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To address the issue of multiple closed circuits arising from applying the traditional Hungarian algorithm to the travelling salesman problem (TSP), a breaking mechanism was proposed, leading to the development of the Break-Cycle Hungarian Algorithm. By adopting the description method of the assignment problem for modeling the TSP and establishing the conversion relationship between them, it is demonstrated that a sufficient and necessary condition for a feasible solution to the TSP is that the feasible solution of the corresponding assignment problem, combined with auxiliary edges, contains only one cycle. The effectiveness of the algorithm was verified through testing and comparative analysis on six standard travelling salesmen, showing that the improved Hungarian algorithm can effectively solve the TSP across various datasets. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel solution to address the current challenges related to charging an Electric Vehicle (EV). The Power on the Go: Single-drop and Double-drop problems allow an EV to be charged at a convenient location, where a service vehicle (drone), which is launched from a nearby charging station, can bring a compatible power bank at the request of the driver through an app. The objective is to reduce the cumulative wait time between service requests and the start of charging. We present mathematical formulations and two order-first split-second-based heuristic approaches for both problems. While the mathematical formulations can generate optimal solutions for small instances in a reasonable amount of time, the heuristics are fast and perform very well, with gaps < 5% for up to 20 node instances. Moreover, the formulations highlight the mean savings in wait time (29.37%) when the power bank can charge two EVs consecutively before a replacement is needed. The implications of the proposed model can be extensive, as we seek to overcome the availability and technological challenges of EV charging while advocating its adoption. [ABSTRACT FROM AUTHOR]

Turkey's Aegean region is a very suitable region for fruit production in terms of climatic conditions and soil characteristics. Fruit and vegetable production in the Aegean region has an important position in terms of Turkey's agricultural economy. The fruit growing sector has a very important place in Turkey's agricultural economy. The aim of the study is to prevent unbalanced fruit production in the Aegean region and to ensure more efficient fruit growing. In the study, it was aimed to assign a balanced production of fruits grown under different conditions in provinces with different characteristics in the Aegean region. For the assignment problem, the conditions of the cities in the Aegean region and the growing conditions of the fruits are considered together. These conditions are altitude, temperature, soil quality, climate, humidity, labor and irrigation. Conditions for fruit production were analyzed with the AHP method and factor weights were calculated. ARAS and Fuzzy Logic methods were used to solve the assignment problem of fruits. These methods enable to reach the result by digitizing the non-computable features of a particular situation. Aydın, Manisa, Denizli and Afyonkarahisar provinces have been proposed, respectively, for the production of figs, grapes, thyme and cherries, which have high industrial value and export income. The study has shown that unbalanced production can be prevented by assigning fruits and vegetables in this way in every region of the country. As a result, the country's agricultural lands will be used effectively and the contribution of agriculture to the national economy will increase. [ABSTRACT FROM AUTHOR]

Jacobi's results on the computation of the order and of the normal forms of a differential system are translated in the formalism of differential algebra. In the quasi-regular case, we give complete proofs according to Jacobi's arguments. The main result is Jacobi's bound, still conjectural in the general case: the order of a differential system P 1 , ... , P n is not greater than the maximum O of the sums ∑ i = 1 n a i , σ (i) , for all permutations σ of the indices, where a i , j : = ord x j P i , viz. the tropical determinant of the matrix (a i , j) . The order is precisely equal to O iff Jacobi's truncated determinant does not vanish. Jacobi also gave a polynomial time algorithm to compute O , similar to Kuhn's "Hungarian method" and some variants of shortest path algorithms, related to the computation of integers ℓ i such that a normal form may be obtained, in the generic case, by differentiating ℓ i times equation P i . Fundamental results about changes of orderings and the various normal forms a system may have, including differential resolvents, are also provided. [ABSTRACT FROM AUTHOR]

Due to present condition, the expenses of allocating a job to a specific person or scheduling transport with a precise value may result in ambiguity. To deal with this, neutrosophic sets which is an extended form of fuzzy sets, appear alongside membership, non-membership and indeterminacy. The assignment problem in a trapezoidal neutrosophic environment with cost as the trapezoidal neutrosophic numbers is discussed in this work. The paper's motive is to convert the trapezoidal neutrosophic numbers into new interval arithmetic form and the efficiency of the same is shown by comparing the existing method with other assignment models using examples. [ABSTRACT FROM AUTHOR]

Great efforts have been made to develop precision medicine-based treatments using machine learning. In this field, where the goal is to provide the optimal treatment for each patient based on his/her medical history and genomic characteristics, it is not sufficient to make excellent predictions. The challenge is to understand and trust the model's decisions while also being able to easily implement it. However, one of the issues with machine learning algorithms—particularly deep learning—is their lack of interpretability. This review compares six different machine learning methods to provide guidance for defining interpretability by focusing on accuracy, multi-omics capability, explainability and implementability. Our selection of algorithms includes tree-, regression- and kernel-based methods, which we selected for their ease of interpretation for the clinician. We also included two novel explainable methods in the comparison. No significant differences in accuracy were observed when comparing the methods, but an improvement was observed when using gene expression instead of mutational status as input for these methods. We concentrated on the current intriguing challenge: model comprehension and ease of use. Our comparison suggests that the tree-based methods are the most interpretable of those tested. [ABSTRACT FROM AUTHOR]

