Combinatorial Optimization Approach Research Articles

Combinatorial Optimization in Project Selection Using Genetic Algorithm

This paper discusses the problem of project selection in the presence of two objective functions that maximize profit and minimize cost and the existence of some limitations is limited resources availability and time available so that there is need allocation of resources in each project. These resources are human resources, machine resources, raw material resources. This is treated as a consideration to not exceed the budget that has been determined. So that can be formulated mathematics for objective function (multi-objective) with boundaries that fulfilled. To assist the project selection process, a multi-objective combinatorial optimization approach is used to obtain an optimal solution for the selection of the right project. It then described a multi-objective method of genetic algorithm as one method of multi-objective combinatorial optimization approach to simplify the project selection process in a large scope.

Multi-cloud service composition using Formal Concept Analysis

Formal Concept Analysis is adapted to the multi-cloud service composition problem.Multi-cloud environment is modelled using lattice theory.Algorithms for optimal cloud combination are proposed.Experiments proved the ability of FCA to reduce the number of clouds and inter-cloud communication cost. Recent years have witnessed a rapid growth in exploiting Cloud environments to deliver various types of resources as services. To improve the efficiency of software development, service reuse and composition is viewed as a powerful means. However, effectively composing services from multiple clouds has not been solved yet. Indeed, existing solutions assume that the services participating to a composition come from a single cloud. This approach is unrealistic since the other existing clouds may host more suitable services. In order to deliver high quality service compositions, the user request must be checked against the services in the multi-cloud environment (MCE) or at least clouds in the availability zone of the user. In this paper, we propose a multi-cloud service composition (MCSC) approach based on Formal Concept Analysis (FCA). We use FCA to represent and combine information of multiple clouds. FCA is based on the concept lattice which is a powerful mean to classify clouds and services information. We first model the multi-cloud environment as a set of formal contexts. Then, we extract and combine candidate clouds from formal concepts. Finally, the optimal cloud combination is selected and the MCSC is transformed into a classical service composition problem. Conducted experiments proved the effectiveness and the ability of FCA based method to regroup and find cloud combinations with a minimal number of clouds and a low communication cost. Also, the comparison with two well-known combinatorial optimization approaches showed that the adopted top-down strategy allowed to rapidly select services hosted on the same and closest clouds, which directly reduced the inter-cloud communication cost, compared to existing approaches.

Negotiation mechanisms for an order subcontracting and scheduling problem

We consider a decentralized decision-making environment in which a firm and its subcontractor make decisions on subcontracting heterogeneous orders for processing with private information. We design two market-like negotiation mechanisms that adopt the multi-round ascending pricing framework under two negotiation protocols, labeled as Protocols 1 and 2. Applying game-theoretic and combinatorial optimization approaches, we analyze the decision behaviors of both players and derive the final negotiation outcomes. We find that the negotiation mechanism under Protocol 1 cannot guarantee the existence of the equilibrium price, while the negotiation mechanism under Protocol 2 result in equilibrium solutions. For some special cases, we investigate the system performance bounds under the two negotiation mechanisms and find that the performance bounds under the former are better than those under the latter.

A combinatorial optimisation approach to energy management strategy for a hybrid fuel cell vehicle

Hybrid Electric Vehicles are becoming more and more prevalent for economic and environmental reasons. Many studies have been conducted in order to improve Hybrid Electric Vehicle performance by increasing their autonomy while respecting the power demand of the electric motor and various constraints. Focusing on the Hybrid Electric Vehicle energy management problem, different approaches and strategies already exist based on non-linear modelling, selection of adequate architecture and source design or the expertise of the manufacturer in the domain. In this paper, a new combinatorial approach is presented to optimally manage offline Hybrid Electric Vehicle energy distribution, composed of two energy sources: a fuel cell as a main source and a super-capacitor for energy storage. New mathematical modelling has been developed that reflects the functioning of the Hybrid Electric Vehicle energy chain, using an exact method to provide an optimal solution that corresponds to hydrogen consumption. Simulations were performed on different realistic mission profiles that showed a significant gain in solution quality and computation time compared with other approaches presented in the literature. Since the quality of solutions depends on the reliability of input data, including disruptions, a robustness study also is carried out.

