Combinatorial Solution Research Articles

A dynamic programming algorithm for order picking in robotic mobile fulfillment systems

AbstractThe order scheduling and rack sequencing problem deals with the order picking process in robotic mobile fulfillment systems: automated guided vehicles lift and transport movable storage racks to picking stations to supply items requested by customer orders which are put together in cardboard boxes on a workbench of limited capacity. To efficiently operate the station, the sequence in which racks visit the station one after another and the intervals at which customer orders are scheduled must be coordinated. We present a dynamic programming algorithm for the order scheduling and rack sequencing problem at a single picking station minimizing the number of rack visits. Despite monolithic mixed integer linear programming formulations, our approach appears to be the first combinatorial solution method for the problem in literature. A computational study demonstrates the effectiveness of the approach.

Genetic-Algorithm-Aided Deep Reinforcement Learning for Multi-Agent Drone Delivery

The popularity of commercial unmanned aerial vehicles has drawn great attention from the e-commerce industry due to their suitability for last-mile delivery. However, the organization of multiple aerial vehicles efficiently for delivery within limitations and uncertainties is still a problem. The main challenge of planning is scalability, since the planning space grows exponentially to the number of agents, and it is not efficient to let human-level supervisors structure the problem for large-scale settings. Algorithms based on Deep Q-Networks had unprecedented success in solving decision-making problems. Extension of these algorithms to multi-agent problems is limited due to scalability issues. This work proposes an approach that improves the performance of Deep Q-Networks on multi-agent delivery by drone problems by utilizing state decompositions for lowering the problem complexity, Curriculum Learning for handling the exploration complexity, and Genetic Algorithms for searching efficient packet-drone matching across the combinatorial solution space. The performance of the proposed method is shown in a multi-agent delivery by drone problem that has 10 agents and ≈1077 state–action pairs. Comparative simulation results are provided to demonstrate the merit of the proposed method. The proposed Genetic-Algorithm-aided multi-agent DRL outperformed the rest in terms of scalability and convergent behavior.

Accurate Summary-based Cardinality Estimation Through the Lens of Cardinality Estimation Graphs

We study two classes of summary-based cardinality estimators that use statistics about input relations and small-size joins: (i) optimistic estimators, which were defined in the context of graph database management systems, that make uniformity and conditional independence assumptions; and (ii) the recent pessimistic estimators that use information theoretic linear programs (LPs). We show that optimistic estimators can be modeled as picking bottom-to-top paths in a cardinality estimation graph (CEG), which contains subqueries as nodes and edges whose weights are average degree statistics. We show that existing optimistic estimators have either undefined or fixed choices for picking CEG paths as their estimates and ignore alternative choices. Instead, we outline a space of optimistic estimators to make an estimate on CEGs, which subsumes existing estimators. We show, using an extensive empirical analysis, that effective paths depend on the structure of the queries. We next show that optimistic estimators and seemingly disparate LP-based pessimistic estimators are in fact connected. Specifically, we show that CEGs can also model some recent pessimistic estimators. This connection allows us to provide insights into the pessimistic estimators, such as showing that they have combinatorial solutions.

An Approach to Logical Compatibility Determination for Solution Principles in Morphological Matrix-Based Conceptual Design

Morphological matrix-based conceptual design has been proven to enable the generation of high-quantity, variety, and novelty concepts. Indeed, many studies have proposed methods for enhancing it. However, logical relations for determining the compatibility of solution principles (SPs) in combinatorial solution chain is yet to be established in the literature. This study attempts to develop a logical relation for determining the compatibility of SPs in solution variants chain. The features of the interaction boundary of each solution principle were characterised and vectorially numerated for onward matching of adjacent SPs in a combinatorial solution chain to determine compatibility. The consistency of the compatibility determinant (CD) was tested on engineering designer students. It was found that the students could determine the CD with excellent consistency. Besides, the applicability of logical relation for determining the feasibility of solution variants was tested and found applicable in many trials. Despite the limitation of the study, the results indicate that the logical compatibility determinant is consistent and applicable for the complete exploration of the morphological matrix design space. Therefore, this study provides a foundation for the development of a reliable CAD system for conceptual design.