In this article, we focus on a periodic resource allocation problem applied on a dynamical system which comes from a biological system. More precisely, we consider a system with N$$ N $$ resources and N$$ N $$ activities, each activity use the allocated resource to evolve up to a given time T>0$$ T>0 $$ where a control (represented by a given permutation) will be applied on the system to reallocate the resources. The goal is to find the optimal control strategies which optimize the cost or the benefit of the system. This problem can be illustrated by an industrial biological application, namely, the optimization of a mixing strategy to enhance the growth rate in a microalgal raceway system. A mixing device, such as a paddle wheel, is considered to control the rearrangement of the depth of the algae cultures, hence the light perceived at each lap. We prove that if the dynamics of the system is periodic, then the period corresponds to one reallocation whatever the order of the involved permutation matrix is. A nonlinear optimization problem for one reallocation process is then introduced. Since N!$$ N! $$ permutations need to be tested in the general case, it can be numerically solved only for a limited number of N$$ N $$. To overcome this difficulty, we introduce a second optimization problem which provides a suboptimal solution of the initial problem, but whose solution can be determined explicitly. A sufficient condition to characterize cases where the two problems have the same solution is given. Some numerical experiments are performed to assess the benefit of optimal strategies in various settings. [ABSTRACT FROM AUTHOR]

The assignment problem is one of the core combinatorial optimization problems in the optimization branch, and the theory and applications of fractional programming have made great strides in recent years. Usually, the possible coefficient values of linear fractional programming and real-world problems are frequently only known to the decision in vague or uncertain terms. Hence, it would be more acceptable to interpret the coefficients for as fuzzy numerical information. In this paper, a fuzzy bi-objective fractional assignment (FBOFAP) has been formulated. A problem has been defined. Here, triangular shapes are used to indicate the parameters. The fuzzy problem is turned into a typical crisp problem through α-cut using a fuzzy number and then the compromise solution is generated by fuzzy programming. [ABSTRACT FROM AUTHOR]

Under just-in-time production, this paper studies a single machine common due-window (denoted by CONW) assignment scheduling problem with position-dependent weights and resource allocations. A job's actual processing time can be determined by the resource assigned to the job. A resource allocation model is divided into linear and convex resource allocations. Under the linear and convex resource allocation models, our goal is to find an optimal due-window location, job sequence and resource allocation. We prove that the weighted sum of scheduling cost (including general earliness–tardiness penalties with positional-dependent weights) and resource consumption cost minimization is polynomially solvable. In addition, under the convex resource allocation, we show that scheduling (resp. resource consumption) cost minimization is solvable in polynomial time subject to the resource consumption (resp. scheduling) cost being bounded. [ABSTRACT FROM AUTHOR]

The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution, and scheduling problems. Showing such correlations is one of the aims of this paper. For some of the derived problems having exponential time complexity, the question arises of their solvability for larger instances. Instead of the traditional approach based on the use of approximate or stochastic heuristic methods, we focus here on the direct use of mixed integer programming models in the GAMS environment, which is now capable of solving instances much larger than in the past and does not require complex parameter settings or statistical evaluation of the results as in the case of stochastic heuristics because the computational core of software tools, nested in GAMS, is deterministic in nature. The source codes presented may be an aid because this tool is not yet as well known as the MATLAB Optimisation Toolbox. Benchmarks of the permutation flow shop scheduling problem with the informally derived MIP model and the traveling salesman problem are used to present the limits of the software's applicability. [ABSTRACT FROM AUTHOR]

Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from everyday activities to large-scale industrial operations. In this study, a MOAP with fuzzy parameters is investigated, and the fuzziness is represented by a Type-2 fuzzy logic system. Because the T2FLS is more efficient in dealing with the uncertainty of a decision-making process, the current problem's many parameters are represented by Type-2 trapezoidal fuzzy numbers (T2TpFNs). T2TpFNs are first reduced to Type-1 fuzzy numbers, then to crisp numbers. Finally, the neutrosophic compromise programming technique (NCPT) is applied to produce a problem compromise solution. A numerical problem is used to demonstrate the validity and applicability of the NCPT for the current MOAP. Furthermore, a comparison of NCPT to other techniques such as FPT and IFPT shows its superiority. [ABSTRACT FROM AUTHOR]

The optimal strategy selection is an influential factor to enhance the efficiency of land reclamation projects. On the other hand, the process of desertification of the land during environmental degradation is the consequence of the interaction between various factors that make it challenging to select appropriate solutions. Therefore, this study aimed to provide systematic optimization strategies in the form of a group decision-making model in the Yazd-Khezrabad plain. The important strategies were identified using the Delphi model. Then, the alternative initial ranking was formed by Cook and Seiford method framework using the vote taken from the decision makers on strategies. Finally, by estimating the linear distance of each option and including the matrix of the intervals, the last priority of the strategies was obtained from solving the assignment problem. The results indicated that the strategies of "prevent land use inappropriate change" (A18) and "the regeneration of vegetation cover" (A23) with Value=1 and Reduced Cost=0, were identified as the most important combating-desertification strategies in the region, respectively. The results of this study help desert managers to utilize limited facilities and capital dedicated to controlling the desertification process efficiently and effectively. [ABSTRACT FROM AUTHOR]

