Integer Programming-based Method Research Articles

A room-oriented artificial bee colony algorithm for optimizing the patient admission scheduling problem

Patient admission scheduling (PAS) is a tasking combinatorial optimization problem where a set of patients is assigned to limited facilities such as rooms, timeslots, and beds subject to satisfying a set of predefined constraints. The investigations into the performance of population-based algorithms that utilized to tackle the PAS problem considered in this paper reveal their weaknesses in obtaining quality solutions that create a space to investigate the performance of another population-based method. Thus, in this paper, an Artificial Bee Colony Algorithm (ABC) is proposed to tackle the formulation of the PAS problem under consideration. It is a class of swarm intelligence metaheuristic algorithms based on the intelligent foraging behaviour of honey bees developed to solve continuous and complex optimization problems. Due to the discretization of the PAS, the continuous nature of the ABC algorithm is changed to cope with the rugged solution space of the PAS. The initial feasible solution to the PAS problem is obtained using the room-oriented approach. Then the ABC algorithm optimizes the feasible solutions with the aid of three neighbourhood structures embedded within the employed bee and the onlooker bee operators of the algorithm. The performance of the proposed ABC algorithm based on three different parameters, the solution number (SN), limit value (LV), and the maximum cycle number (MCN) is evaluated on six standard benchmark datasets of the PAS. Two of these main parameters (i.e. SN and LV) are fine-tuned to obtain the best solutions on instances like Test-data 1 = 679.80, Test-data 2 = 1180.40, Test-data 3 = 787.40, Test-data 4 = 1198.60, Test-data 5 = 636.80, and Test-data 6 = 818.60. The best solutions obtained by the proposed method are evaluated against the results of the 19 comparative algorithms comprising five population-based methods, eleven heuristic, and hyperheuristic-based methods, and three integer programming-based methods. The proposed method shows its supremacy in the performance by achieving the best results in all the instances of the dataset when compared with five population-based methods (DFPA, HSA, MBBO-GBS, BBO-GBS, and BBO-RBS) and producing the best results in five instances when compared with eleven heuristic and hyperheuristic-based methods (LAHC, DHS-GD, HTS, DHS-SA, ADAPTIVE GD, GD, HH-GD, DHS-IO, HH-SA, HH-IE, TA) and Finally, it had a competitive performance with the other three Integer programming methods (MIP warm start, MIP-Heuristic, CG) that worked on the same formulations of the PAS. In a nutshell, the proposed ABC algorithm could be adopted as a new template algorithm for the PAS community.

Operations Research Transforms the Scheduling of Chilean Soccer Leagues and South American World Cup Qualifiers

For the past 12 years, the Chilean Professional Soccer Association (ANFP) has applied operations research (OR) techniques to schedule soccer leagues in Chile. Using integer programming-based methods, the ANFP decides which matches are played in each round, taking into account various objectives, such as holding down costs and ensuring engaging tournaments for the fans. It has scheduled more than 50 tournaments using this approach, resulting in an estimated direct economic impact of about $59 million, including reductions in television broadcaster operating costs, growth in soccer pay-television subscriptions, increased ticket revenue, and lower travel costs for the teams. This application of OR has also had significant noneconomic impacts. First, the incorporation of team requirements and various sporting criteria has improved process transparency and schedule fairness, increasing fans’ interest in local professional tournaments; second, because of the high portability of these techniques, they have been used successfully to schedule sports leagues in other countries (examples include volleyball and basketball in Argentina, and the South American qualifiers for the 2018 Soccer World Cup). Furthermore, the models and methods used in this scheduling application have been disseminated widely, helping to promote OR as an effective tool for addressing practical problems. Our outreach activities have reached thousands of high school and university students in four countries and a more general audience of millions of television viewers and Internet users.

