes may make crane scheduling more difficult. As a result, the crane operations schedules developed statically become suboptimal or even infeasible. In this paper, we propose a dynamic scheduling problem considering uncertain delivery sequences. A mixed-integer linear program is developed to assign tasks to cranes and minimize the makespan of crane operations. We propose an iterative solution framework in which the schedules are re-optimized whenever the delivery sequence change is revealed. A genetic algorithm is proposed to solve the problem, and a greedy algorithm is designed to re-optimize and update the solution. To make the updated solution take effect as soon as possible, regarding batch-based task assignment, the tasks in the scheduling period are divided into several batches. In this case, the instant requests arising from the delivery sequence change are added to corresponding batch tasks and re-optimized together with the tasks of this batch. In addition, a relaxation model is formulated to derive a lower bound for demonstrating the performance of the proposed algorithm. Experimental results show that the average gap between the algorithm and the lower bound does not exceed 5%. The greedy insertion algorithm can re-optimize the instant requests in time. Therefore, the proposed iterative re-optimization framework is feasible and has the advantages (necessity) of batch-based task assignment.

Combined MILP-constraint programming approach for the optimal scheduling of multistage batch processes

The study deals with the multi-choice mathematical programming problem, where the right hand side of the constraints is multi-choice in nature. However, the problem of multi-choice linear programming cannot be solved directly by standard linear or nonlinear programming techniques. The aim of this paper is to transform such problems to a standard mathematical linear programming problem. For each constraint, exactly one parameter value is selected out of a multiple number of parameter values. This process of selection can be established in different ways. In this paper, we present a new simple technique enabling us to handle such problem as a mixed integer linear programming problem and consequently solve them by using standard linear programming software. Our main aim depends on inserting a specific number of binary variables and using them to construct a linear combination which gives just one parameter among the multiple choice values for each choice of the values of the binary variables. A numerical example is presented to illustrate our analysis.

We present a general approach to the FPGA technology mapping problem that applies to any logic block composed of lookup tables (LUTs) and can yield optimal solutions. The connections between LUTs of a logic block are modeled by virtual switches, which define a set of multiple-LUT blocks (MLBs) called an MLB-basis. We identify the MLB-bases for various commercial logic blocks. Given a n MLB-basis, we formulate FPGA mapping as a mixed integer linear programming (MILP) problem to achieve both the generality and the optimality objectives. We solve the MILP models using a general-purpose MILP solver, and present the results of mapping some ISCAS.85 benchmark circuits with a variety of commercial FPGAs. Circuits of a few hundred gates can be mapped in reasonable time using the MILP approach directly. Larger circuits can be handled by partitioning them prior to technology mapping. We show that optimal or provably near-optimal solutions can be obtained for the large ISCAS.85 benchmark circuits using partitions defined by their high-level functions.

The problem of selecting processes and capacity expansion policies for a chemical complex consisting of continuous chemical processes can be formulated as a multiperiod, mixed integer linear programming (MILP) problem. Based on a variable disaggregation technique which exploits lot sizing substructures, we propose two reformulations of the conventional MILP model. The first one is an NLP reformulation which very quickly yields good suboptimal solutions. The second is an MILP reformulation for exact solutions which leads to up to an order of magnitude faster computational results for large problems due to its tighter linear programming relaxation.

Relay stations can be deployed in a wireless network to extend its coverage and improve its capacity. In this paper, we study a scheduling problem in OFDMA-based wireless relay networks with consideration for multi-user diversity, channel diversity and spatial reuse. First, we present a Mixed Integer Linear Programming (MILP) formulation to provide optimum solutions. It has been shown by previous research that performance of a wireless scheduling algorithm is usually related to the interference degree delta, which is the maximum number of links that interfere with a common link but do not interfere with each other. Therefore, we then show that the interference degree delta is at most 4 for any 2-hop relay network and 14 for any general h-hop (h >; 1) relay network. Furthermore, we present a simple greedy algorithm for the scheduling problem and show it has an approximation ratio of 1/(1+δ), which leads to an approximation ratio of 1/5 for the 2-hop case and 1/15} for the general case. In addition, we present three heuristic algorithms, namely, the weighted degree greedy algorithm, the Maximum Weighted Independent Set (MWIS) algorithm and the Linear Programming (LP) rounding algorithm, to solve the scheduling problem. Extensive simulation results have showed that the LP rounding algorithm performs best and always provides close-to-optimum solutions. The performance of the simple greedy algorithm is comparable to that of the other algorithms.

Faster integer-feasibility in mixed-integer linear programs by branching to force change