The conventional assignment problem is unable to handle scenarios that may arise due to different working modes of machines leading to multiple cost and time entries corresponding to a job–machine pair. The present article deals with this problem and models it as a multi-choice bi-objective assignment problem, the two objectives being assignment cost and bottleneck time. Two different solution procedures are presented based on the Decision-Maker's (DM's) preference structure. First, when the DM provides his/her preference structure as goals, a solution methodology is proposed using goal programming and its different multi-choice variants. In the second case, when no preference is provided by the DM, a two-step approach is presented that iteratively solves a multi-choice cost-minimizing assignment problem to obtain all Pareto-optimal time–cost pairs and finally, based on the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), a single efficient pair is obtained. The algorithm is successfully implemented using the CPLEX ® optimization package and tested on various test problems. [ABSTRACT FROM AUTHOR]

Assignment problems (AP) are well-known topics in engineering and management science and are used frequently to analyze problems. A linear programming problem form was used in transforming assignment problem for crisp problem and in solving as per Hungarian methodology. Assigning n objects over m objects is an exciting problem that arises in different situations. Here we explore the optimal ways for assigning in n objects over m other objects. Numerous numerical applications are needed in production planning, Sales proportions, airline operators, etc. The existing Hungarian methods and maximized (or minimized) assignment methods have been solved using these methods. Entry details in the cost matrix are not always clear. This parameter is uncertain in many applications, and these uncertain parameters are represented by intervals. To solve interval linear assignment problems, we present interval Hungarian method and interval analysis concept. [ABSTRACT FROM AUTHOR]

Assignment problems were widely applied in the field of production planning, telecommunication VLSI design, economic etc. Generally Fuzzy Numbers plays a vital role in many decision making problems. Here an optimal solution of the assignment problem had been derived from Hungarian method. The parameters were being given by using pentagonal fuzzy numbers which are further decomposed into triangular fuzzy numbers. The fuzzy numbers were defuzzfied into real numbers by using pascal's graded mean technique. Numerical example had been given to illustrate the solution procedure. [ABSTRACT FROM AUTHOR]

Now a days Assignment problems were widely applied in the field of manufacturing sectors, production planning, etc to earn more profit with minimum inventory. Generally Fuzzy Numbers plays a vital role in many decision making problems. Here an optimal solution of the assignment problem had been derived from Hungarian method. The parameters were being given by using Heptagonal fuzzy numbers which are further decomposed into pentagonal fuzzy numbers. The fuzzy numbers were defuzzfied into real numbers by using pascal's graded mean technique. Numerical example had been given to illustrate the solution procedure. [ABSTRACT FROM AUTHOR]

In this paper, we propose a collaborative model for the supplier selection for the purchasing activity in the supply chain. The problem addresses a set of firms that try to look for a cost saving configuration to optimise their ordering plans, given a set of suppliers with quantity discounts options. Possible collaborations between firms, modelled as a coalition formation, can be beneficial in the sense that the gathering of their orders generates a cost minimisation regarding the stand-alone situation. We propose the mathematical formulation of firms' collaborative ordering modelled as a cost-dependent assignment problem. The collaborative scenario is viewed as a two independent steps: the first step is based on game-theoretic approach to model possible coalitions of firms and to generate stable coalition structures according to the core concept. Once coalitions are formed, the second step consists mainly on the genetic algorithm is trigged to assign coalitions to shared suppliers. The assignment problem is solved using a specifically designed hybrid genetic algorithm. Experiments, driven on a large test-bed, highlight the effectiveness of the collaboration in handling the ordering activity within the supply chain and the usefulness of hybrid genetic algorithm in solving such supplier selection problems. We show that in all cases the collaborative scenario is more profitable regarding the stand-alone position. The obtained results show that the hybrid genetic algorithm is able to generate good quality solutions in a reasonable run time regarding Cplex results. [ABSTRACT FROM AUTHOR]

This work proposes metric learning for fast similarity-based scene retrieval of unstructured ensembles of trajectory data from large databases. We present a novel representation learning approach using Siamese Metric Learning that approximates a distance preserving low-dimensional representation and that learns to estimate reasonable solutions to the assignment problem. To this end, we employ a Temporal Convolutional Network architecture that we extend with a gating mechanism to enable learning from sparse data, leading to solutions to the assignment problem exhibiting varying degrees of sparsity. Our experimental results on professional soccer tracking data provides insights on learned features and embeddings, as well as on generalization, sensitivity, and network architectural considerations. Our low approximation errors for learned representations and the interactive performance with retrieval times several magnitudes smaller shows that we outperform previous state of the art. [ABSTRACT FROM AUTHOR]