An Incorporation of the Fuzzy Greedy Search Heuristic With Evolutionary Approaches for Combinatorial Optimization in Operations Management

Although greedy algorithms are important, nowadays it is well assumed that the solutions they obtain can be used as a starting point for more sophisticated methods. This paper describes an evolutionary approach which is based on genetic algorithms (GA). A constructive heuristic, so-called fuzzy greedy search (FGS) is employed to generate an initial population for the proposed GA. The effectiveness and efficiency of the proposed hybrid method are demonstrated on permutation flow-shop scheduling as one of the most widely studied hard combinatorial optimization problems in the area of operational research.

On global integer extrema of real-valued box-constrained multivariate quadratic functions

Determining global integer extrema of an real-valued box-constrained multivariate quadratic functions is a very difficult task. In this paper, we present an analytic method, which is based on a combinatorial optimization approach in order to calculate global integer extrema of a real-valued box-constrained multivariate quadratic function, whereby this problem will be proven to be as NP-hard via solving it by a Travelling Salesman instance. Instead, we solve it using eigenvalue theory, which allows us to calculate the eigenvalues of an arbitrary symmetric matrix using Newton’s method, which converges quadratically and in addition yields a Jordan normal form with $$1 \times 1$$ -blocks, from which a special representation of the multivariate quadratic function based on affine linear functions can be derived. Finally, global integer minimizers can be calculated dynamically and efficiently most often in a small amount of time using the Fourier–Motzkin- and a Branch and Bound like Dijkstra-algorithm. As an application, we consider a box-constrained bivariate and multivariate quadratic function with ten arguments.

A combinatorial optimization approach for multi-hazard design of building systems with suspended floor slabs under wind and seismic hazards

The possibility of structures experiencing multiple hazards of different types during their service life has always been present. However, design of structures has primarily been geared towards addressing the most dominant hazard at the location of interest. In recent years, the design philosophy of structures has shifted towards a more holistic approach of addressing multiple hazards to ensure adequate performance under different loading scenarios. This requires the utilization of new structural systems and the development of effective optimization methods that can address multiple hazards. In this study, a suspended floor slab-isolated structure is utilized as an optimization test system subjected to wind and seismic demands. To perform the optimization a new combinatorial optimization approach is proposed, which is a combination of two methods – Nelder-Mead and Coevolutionary Matrix Adaptation Evolution Strategy (CMA-ES). The two algorithms are integrated simultaneously to optimize three key design variables of the suspended slab system and to obtain a family of optimal solutions that can accommodate varying level of participation of each hazard. In doing so, a set of alternatives is provided to the designer to accommodate wide variations and combinations in hazards intensities. The results of the study highlight the effectiveness of tuning the suspended slab system to meet the wind and seismic performance objectives. The system is seen to be more effective in case of taller structures than shorter structures. For taller structures, the system can be optimized to improve performance under both wind and seismic hazards without significant trade-off on individual hazard performance. Furthermore, the system is seen to be more sensitive to wind loading than earthquake loading.

Enabling a Freight Traffic Controller for Collaborative Multidrop Urban Logistics

There is increasing interest in how horizontal collaboration between parcel carriers might help alleviate problems associated with last-mile logistics in congested urban centers. Through a detailed review of the literature on parcel logistics pertaining to collaboration, along with practical insights from carriers operating in the United Kingdom, this paper examines the challenges that will be faced in optimizing multi-carrier, multidrop collection, and delivery schedules. A “freight traffic controller” (FTC) concept is proposed. The FTC would be a trusted third party, assigned to equitably manage the work allocation between collaborating carriers and the passage of vehicles over the last mile when joint benefits to the parties could be achieved. Creating this FTC concept required a combinatorial optimization approach for evaluation of the many combinations of hub locations, network configuration, and routing options for vehicle or walking to find the true value of each potential collaboration. At the same time, the traffic, social, and environmental impacts of these activities had to be considered. Cooperative game theory is a way to investigate the formation of collaborations (or coalitions), and the analysis used in this study identified a significant shortfall in current applications of this theory to last-mile parcel logistics. Application of theory to urban freight logistics has, thus far, failed to account for critical concerns including ( a) the mismatch of vehicle parking locations relative to actual delivery addresses; ( b) the combination of deliveries with collections, requests for the latter often being received in real time during the round; and ( c) the variability in travel times and route options attributable to traffic and road network conditions.