Grammar-based compression approach to extraction of common rules among multiple trees of glycans and RNAs

BackgroundMany tree structures are found in nature and organisms. Such trees are believed to be constructed on the basis of certain rules. We have previously developed grammar-based compression methods for ordered and unordered single trees, based on bisection-type tree grammars. Here, these methods find construction rules for one single tree. On the other hand, specified construction rules can be utilized to generate multiple similar trees.ResultsTherefore, in this paper, we develop novel methods to discover common rules for the construction of multiple distinct trees, by improving and extending the previous methods using integer programming. We apply our proposed methods to several sets of glycans and RNA secondary structures, which play important roles in cellular systems, and can be regarded as tree structures. The results suggest that our method can be successfully applied to determining the minimum grammar and several common rules among glycans and RNAs.ConclusionsWe propose integer programming-based methods MinSEOTGMul and MinSEUTGMul for the determination of the minimum grammars constructing multiple ordered and unordered trees, respectively. The proposed methods can provide clues for the determination of hierarchical structures contained in tree-structured biological data, beyond the extraction of frequent patterns.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0558-4) contains supplementary material, which is available to authorized users.

Integer programming-based method for designing synthetic metabolic networks by Minimum Reaction Insertion in a Boolean model.

In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at “http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html.”

On control of singleton attractors in multiple Boolean networks: integer programming-based method

BackgroundBoolean network (BN) is a mathematical model for genetic network and control of genetic networks has become an important issue owing to their potential application in the field of drug discovery and treatment of intractable diseases. Early researches have focused primarily on the analysis of attractor control for a randomly generated BN. However, one may also consider how anti-cancer drugs act in both normal and cancer cells. Thus, the development of controls for multiple BNs is an important and interesting challenge.ResultsIn this article, we formulate three novel problems about attractor control for two BNs (i.e., normal cell and cancer cell). The first is about finding a control that can significantly damage cancer cells but has a limited damage to normal cells. The second is about finding a control for normal cells with a guaranteed damaging effect on cancer cells. Finally, we formulate a definition for finding a control for cancer cells with limited damaging effect on normal cells. We propose integer programming-based methods for solving these problems in a unified manner, and we conduct computational experiments to illustrate the efficiency and the effectiveness of our method for our multiple-BN control problems.ConclusionsWe present three novel control problems for multiple BNs that are realistic control models for gene regulation networks and adopt an integer programming approach to address these problems. Experimental results indicate that our proposed method is useful and effective for moderate size BNs.

A Systematic Method for Constructing Feasible Solution to SCUC Problem With Analytical Feasibility Conditions

Obtaining high-quality feasible solution is the core and the major difficulty in solving security-constrained unit commitment (SCUC) problems. This paper presents a systematic method for constructing feasible solutions to SCUC problem based on a group of analytical feasibility conditions. The feasibility check is performed based on the analytical necessary conditions such that most of infeasible UC states can be identified without solving LP problem. If a UC state is infeasible, it is adjusted with the possibly minimal operating cost increase based on the cost information. This UC adjusting issue is formulated as a zero-one programming problem and a branch and bound (B&B) method is established based on these feasibility conditions. Numerical testing is performed for a 31-bus system, an IEEE 24-bus system, and an IEEE 118-bus system. The testing results suggest that over 95% of infeasible UC states are identified by the analytical necessary conditions. The near-optimal feasible schedules for SCUC problem can be obtained efficiently by the proposed method. The feasible schedules obtained are compared with those obtained from mixed integer programming-based method in the IEEE 118-bus system. It is shown that the new method can produce competitive results in terms of solution quality and computational efficiency.

Integer Programming-Based Approach to Attractor Detection and Control of Boolean Networks

SUMMARY The Boolean network (BN) can be used to create discrete mathematical models of gene regulatory networks. In this paper, we consider three problems on BNs that are known to be NP-hard: detection of a singleton attractor, finding a control strategy that shifts a BN from a given initial state to the desired state, and control of attractors. We propose integer programming-based methods which solve these problems in a unified manner. Then, we present results of computational experiments which suggest that the proposed methods are useful for solving moderate size instances of these problems. We also show that control of attractors is Σ p hard, which suggests that control of attractors is harder than the other two problems.

Protein complex prediction via improved verification methods using constrained domain-domain matching

Identification of protein complexes within protein-protein interaction networks is one of the important objectives in functional genomics. Ozawa et al. proposed a verification method of protein complexes by introducing a structural constraint. In this paper, we propose an improved integer programming-based method based on the idea that a candidate complex should not be divided into many small complexes, and combination methods with maximal components and extreme sets. The results of computational experiments suggest that our methods outperform the method by Ozawa et al. We prove that the verification problems are NP-hard, which justifies the use of integer programming.