The multi-resource generalized assignment problem (MRGAP) is the assignment of jobs to agents under capacity constraints to minimize the total assignment. In this problem, each agent has multiple resources, each job is assigned to only one agent, and multiple jobs can be assigned to one agent. In the MRGAP problem, it is essential to distribute the loads in balance to the agents. In the literature, for balancing agent loads, bottleneck MRGAP with the aim of minimizing the maximum agent load, and balanced assignment MRGAP models with the aim of minimizing the difference between the maximum agent load and the minimum agent load have been proposed. In this study, the sum of load squares model has been adapted for MRGAP, as well as a new goal programming MRGAP model and a matheuristic algorithm for the solution of this model are developed. The performances of the proposed model and the algorithm were compared with the models taken from the literature by using randomly derived test problems. The quality of the obtained solutions is determined by considering the maximum load, coefficient of variation and total load criteria. The test results are evaluated in terms of these three criteria. The results obtained revealed the success of the proposed goal programming model and the matheuristic algorithm. [ABSTRACT FROM AUTHOR]

Smart device networks form the backbone of many Internet of Things (IoT) applications. The performance of these systems depended on many factors. This includes their ability to connect to each other and network latency. In this paper, two algorithms are discussed that build a Peer-to-peer (P2P) overlay network. The focus is on real-time end-to-end remote instrumentation for IoT applications. P2P overlay networks are used for various purposes from content distribution through to media sharing. In contrast to traditional P2P systems, IoT systems can be highly sensitive to network latency and require low bandwidth. The main contributions of this paper are two algorithms to create overlay networks that assign peer nodes to super-peer nodes. The network contains a large number of smart devices and the key aim is to minimize system wide network latency. Other constraints regarding the nodes ability include the ability to become a super-peer node such as connectivity and limited processing capacities of the smart devices are also considered in context of a P2P remote instrumentation system. Both algorithms create a 3-hop network where the latency is lowered as much as possible with the given set of nodes. The algorithms have been validated through simulation. [ABSTRACT FROM AUTHOR]

Decomposition NLP/LP/NLP methods are considered for the automated process design of the economically optimal distributed heat exchange networks between process streams using the assignment problem. The principle of fixation of intermediate variables and issues of the design of the superstructures of a heat exchange network and their decomposition are discussed. Methods to reduce the computational effort to solve the problems of the optimal heat integration are analyzed. The proposed synthesis methods are studied using the example of a mash distillation plant, and the problem of synthesizing the optimal multistage heat exchange network and the split-stream heat exchange network is solved. [ABSTRACT FROM AUTHOR]

We consider the Random Euclidean Assignment Problem in dimension d = 1 , with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings (say, ∼ exp (S N) at size N). We characterize all possible optimal matchings of a given instance of the problem, and we give a simple product formula for their number. Then, we study the probability distribution of S N (the zero-temperature entropy of the model), in the uniform random ensemble. We find that, for large N, S N ∼ 1 2 N log N + N s + O log N , where s is a random variable whose distribution p(s) does not depend on N. We give expressions for the moments of p(s), both from a formulation as a Brownian process, and via singularity analysis of the generating functions associated to S N . The latter approach provides a combinatorial framework that allows to compute an asymptotic expansion to arbitrary order in 1/N for the mean and the variance of S N . [ABSTRACT FROM AUTHOR]

We consider the problem of automated assignment of papers to reviewers in conference peer review, with a focus on fairness and statistical accuracy. Our fairness objective is to maximize the review quality of the most disadvantaged paper, in contrast to the commonly used objective of maximizing the total quality over all papers. We design an assignment algorithm based on an incremental max-flow procedure that we prove is near-optimally fair. Our statistical accuracy objective is to ensure correct recovery of the papers that should be accepted. We provide a sharp minimax analysis of the accuracy of the peer-review process for a popular objective-score model as well as for a novel subjective-score model that we propose in the paper. Our analysis proves that our proposed assignment algorithm also leads to a near-optimal statistical accuracy. Finally, we design a novel experiment that allows for an objective comparison of various assignment algorithms, and overcomes the inherent difficulty posed by the absence of a ground truth in experiments on peer-review. The results of this experiment as well as of other experiments on synthetic and real data corroborate the theoretical guarantees of our algorithm. [ABSTRACT FROM AUTHOR]

Contractors attempt to manage optimal collection of human capital that can optimize the company's performance. The skills and competency of human resources contribute considerably to the competitive advantage of the firm. Yet the skill shortage problem encourages utilizing strategies that bring more flexibility to workforce management. Multiskilling has been suggested as a potential strategy that assists workforce assignment across multiple projects. However, it brings new challenges for company workforce managers. This study contributes to the construction project management body of knowledge by proposing a simulation framework for assigning multiskilled, mainly managerial, workforces across multiple projects of one company. Meanwhile, it is a combination of a staffng and scheduling decision model, incorporating workers' competency status. A cohesive mathematical model using the cost objective function optimizes the entire allocation process toward minimizing resource usage and fluctuations, minimizing costs, and maximizing social sustainability. Ultimately, a validation example incorporating diverse workers' competency data is provided to exemplify how the optimization model performs in an academic setting compared with three commonly used methods in workforce assignment. This approach provides insight into simulating workforce assignments across multiple projects regarding competency. [ABSTRACT FROM AUTHOR]