A combinatorial optimisation approach for closed-loop supply chain inventory planning with deterministic demand

Supply chains in equipment-intensive service industries often involve repair operations. In this context, tactical inventory planning is concerned with optimally planning supplies and repairs based on demand forecasts and in the face of conflicting business objectives. This paper considers closed-loop supply chains and proposes a mixed-integer programming model and a metaheuristic approach to this problem. The model is open to a variety of network topologies, site functions and transfer policies. It also accommodates multiple objectives by the means of a weighted cost function. We report experiments on pseudo-random instances designed to evaluate plan quality and impact of cost weightings. In particular, we show how appropriate weightings allow to implement common planning strategies (e.g., just-in-time replenishment, minimal repair). [Received 8 May 2016; Revised 24 October 2016; Accepted 2 December 2016]

A Multi-Agent Proposal for the Resolution of BIBD instances

<p>The problem with designing balanced incomplete blocks (BIBD) is enclosed within the combinatorial optimization approach that has been extensively used in experimental design. The present proposal addresses thi problem by using local search techniques known as Hill Climbing, Tabu Search, and an approach based considerable sized the use of Multi-Agents, which allows the exploration of diverse areas of search spaces. Furthermore, the use of a vector vision for the consideration associated with vicinity is presented. The experimental results prove the advantage of this technique compared to other proposals that are reported in the current literature.</p>

Efficient task assignment for spatial crowdsourcing: A combinatorial fractional optimization approach with semi-bandit learning

Spatial crowdsourcing has emerged as a new paradigm for solving problems in the physical world with the help of human workers. A major challenge in spatial crowdsourcing is to assign reliable workers to nearby tasks. The goal of such task assignment process is to maximize the task completion in the face of uncertainty. This process is further complicated when tasks arrivals are dynamic and worker reliability is unknown. Recent research proposals have tried to address the challenge of dynamic task assignment. Yet the majority of the proposals do not consider the dynamism of tasks and workers. They also make the unrealistic assumptions of known deterministic or probabilistic workers’ reliabilities. In this paper, we propose a novel approach for dynamic task assignment in spatial crowdsourcing. The proposed approach combines bi-objective optimization with combinatorial multi-armed bandits. We formulate an online optimization problem to maximize task reliability and minimize travel costs in spatial crowdsourcing. We propose the distance-reliability ratio (DRR) algorithm based on a combinatorial fractional programming approach. The DRR algorithm reduces travel costs by 80% while maximizing reliability when compared to existing algorithms. We extend the DRR algorithm for the scenario when worker reliabilities are unknown. We propose a novel algorithm (DRR-UCB) that uses an interval estimation heuristic to approximate worker reliabilities. Experimental results demonstrate that the DRR-UCB achieves high reliability in the face of uncertainty. The proposed approach is particularly suited for real-life dynamic spatial crowdsourcing scenarios. This approach is generalizable to the similar problems in other areas in expert systems. First, it encompasses online assignment problems when the objective function is a ratio of two linear functions. Second, it considers situations when intelligent and repeated assignment decisions are needed under uncertainty.

A Heuristic Combinatorial Optimisation Approach to Synthesising a Population for Agent Based Modelling Purposes