A heuristic for the maximum value region problem in raster space

From a single-attribute raster layer in which each cell is assigned a numerical value, a connected set of a specified number of cells that has the maximum (or minimum) total value is selected. This is a highly common decision problem in the context of raster-based geographic information systems (GIS) and seems general enough to deserve inclusion in the standard functionality of such systems. Yet it is a computationally difficult optimization problem, for which no efficient exact solution method has been found. This article presents a new dynamic programming-based heuristic method for the problem. Its performance is tested with randomly generated raster layers with various degrees of spatial autocorrelation. Results suggest that the proposed heuristic is a promising alternative to the existing integer programming-based exact method, as it can handle significantly larger raster data with fair accuracy.

Integer programming-based method for grammar-based tree compression and its application to pattern extraction of glycan tree structures

BackgroundA bisection-type algorithm for the grammar-based compression of tree-structured data has been proposed recently. In this framework, an elementary ordered-tree grammar (EOTG) and an elementary unordered-tree grammar (EUTG) were defined, and an approximation algorithm was proposed.ResultsIn this paper, we propose an integer programming-based method that finds the minimum context-free grammar (CFG) for a given string under the condition that at most two symbols appear on the right-hand side of each production rule. Next, we extend this method to find the minimum EOTG and EUTG grammars for given ordered and unordered trees, respectively. Then, we conduct computational experiments for the ordered and unordered artificial trees. Finally, we apply our methods to pattern extraction of glycan tree structures.ConclusionsWe propose integer programming-based methods that find the minimum CFG, EOTG, and EUTG for given strings, ordered and unordered trees. Our proposed methods for trees are useful for extracting patterns of glycan tree structures.

Finding Minimum Reaction Cuts of Metabolic Networks Under a Boolean Model Using Integer Programming and Feedback Vertex Sets

In this paper, the authors consider the problem of, given a metabolic network, a set of source compounds and a set of target compounds, finding a minimum size reaction cut, where a Boolean model is used as a model of metabolic networks. The problem has potential applications to measurement of structural robustness of metabolic networks and detection of drug targets. They develop an integer programming-based method for this optimization problem. In order to cope with cycles and reversible reactions, they further develop a novel integer programming (IP) formalization method using a feedback vertex set (FVS). When applied to an E. coli metabolic network consisting of Glycolysis/Glyconeogenesis, Citrate cycle and Pentose phosphate pathway obtained from KEGG database, the FVS-based method can find an optimal set of reactions to be inactivated much faster than a naive IP-based method and several times faster than a flux balance-based method. The authors also confirm that our proposed method works even for large networks and discuss the biological meaning of our results.

An AI approach for optimizing multi-pallet loading operations

For pallet loading operations, it is found that space optimization does not necessarily lead to profit optimization, which is the ultimate goal of forwarders after numerous site evaluations and end-user feedbacks. To the best of the authors’ knowledge, there are only a few research studies related to profit optimization in this area. This paper presents a hybrid approach, using heuristic and genetic algorithms (GA), for solving the profit-based multi-pallet loading problem which was mathematically formulated as a nonlinear integer programming problem. The major novelties in this paper are the simultaneous consideration of priority for loading more profitable cargoes and cargo stability in heuristic and innovatively designed crossover and mutation operations in GA to suit the profit optimization. To validate the approach, simulations were carried out with 10 weakly and 10 strongly heterogeneous sets of cargoes. The simulation results obtained by our proposed GA were compared with those obtained by two other stochastic search methods, namely simulated annealing (SA) and Tabu search (TS), as well as a nonlinear integer programming-based method, branch-and-bound (BB). The results showed that GA can search more profitable solutions than SA, TS and BB in this multi-pallet loading problem.

Integer programming-based approach to allocation of reporter genes for cell array analysis

In this paper, we consider the problem of selecting the most effective set of reporter genes for analysis of biological networks using cell microarrays. We propose two graph theoretic formulations of the reporter gene allocation problem, and show that both problems are hard to approximate. We propose integer programming-based methods for solving practical instances of these problems optimally. We apply them to apoptosis pathway maps, and discuss the biological significance of the result. We also apply them to artificial networks, the result of which shows that optimal solutions can be obtained within several seconds for networks with 10,000 nodes.