In 1982, Pawlak set up a fresh approach to deal with uncertainties namely rough set theory, Multiple-Criteria Decision Making (MCDM) first traced by Benjamin Franklin in 17th century. Several researchers did significant contribution to MCDM thereafter. An assignment problem involves what happens to the effective function when each of a number of sources is associated with the same number of destinations. Using MCDM, Rough matrices and Assignment model we are inducing an idea to pick Best'11 in all three formats (Test, One Day Internationals (ODI), Twenty20 International matches (T20I)) in the game of cricket with players from two nationals. Using the existing data, we are providing best batting position for any player to maximize team's run. In addition, based on the preprocessing of informations, we are bringing some new indices to pick Indian squad for the 2019 World Cup cricket held in England from May 2019 to July 2019. After making a selection from our framework, we will compare the list of selected players by Board of Cricket Control Board in India (BCCI) and giveaway the percentage of similarity between the our selection against BCCI's selection. We pick 11 players after selecting 15 players from 24 players to formulate the assignment model and offer the best batting order to optimize team's run. [ABSTRACT FROM AUTHOR]

Assignment problem (AP) is well-studied and important area in optimization. In this research manuscript, an assignment problem in neutrosophic environment, called as neutrosophic assignment problem (NAP), is introduced. The problem is proposed by using the interval-valued trapezoidal neutrosophic numbers in the elements of cost matrix. As per the concept of score function, the interval-valued trapezoidal neutrosophic assignment problem (IVTNAP) is transformed to the corresponding an interval-valued AP. To optimize the objective function in interval form, we use the order relations. These relations are the representations of choices of decision maker. The maximization (or minimization) model with objective function in interval form is changed to multi- objective based on order relations introduced by the decision makers' preference in case of interval profits (or costs). In the last, we solve a numerical example to support the proposed solution methodology. [ABSTRACT FROM AUTHOR]

Due to cope with relying on controllers badly and lacking of quantitative models to assist decision-making in air traffic flow management, this paper studied the delay optimization model and its solving algorithm for route network. Firstly, it established a traffic flow assignment model with the objective function of minimum flight time and capacity constraints. Secondly, considering that classical Hungarian algorithm was only suitable for small and medium-sized operations, it made the improvement of the calculation of efficiency matrix by making the maximum probability of the number of zero elements in the circle equal to the order of the efficiency matrix. Next, it constructed the cost function of the en-route by using the MIMIC queuing theory model. The function, which replaced the constant efficiency value in the efficiency matrix with a variable cost, made the efficiency matrix change with time and flow. Finally,it took part airspaces of China and the actual operational data of 2016 as examples. The results show that the algorithm can increase the access capacity by 8. 372% and the departure capacity by 8. 999%; In terms of delay optimization,it can reduce the average delay of each aircraft. In terms of algorithm performance, it has less iterations and less solution time than the classical Hungarian algorithm, and is more suitable for actual control operation. [ABSTRACT FROM AUTHOR]

A new approach to the synthesis of a multistage heat exchange network is proposed based on the principle of fixation of variables. This principle enables one to reduce a discrete-continuous programming problem to a sequence of linear and nonlinear programming problems. For their formalization, a new variant of the superstructure of a heat exchange network is put forward which includes all the possible flow patterns of material and heat streams. A computational experiment has proven that this problem is multiextremal. The vertical decomposition of the superstructure decreases the number of local minima of an economic criterion and reduces the computational difficulty of the synthesis problem, which is useful for modeling large-scale engineering systems. The performance of the proposed algorithm is demonstrated by a number of model examples in comparison with that of the efficient SYNHEAT software. [ABSTRACT FROM AUTHOR]

Image processing methods combined with scanning techniques—for example, microscopy or microtomography—are now frequently being used for constructing realistic microstructure models that can be used as representative volume elements (RVEs) to better characterize heterogeneous material behavior. As a complement to those efforts, the present study introduces a computational homogenization method that bridges the RVE and material-scale properties in situ. To define the boundary conditions properly, an assignment problem is solved using Euclidean bipartite matching through which the boundary nodes of the RVE are matched with the control nodes of the rectangular prism bounding the RVE. The objective is to minimize the distances between the control and boundary nodes, which, when achieved, enables the bridging of scale-based features of both virtually generated and image-reconstructed domains. Following the minimization process, periodic boundary conditions can be enforced at the control nodes, and the resulting boundary value problem can be solved to determine the local constitutive material behavior. To verify the proposed method, virtually generated domains of closed-cell porous, spherical particle-reinforced, and fiber-reinforced composite materials are analyzed, and the results are compared with analytical Hashin-Shtrikman and Halpin-Tsai methods. The percent errors are within the ranges from 0.04% to 3.3%, from 2.7% to 14.9%, and from 0.5% to 13.2% for porous, particle-reinforced, and fiber-reinforced composite materials, respectively, indicating that the method has promising potential in the fields of image-based material characterization and computational homogenization. [ABSTRACT FROM AUTHOR]

We consider a variant of the assignment problem where entries of the matrix belong to an ordinal scale L. The objective is to find the set of optimal assignments according to a particular dominance criterion which is relevant in the context of ordinal data. This paper aims is to explore the frontier between easy and hard cases depending on |L|, the size of the ordinal scale. We give a polynomial time algorithm that solve the problem for |L| = 3. When |L| is polynomial in the size of the instance we show that the decision version of the problem is NP-complete. [ABSTRACT FROM AUTHOR]