This paper presents an algorithm that follows the sample-free approach to synthesise a population foragentbasedmodellingpurposes. Whilemostexistingalgorithmsrelyonasampledataset,thefactthatthis algorithmdoesnotrelyononemakesitanovelcontribution. Ithaspotentiallywidespreadapplicationforsitu- ationsinwhichsuchsurveydataisnotavailable. Incontrasttoexistingsample-freealgorithms,thepopulation synthesis presented in this paper applies the heuristics to part of the allocation of synthetic individuals into synthetic households. As a result the iterative process which does this and which is normally the most compu- tationally demanding and time consuming process, is required only for a subset of synthetic individuals. This meansthatthepopulationsynthesiserinthisworkiscomputationallyeici entenoughforpracticalapplication to build a large synthetic population (many millions) for many thousands target areas at the smallest possible geographicallevel. Thiscapabilityensuresthatthegeographicalheterogeneityoftheresultingsyntheticpopu- lationispreserved. ThepaperpresentstheapplicationofthenewmethodtosynthesisethepopulationforNew South Wales in Australia in 2006. The resulting total synthetic population has approximately 6 million people living in over 2.3 million households residing in private dwellings across over 11,000 census collection districts (CCDs). Analyses show evidence that the synthetic population matches very well with the census data across seven demographic attributes that characterise the population at both household level and individual level. A Java-based open source implementation of the population synthesiser as well as sample input data is freely available at .

A survey about methods dedicated to epistasis detection.

During the past decade, findings of genome-wide association studies (GWAS) improved our knowledge and understanding of disease genetics. To date, thousands of SNPs have been associated with diseases and other complex traits. Statistical analysis typically looks for association between a phenotype and a SNP taken individually via single-locus tests. However, geneticists admit this is an oversimplified approach to tackle the complexity of underlying biological mechanisms. Interaction between SNPs, namely epistasis, must be considered. Unfortunately, epistasis detection gives rise to analytic challenges since analyzing every SNP combination is at present impractical at a genome-wide scale. In this review, we will present the main strategies recently proposed to detect epistatic interactions, along with their operating principle. Some of these methods are exhaustive, such as multifactor dimensionality reduction, likelihood ratio-based tests or receiver operating characteristic curve analysis; some are non-exhaustive, such as machine learning techniques (random forests, Bayesian networks) or combinatorial optimization approaches (ant colony optimization, computational evolution system).

Material optimization via combinatorial deposition and analysis for thermoelectric thin films

This work presents a custom, high-throughput combinatorial approach for the optimization of thermoelectric thin films consisting of materials with complex chemistry and structures (e.g., the layered misfit cobaltite, Ca3FexCo4−xO9). Combinatorial thin films with graded compositions are produced on 100mm Si wafers from multiple target materials using pulsed laser deposition. Film thickness and composition are mapped as a function of wafer location. Crystal structures are determined using x–y mapping XRD analysis with specially designed algorithms for automated peak location and analysis. Thermoelectric properties, specifically the Seebeck coefficient and the electrical resistivity, are screened using a custom designed automated probe system. By combining the rapid synthesis of many compositions and structures simultaneously using combinatorial deposition and automated analytical tools capable of spatial mapping, trends in material performance are shown to be quickly obtained primarily due to the elimination of one-at-a-time synthesis and analysis. The possible approaches for such complex multivalent combinatorial optimization of thin films are identified and discussed.For the Ca3FexCo4−xO9 system presented, variations to the thermoelectric power factor are dominated by changes in the electrical resistivity. Enhancements to the Seebeck coefficient are observed due to the incorporation of Fe into the Ca3FexCo4−xO9 structure; however, this improvement is overshadowed by increases in the electrical resistivity due to variations in film thickness and the presence of secondary phases (Co3O4 and Ca2Fe2O5) which result from increasing Fe content and off-axis pulsed laser deposition.

A New Combinatorial Optimization Approach for Integrated Feature Selection Using Different Datasets: A Prostate Cancer Transcriptomic Study.