New method for solving non-homogeneous periodic second-order difference equation and some applications

In the present study, we are interested in solving the nonhomogeneous second-order linear difference equation with periodic coefficients of period pge 2, by bringing two new approaches enabling us to provide both analytic and combinatorial solutions to this family of equations. First, we get around the problem by converting this kind of equations to an equivalent family of nonhomogeneous linear difference equations of order p with constant coefficients. Second, we propose new expressions of the solutions of this family of equations, using our techniques of calculating the powers of product of companion matrices and some properties of generalized Fibonacci sequences. The study of the special case p=2 is provided. And to enhance the effectiveness of our approaches, some numerical examples are discussed.

General Motors Optimizes Vehicle Content for Customer Value and Profitability

General Motors (GM) vehicles have more than 100 customer-facing features, known as vehicle content. Decisions about how to package and price these features have a significant impact on our customers’ experiences and on GM’s business results. Vehicle features are assigned as standard, optional, or unavailable on different trim levels, resulting in an enormous combinatorial solution space. Vehicle content optimization (VCO) combines customer market research, discrete choice models, and custom multiobjective nonlinear optimization algorithms to optimize vehicle contenting and pricing decisions. VCO comprehends complex dynamics and tradeoffs and allows GM to optimally balance customer preferences and profitability. After six years of development and multiple proof-of-concept and pilot studies, VCO was officially integrated into GM’s Global Vehicle Development Process in 2014. As of 2021, VCO has been used on more than 85 vehicle programs globally. It has enabled customer-centric product development and more efficient engineering, sourcing, and manufacturing. GM Finance verified that VCO enabled $4.4 billion of incremental profit over the average product life cycle (i.e., six years on average) since 2018, making it a vastly impactful example of operations research and applied analytics.

METHODICAL ASPECTS OF DESIGN-PROJECTION IN THE COURSE OF FUTURE TEACHERS’ TECHNOLOGICAL EDUCATION

Analyzing the curricula and methods of professional future teacher training in higher education, we see that this educational process involves comprehensive mastering of knowledge in the field of art, functional-technological process, structures and materials science, formal composition, drawing and perspective, colorists in the organization of the environment, architecture, basics of environment design and the functional and constructive component of spatial composition.
 The analysis of the professional activity of specialists in the field of technological education shows that for successful design, the presence of knowledge of modern design-projection methods, engineering-technological foundations, tectonic regularities of the formation of objects of the subject environment, principles of combinatorial solution of the shape of the object being created. The lack of practical experience of university graduates leads to their difficult adaptation to pedagogical activities, which is a consequence of insufficient attention to the formation of special knowledge and skills, to the practical orientation of solving educational creative tasks related to professional activities in the field of design. The mentioned circumstances make it possible to consider the issue of the formation of special knowledge and skills in the process of design-projecting as relevant and timely.
 In this regard, design-projecting in the teacher's activity is characterized by the uniqueness of the search program, multivariate problem solving, and the ability to independently evaluate intermediate and final options, and choose an effective specific algorithm. Accordingly, we understand the teacher's creative project activity as an intellectual activity to ensure the quality of a technical solution from the point of view of functional, ergonomic, aesthetic, technological, and psychological factors. The conducted research does not exhaust all issues related to the formation of special knowledge and skills of higher education students in the design-projecting process and requires further improvement of the stages of quasi-professional educational activity, taking into account the optimal choice of methods for solving creative tasks, development of personal qualities of graduates of higher education institutions.