In fields like transport or materials sourcing, it is common industrial practice nowadays to contract several partners for the fulfilment of similar sets of tasks. A typical approach is to include quotes to the contracts that specify which portion of the total volume should be given to each partner. In this study, which is inspired by a real-world problem, we examine the question of operationally distributing jobs to a set of partners in order to meet the contracted quotes in different dimensions as closely as possible. We propose the term fair task allocation problem and analyze its complexity. While the problem is NP-hard in the strong sense for the general case, we show that it is solvable in pseudopolynomial time for a given number of partners and dimensions. Besides an exact solution approach based on dynamic programming, we present an efficient Tabu Search procedure. The Tabu Search is applied to real world as well as to self-generated instances. To verify its quality, the results are compared to the solutions of a commercial MIP-solver. [ABSTRACT FROM AUTHOR]

In this paper we describe a heuristic procedure for solving the travelling salesman problem in the symmetric case without using the triangle inequality cij ≤ cik + ckj. A complete proof of the correctness of the algorithm and example of the presentation how the method works are given. There is estimated computational complexity, which is at most O(m2), where m is a number of the edges of the complete graph with n vertices -Kn. There is shown also, it is possible obtain the following bound that HEURISTIC SOLUTION OPTIMAL SOLUTION < 3 , if some specific inequality considering weights (costs) of edges is satisfied. [ABSTRACT FROM AUTHOR]

This paper presents a model-driven multiobjective avionics system optimization method developed over six years at its final destination, the application in real-world integrated modular avionics systems. It documents the methods, the application scenario, and the results of large-scale optimization studies carried out for the Airbus A350 peripheral acquisition system. The results predict that a significantly lighter system could be possible. [ABSTRACT FROM AUTHOR]

Uncertain random simulation plays an important role in solving uncertain random optimization problems that include random variables and uncertain variables. In this paper, an uncertain random simulation is proposed and developed to obtain the chance distribution, α -pessimistic value and α -optimistic value. Further, an α -optimal model for the uncertain random bottleneck assignment problem under the Hurwicz criterion is presented. Finally, a numerical example is given to illustrate how to use the proposed simulation algorithm to solve an uncertain random bottleneck assignment problem. [ABSTRACT FROM AUTHOR]

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomised mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomised mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of e e - 1 . The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. By using a characterisation result of Bade, we show that any randomised mechanism that is a symmetrisation of a truthful, non-bossy and Pareto optimal mechanism has an improved lower bound of e e - 1 . Since our new mechanism is a symmetrisation of RSDM for strict preferences, it follows that this lower bound is tight. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomised strategy of the administrator who interviews the applicants. [ABSTRACT FROM AUTHOR]

In the classical secretary problem, multiple secretaries arrive one at a time to compete for a single position, and the goal is to choose the best secretary to the job while knowing the candidate's quality only with respect to the preceding candidates. In this paper we define and study a new variant of the secretary problem, in which there are multiple jobs. The applicants are ranked relatively upon arrival as usual, and, in addition, we assume that the jobs are also ranked. The main conceptual novelty in our model is that we evaluate a matching using the notion of blocking pairs from Gale and Shapley's stable matching theory. Specifically, our goal is to maximize the number of matched jobs (or applicants) that do not take part in a blocking pair. We study the cases where applicants arrive randomly or in adversarial order, and provide upper and lower bounds on the quality of the possible assignment assuming all jobs and applicants are totally ordered. Among other results, we show that when arrival is uniformly random, a constant fraction of the jobs can be satisfied in expectation, or a constant fraction of the applicants, but not a constant fraction of the matched pairs. [ABSTRACT FROM AUTHOR]

• Review of alternative methods to produce energy using poultry litter. • Use of an assignment model to allocate litter from poultry farms to electric reactors. • Solutions are obtained for single and multiple electric reactors. • Economic impact analysis show potential positive effects from building electric reactors. • An empirical model consists of real-world data from Louisiana, USA. Poultry litter has the potential to cause water quality problems if it is not applied properly to the land as a crop nutrient. Based on the data available from a survey of Louisiana poultry producers, we find that it is not cost effective to transport poultry litter farther than 38.6 km from the production facilities for crop nutrient purposes. This limited breakeven distance restricts the movement of poultry litter and points to a need to identify an alternative disposal method. We review common methods of producing electricity from poultry litter. We identify the minimum cost solution for assigning poultry litter when one large or three small electric reactors are chosen to be built for electricity production in the poultry production region. We calculate the cost-return analysis of building electric reactors and expand it to find the economic impact of starting such electric reactors to the local and regional economies. [ABSTRACT FROM AUTHOR]