BackgroundThe joint study of multiple datasets has become a common technique for increasing statistical power in detecting biomarkers obtained from smaller studies. The approach generally followed is based on the fact that as the total number of samples increases, we expect to have greater power to detect associations of interest. This methodology has been applied to genome-wide association and transcriptomic studies due to the availability of datasets in the public domain. While this approach is well established in biostatistics, the introduction of new combinatorial optimization models to address this issue has not been explored in depth. In this study, we introduce a new model for the integration of multiple datasets and we show its application in transcriptomics.MethodsWe propose a new combinatorial optimization problem that addresses the core issue of biomarker detection in integrated datasets. Optimal solutions for this model deliver a feature selection from a panel of prospective biomarkers. The model we propose is a generalised version of the (α,β)-k-Feature Set problem. We illustrate the performance of this new methodology via a challenging meta-analysis task involving six prostate cancer microarray datasets. The results are then compared to the popular RankProd meta-analysis tool and to what can be obtained by analysing the individual datasets by statistical and combinatorial methods alone.ResultsApplication of the integrated method resulted in a more informative signature than the rank-based meta-analysis or individual dataset results, and overcomes problems arising from real world datasets. The set of genes identified is highly significant in the context of prostate cancer. The method used does not rely on homogenisation or transformation of values to a common scale, and at the same time is able to capture markers associated with subgroups of the disease.

A combinatorial optimization approach to the selection of statistical units

In the case of some large statistical surveys, the set of units that will constitute the scope of the survey must be selected. We focus on the real case of a Census of Agriculture, where the units are farms. Surveying each unit has a cost and brings a different portion of the whole information. In this case, one wants to determine a subset of units producing the minimum total cost for being surveyed and representing at least a certain portion of the total information. Uncertainty aspects also occur, because the portion of information corresponding to each unit is not perfectly known before surveying it. The proposed approach is based on combinatorial optimization, and the arising decision problems are modeled as multidimensional binary knapsack problems. Experimental results show the effectiveness of the proposed approach.

Heuristic and Exact Algorithms for the Interval Min–Max Regret Knapsack Problem

We consider a generalization of the 0–1 knapsack problem in which the profit of each item can take any value in a range characterized by a minimum and a maximum possible profit. A set of specific profits is called a scenario. Each feasible solution associated with a scenario has a regret, given by the difference between the optimal solution value for such scenario and the value of the considered solution. The interval min–max regret knapsack problem (MRKP) is then to find a feasible solution such that the maximum regret over all scenarios is minimized. The problem is extremely challenging both from a theoretical and a practical point of view. Its decision version is complete for the second level of the polynomial hierarchy hence it is most probably not in 𝒩𝒫. In addition, even computing the regret of a solution with respect to a scenario requires the solution of an 𝒩𝒫-hard problem. We examine the behavior of classical combinatorial optimization approaches when adapted to the solution of the MRKP. We introduce an iterated local search approach and a Lagrangian-based branch-and-cut algorithm and evaluate their performance through extensive computational experiments.

Identification of genome-wide SNP-SNP and SNP-clinical Boolean interactions in age-related macular degeneration.

We propose here a methodology to uncover modularities in the network of SNP-SNP interactions most associated with disease. We start by computing all possible Boolean binary SNP interactions across the whole genome. By constructing a weighted graph of the most relevant interactions and via a combinatorial optimization approach, we find the most highly interconnected SNPs. We show that the method can be easily extended to find SNP/environment interactions. Using a modestly sized GWAS dataset of age-related macular degeneration (AMD), we identify a group of only 19 SNPs, which include those in previously reported regions associated to AMD. We also uncover a larger set of loci pointing to a matrix of key processes and functions that are affected. The proposed integrative methodology extends and overlaps traditional statistical analysis in a natural way. Combinatorial optimization techniques allow us to find the kernel of the most central interactions, complementing current methods of GWAS analysis and also enhancing the search for gene-environment interaction.

Solving air traffic conflict problems via local continuous optimization

This paper first introduces an original trajectory model using B-splines and a new semi-infinite programming formulation of the separation constraint involved in air traffic conflict problems. A new continuous optimization formulation of the tactical conflict-resolution problem is then proposed. It involves very few optimization variables in that one needs only one optimization variable to determine each aircraft trajectory. Encouraging numerical experiments show that this approach is viable on realistic test problems. Not only does one not need to rely on the traditional, discretized, combinatorial optimization approaches to this problem, but, moreover, local continuous optimization methods, which require relatively fewer iterations and thereby fewer costly function evaluations, are shown to improve the performance of the overall global optimization of this non-convex problem.

Combinatorial optimization approaches for multi-part cyclic hoist scheduling problem

Combinatorial optimization approaches for multi-part cyclic hoist scheduling problem