Dual-Space Co-Evolutionary Memetic Algorithm for Scheduling Hybrid Differentiation Flowshop With Limited Buffer Constraints

This article proposes a novel and efficient dual-space co-evolutionary memetic algorithm (DCMA) to tackle a practical hybrid differentiation flowshop scheduling problem with limited buffer constraints. In this scheduling problem, jobs are divided into different types and each job consists of multiple parts. The manufacturing of a job involves three stages: 1) parts fabrication on first-stage parallel machines; 2) parts assembly on second-stage single machine; and 3) job differentiation on one of third-stage dedicated machines. Due to the assembly operation and limited buffers between adjacent stages, deadlock and blocking will occur. We formulate the problem and present a deadlock handling policy to guarantee all schedules feasible. Then, we propose the DCMA metaheuristic to approximate the optimal solutions in acceptable time. Global exploration of DCMA is performed by a hybrid of three parts: 1) a continuous optimizer to be executed in continuous search space; 2) a discrete optimizer to be executed in combinatorial solution space; and 3) a meta-Lamarckian learning-based selection mechanism for adaptively determining that which optimizer is more suitable for current global exploration campaign. To balance exploration and exploitation, three problem-special local search strategies are presented, which collaborates with each other and are adaptively started to avoid high computational costs. The effect of parameter setting on DCMA is checked by the Taguchi method of design of experiment. The computational experiments demonstrate the effectiveness of DCMA special designs, and show that DCMA performs better than the existing algorithms for the considered problem.

Rate equationlimit for a combinatorial solution of a stochastic aggregation model.

In a recent series of papers, an exact combinatorial solution was claimed for a variant of the so-called Marcus-Lushnikov model of aggregation. In this model, a finite number of aggregates are initially assumed to be present in the form of monomers. At each time step, two aggregates are chosen according to certain size-dependent probabilities and irreversibly joined to form an aggregate of higher mass. The claimed result given an expression for the full probability distribution over all possible size distributions in terms of the so-called Bell polynomials. In this paper, we develop the asymptotics of this solution in order to check whether the exact solution yields correct expressions for the average cluster size distribution as obtained from the Smoluchowski equations. The answer is surprisingly involved: For the generic case of an arbitrary reaction rate, it is negative, but for the so-called classical rate kernels, constant, additive, and multiplicative, the solutions obtained are indeed exact. On the other hand, for the multiplicative kernel, a discrepancy is found in the full solution between the combinatorial solution and the exact solution. The reasons for this puzzling pattern of agreement and disagreement are unclear. A better understanding of the combinatorial solution's derivation is needed, the better to understand its range of validity.

Generating optimal robust continuous piecewise linear regression with outliers through combinatorial Benders decomposition

Using piecewise linear (PWL) functions to model discrete data has applications for example in healthcare, engineering and pattern recognition. Recently, mixed-integer linear programming (MILP) approaches have been used to optimally fit continuous PWL functions. We extend these formulations to allow for outliers. The resulting MILP models rely on binary variables and big- constructs to model logical implications. The combinatorial Benders decomposition (CBD) approach removes the dependency on the big- constraints by separating the MILP model into a master problem of the complicating binary variables and a linear sub problem over the continuous variables, which feeds combinatorial solution information into the master problem. We use the CBD approach to decompose the proposed MILP model and solve for optimal PWL functions. Computational results show that vast speedups can be found using this robust approach, with problem-specific improvements including smart initialization, strong cut generation and special branching approaches leading to even faster solve times, up to more than 12,000 times faster than the standard MILP approach.

THE SIMPLIFYING OF THE SOLUTION OF LINEAR OPTIMIZATION PROBLEMS IN PROJECT MANAGEMENT

Modern mathematic models of project management processes description can be use in many cases to linear optimization problems. Simplification algorithms provide an efficient method of searching for solution of an optimization problem. If we project a multidimensional process onto a two-dimensional plane, this method will enable graphic visualization of the problem solution matrixes. A significant simplification of the algorithms for preparing the linear optimization problem in computer calculations can be achieved using the concept of duality in linear optimization problems. The linear optimization problem forms are equivalent. This can be achieved provided that transformation techniques are used to move from one form of tasks to another. To simplify the transformation of linear optimization problems, the transition from maximizing to minimizing the objective function is used. This research has proposed a method of simplifying the combinatorial solution of a discrete optimization problem. It is based on decomposition of the system representing a system of constraints of a five-dimensional initial problem into the two-dimensional coordinate plane. There was a model example considered for solving a five-dimensional linear optimization problem based on such projecting of a multidimensional space onto the two-dimensional one. The paper is concerned with construction of a chain of efficient algorithms to simplify the primary mathematic model of problem and realization its computer-aided calculation. Applied value of the proposed approach consists in using the scientific result for enabling the possibility to improve canonical methods of optimization problem solution and, respectively, for simplification of computer-assisted calculation.