This research article contributes to the advancement of the medical and wellness tourism supply chain through the development of a robust mathematical model aimed at optimizing profitability. Rooted in the principles of open innovation, our study delves into innovative avenues to enhance the economic sustainability of the sector. By strategically integrating diverse medical services including health assessments, dental care, beauty treatments, and spa services into the tourism framework, our model captures the intricate interplay among various stakeholders. Our findings underscore the current adequacy of supply chain capacities. However, a substantial challenge emerges in light of an anticipated 30% upswing in tourist volume, which necessitates a corresponding augmentation of medical facilities without commensurate increases in hotel and tourist route capacities. Rectifying this imbalance becomes pivotal in accommodating forthcoming demands effectively. The study identifies several pivotal factors—tourist numbers, medical center capacities, and resultant profits for supply chain participants—as key drivers of overall profitability. Embracing the tenets of open innovation empowers stakeholders to cultivate collaboration, shared knowledge, and collaborative solutions that optimize these factors, thereby fostering the economic viability of the broader ecosystem. This research offers insightful strategies for resource allocation optimization, operational efficiency enhancement, and sustainable economic growth within the realm of medical and wellness tourism. This contribution is intended to resonate with practitioners, policymakers, and industry stakeholders. [ABSTRACT FROM AUTHOR]

We deal with the classical problem of testing two simple statistical hypotheses but, as a new element, it is assumed that the data vector is observed after an unknown permutation of its entries. What is the fundamental limit for the detection performance in this case? How much information for detection is contained in the entry values and how much in their positions? In the first part of this paper, we answer these questions. In the second part, we focus on practical algorithms. A low-complexity detector solves the detection problem without attempting to estimate the permutation. A modified version of the auction algorithm is then considered, and two greedy algorithms with affordable worst case complexity are presented. The detection operational characteristics of these detectors are investigated by computer experiments. The problem we address is referred to as unlabeled detection and is motivated by large sensor network applications, but applications are also foreseen in different fields, including image processing, social sensing, genome research, and molecular communication. [ABSTRACT FROM AUTHOR]

We describe an extensive channel-measurement campaign, including 325 unique transmitter–receiver configurations, conducted in a lecture room with our 3-D double-directional 60 GHz channel sounder. The receiver was mounted on a mobile robot, with 40 cm spacing between channel acquisitions, enabling the tracking of clustered multipath components in the multidimensional delay-angle space. To mitigate against angle-estimation error and multipath blockage, we introduce a robust tracking algorithm based on the Assignment Problem. For the purpose of validation, the clusters were transformed from the delay-angle space onto a 2-D map of the environment and compared against the locations of cluster-generating reflectors, such as walls and tables. The location errors were typically within 30–50 cm. The clusters identified were then reduced to a stochastic map-based channel model, including reflection loss and dispersion characteristics such as the Ricean K-factor and angular spread. Given the 0.5 ns delay resolution of the channel sounder and angle-estimation error around 2°, the parameters were reported with high fidelity. [ABSTRACT FROM AUTHOR]

We consider a one-to-one assignment problem consisting of matching n objects with n agents. Any matching leads to a utility vector whose n components measure the satisfaction of the various agents. We want to find an assignment maximizing a global utility defined as an ordered weighted average (OWA) of the n individual utilities. OWA weights are assumed to be non-increasing with ranks of satisfaction so as to include an idea of fairness in the definition of social utility. We first prove that the problem is NP-hard; then we propose a polynomial algorithm under some restrictions on the set of admissible weight vectors, proving that the problem belongs to XP. [ABSTRACT FROM AUTHOR]

A shortage of large power system data sets, as well as the frequent restrictions on sharing such models, have led to newfound interest in creating synthetic data that can be easily shared among researchers. This paper considers the problem of forming a power system test case from the constituent parts of realistic power grid samples. Starting from a topology, and samples of generation, load, and branches, we assemble systems while respecting the constraints imposed by a typical Optimal Power Flow problem. Expressed in this manner, the problem involves solving for permutations of the input data. Since permutations matrices are binary, the problem is linearized, allowing for a Mixed Integer Linear Problem formulation. The problem is further decomposed using the Alternating Direction Method of Multipliers as well as an Evolutionary Algorithm to facilitate scaling to larger system sizes. A post processing step is used to add shunt elements for reactive power planning. The resulting systems demonstrate statistically similar power flow behavior to reference systems. Finally, new analysis avenues, opened by synthesizing test cases according to the proposed method, are briefly introduced by creating fictitious systems with different topology models and examining how these affect power flow behavior. [ABSTRACT FROM AUTHOR]

The mission of an earth observation satellite (EOS) is to acquire images of specified areas of the Earth surface related to observation requests from customers. This paper proposes an optimization approach for the daily photograph selection problem (DPSP) of EOSs. DPSP is related to operational management of EOSs and about the scheduling of observations for an EOS. Each photograph related to a customer order generates a profit but not all of the requests can be satisfied due to some physical and technological constraints. Then the problem is to select a subset of requests of maximal profit. The proposed algorithm inherits the hyper-cube framework of ant colony optimization (ACO) metaheuristic. Realistic instances are used as benchmark problems. Computational results demonstrate that the proposed algorithm is capable of generating competitive and promising solutions. [ABSTRACT FROM AUTHOR]