Handling topic dependencies alongside topology interactions using fuzzy inferences for discovering communities in social networks

Social network analysis is one of the significant research areas. Discovering communities that satisfies simultaneously the topological and semantic requirements has become a challenging and useful topic in the analysis of social networks. Structural community detection algorithms do not consider node attributes. The semantic methods lead to the loss of valuable topological information. The combinatorial solutions favor one of the mentioned kinds. Moreover all and importantly, relationships between attributes and social topics have been neglected by existing methods. Content features in the real social networking space are not completely independent, but the strength of dependencies and relations is different. At first, this paper updates social network definitions to identify communities and adds attribute relationships. Then, we propose a two-phase method based on fuzzy inferences to basically combine structure and semantic and detect meaningful communities in social networks. Finally, two new metrics, Semantic Coherency and SSte are introduced to attributed relational and fairness measurements and are used along with Modularity as the three objective criteria of the proposed method to be maximized. Quantitative experiments reveal that the proposed method performs effectively regarding both network coherence and nodes attributes and achieves favorable outcomes to identify communities.

Genetic Algorithm and LSTM Artificial Neural Network for Investment Portfolio Optimization

The present research aimed to construct a genetic algorithm and artificial neural network to optimize investment portfolios, considering that in modern investment portfolio theory, optimization is a multi-objective problem involving maximizing return and minimizing volatility, also known as risk. This opens up the possibility of a highly combinatorial solution space, making it a computationally complex problem that cannot be solved by deterministic algorithms. To achieve the objective, 255 companies operating within the Peruvian national market and listed on the Lima Stock Exchange were evaluated. The research resulted in a mean squared error of 6.33%, a mean absolute error of 5.07%, and an accuracy of 92.35% related to the artificial neural network, indicating an acceptable generalization capacity for predicting positive trends in the stocks to be used as inputs for the genetic algorithm. Regarding the genetic algorithm, a quality function was successfully modeled, considering 5 factors related to the profitability and volatility of the stocks, as well as portfolio diversification. Ultimately, the best configuration of the genetic algorithm was found to have a fitness value of 0.772482, translating to a return of 1.00058% and volatility of 0.00612%. It is concluded that the genetic algorithm optimizes investment portfolios by achieving higher returns and lower volatility compared to other methods, with volatility specifically being a much lower percentage.

Abstract 5513: Chimeric CD3 fusion receptors expressed on iPSC-derived universal TCR-less CAR-T and -NK cells synergize with bispecific engagers to enhance antitumor activity and limit antigen escape