Abstract Many technical systems like manufacturing plants or software applications generate large event sequences. Knowing the temporal relationship between events is important for gaining insights into the status and behavior of the system. This paper proposes a novel approach for identifying the time lag between different event types. This identification task is formulated as a binary integer optimization problem that can be solved efficiently and close to optimality by means of a linear programming approximation. The performance of the proposed approach is demonstrated on synthetic and real-world event sequences. [ABSTRACT FROM AUTHOR]

A sonobuoy is an underwater acoustic sensor primarily deployed by airdrop. An acoustic sensor plays a significant role in conducting anti-submarine warfare for detecting underwater sounds. As a future underwater acoustic sensor, sonobuoy is expected to have an ability of self-movement, i.e., autonomous sonobuoy. In this study, we consider an optimal linear array deployment of autonomous sonobuoys when detecting an unknown underwater sound, assuming that the initial locations of sonobuoys are random in a specified operational area. Deploying sonobuoys from the initial locations onto a specific line requires to first determine the line and positions on that line. Under the interval equivalence between two adjacent sonobuoys, we propose two lines, one that is perpendicular from the underwater sound source location and the other based on the linear regression analysis using the initial locations of sonobuoys. With these two lines onto which sonobuoys will be deployed, we provide two optimization models, total distance minimization and maximum distance minimization, which turn out to be assignment and bottleneck assignment problems, respectively, with nonlinear cost coefficients in the objectives. Due to non-convexity of the objectives, we solve these problems for a fixed interval repetitively as a linear program and integer program, respectively. Computational results show that regression-based line provides higher solution qualities for both problems. Finally, we suggest an approximate interval in a heuristic manner, which guarantees a highly near-optimality as the number of sonobuoys increases. Our results may support a decision-making and provide practitioners with insight on more variety of effective use of autonomous sonobuoys. [ABSTRACT FROM AUTHOR]

Abstract Several studies have found that students' academic achievement is as much determined by the socioeconomic composition of their school as their own socioeconomic status. In this paper we provide a methodology for assigning students to schools so as to balance the socioeconomic compositions of the schools while taking into consideration the total travel distance. Our technique utilizes a biobjective general 0–1 fractional program that is linearized into a mixed 0–1 linear program that can be submitted directly to a standard optimization package. We show how a parametrized model could be utilized to provide a spectrum of different possible assignments so that a decision maker can decide how to balance socioeconomic factors with transportation costs. As a test case for our approach we analyze data from the Greenville County School District in Greenville, South Carolina. [ABSTRACT FROM AUTHOR]

The layout design for storage vessels is an important issue to keep safe process plants, since the accidents originated in storage areas are almost one-third of all reported accidents. In order to reduce fire and explosion damages different mathematical approaches have been proposed; however, most of them are not suitable for real storage facilities design. In this work, a MILP approach has been developed to find the optimal layout of storage vessels, seeking to minimize the cost associated with potential damage of fire and explosion. This approach allows allocation of suitable sites for storage vessels, reducing accidents propagation, and domino effect while keeping safety as much as possible the plant assets. In this way, the optimization approach provides substantial support for decision-makers during the design stage. The study case used to test the mathematical model considers 19 vessels, six buildings, five process facilities and 25 possible scenarios, which includes 16 fires and 9 explosions. [ABSTRACT FROM AUTHOR]

Abstract: A new algorithmic approach to the synthesis of economically optimum multistage heat exchange network in the design and reconstruction of chemical-technological units has been considered. The problem was proposed to be solved based on the assignment problem and decomposition principle of fixation of variables. The efficiency of the approach was shown on the example of solving a number of typical problems on heat integration. [ABSTRACT FROM AUTHOR]

Motivated by the growth of ridesourcing services and the expected advent of fully-autonomous vehicles (AVs), this paper defines, models, and compares assignment strategies for a shared-use AV mobility service (SAMS). Specifically, the paper presents the on-demand SAMS with no shared rides , defined as a fleet of AVs, controlled by a central operator, that provides direct origin-to-destination service to travelers who request rides via a mobile application and expect to be picked up within a few minutes. The underlying operational problem associated with the on-demand SAMS with no shared rides is a sequential (i.e. dynamic or time-dependent) stochastic control problem. The AV fleet operator must assign AVs to open traveler requests in real-time as traveler requests enter the system dynamically and stochastically. As there is likely no optimal policy for this sequential stochastic control problem, this paper presents and compares six AV-traveler assignment strategies (i.e. control policies). An agent-based simulation tool is employed to model the dynamic system of AVs, travelers, and the intelligent SAMS fleet operator, as well as, to compare assignment strategies across various scenarios. The results show that optimization-based AV-traveler assignment strategies, strategies that allow en-route pickup AVs to be diverted to new traveler requests, and strategies that incorporate en-route drop-off AVs in the assignment problem, reduce fleet miles and decrease traveler wait times. The more-sophisticated AV-traveler assignment strategies significantly improve operational efficiency when fleet utilization is high (e.g. during the morning or evening peak); conversely, when fleet utilization is low, simply assigning traveler requests sequentially to the nearest idle AV is comparable to more-advanced strategies. Simulation results also indicate that the spatial distribution of traveler requests significantly impacts the empty fleet miles generated by the on-demand SAMS. [ABSTRACT FROM AUTHOR]