Abstract Despite success in hematologic malignancies, chimeric antigen receptor (CAR) T cells have been less effective in solid tumors, in part because of the heterogeneous expression of the CAR-specific target antigen (1° Ag) found within the tumor mass. In combination with a CAR, bispecific T cell engagers (BiTEs) can target additional tumor antigens (2° Ag) while engaging CD3 signaling molecules on T cells, providing a unique way to address tumor heterogeneity, mitigate antigen escape and further potentiate durable effector function. However, in generating off-the-shelf universal CAR-T and NK cells, a combination strategy is not feasible as neither modified cell product is compatible to specifically engage with a BiTE. In developing allogeneic CAR-T cells, the T cell receptor (TCR) surface expression must be eliminated to prevent graft versus host disease, but the absence of surface TCR expression leads to loss of surface CD3 expression and BiTE compatibility. Similarly, NK cells naturally lack TCR expression and have no surface CD3 molecules for BiTE engagement. Here we discuss the development of a novel chimeric CD3ε fusion receptor (CD3-CFR) with a modified transmembrane and endodomain enabling surface expression in TCR-less T or NK cells, allowing for a novel combinatorial solution between universal CAR-T or NK cells with BiTEs in an allogeneic setting. CD3-CFR signal transduction was initially investigated in TRAC knockout NFAT reporter (T-KO) Jurkat cells engineered with CD3-CFR and co-cultured with EpCAM+ target cells. When soluble EpCAM-BiTE was added to the co-culture, the observed 6.9-fold increase in NFAT activity indicated successful engagement associated with the interaction of CD3-CFR, target cells and the BiTE. CD3-CFR T-KO Jurkat cells were further modified to secrete the EpCAM-BiTE and showed increased NFAT activity, demonstrating the feasibility of self-secreting BiTE-mediated targeting through CD3-CFR signaling. We next engineered CD3-CFR expressing iPSC-derived CAR-T (iT) cells to show preserved T cell differentiation kinetics and maintained CAR activity against 1° Ag positive targets (>90% cytolysis). Importantly, while CAR-iT cells showed only background lysis of 1° Ag negative tumor cells, CD3-CFR+ CAR-iT cells were able to lyse ~99% of 1° Ag negative tumor cells with the addition of soluble EpCAM-BiTE targeting the 2° Ag. When CD3-CFR+ CAR-iT cells were further engineered to secrete the EpCAM-BiTE, CD3-CFR+ BiTE+ CAR-iT cells demonstrated superior killing of heterogenous tumors compared to CD3-CFR+ BiTE- CAR-iT cells (70% vs. 5% cytolysis). Taken together these data demonstrate for the first time that CD3 expression and BiTE engagement can be combined in a universal iPSC-derived CAR-iT cell product to overcome antigen heterogeneity and enhance efficacy in solid tumor settings. Citation Format: Eigen Peralta, Dan Lu, Mark Landon, Hui-Yi Chu, Amit Mehta, Philip Chu, Alec Witty, Tom Lee, Bahram Valamehr. Chimeric CD3 fusion receptors expressed on iPSC-derived universal TCR-less CAR-T and -NK cells synergize with bispecific engagers to enhance antitumor activity and limit antigen escape [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 5513.

Accurate summary-based cardinality estimation through the lens of cardinality estimation graphs

This paper is an experimental and analytical study of two classes of summary-based cardinality estimators that use statistics about input relations and small-size joins in the context of graph database management systems: (i) optimistic estimators that make uniformity and conditional independence assumptions; and (ii) the recent pessimistic estimators that use information theoretic linear programs (LPs). We begin by analyzing how optimistic estimators use pre-computed statistics to generate cardinality estimates. We show these estimators can be modeled as picking bottom-to-top paths in a cardinality estimation graph (CEG), which contains sub-queries as nodes and edges whose weights are average degree statistics. We show that existing optimistic estimators have either undefined or fixed choices for picking CEG paths as their estimates and ignore alternative choices. Instead, we outline a space of optimistic estimators to make an estimate on CEGs, which subsumes existing estimators. We show, using an extensive empirical analysis, that effective paths depend on the structure of the queries. While on acyclic queries and queries with small-size cycles, using the maximum-weight path is effective to address the well known underestimation problem, on queries with larger cycles these estimates tend to overestimate, which can be addressed by using minimum weight paths. We next show that optimistic estimators and seemingly disparate LP-based pessimistic estimators are in fact connected. Specifically, we show that CEGs can also model some recent pessimistic estimators. This connection allows us to adopt an optimization from pessimistic estimators to optimistic ones, and provide insights into the pessimistic estimators, such as showing that they have combinatorial solutions.

Combinatorial solution of the eclectic spin chain

The one-loop dilatation operator in the holomorphic 3-scalar sector of the dynamical fishnet theory is studied. Due to the non-unitary nature of the underlying field theory this operator, dubbed in [1] the eclectic spin chain Hamiltonian, is non-diagonalisable. The corresponding spectrum of Jordan blocks leads to logarithms in the two-point functions, which is characteristic of logarithmic conformal field theories. It was conjectured in [2] that for certain filling conditions and generic couplings the spectrum of the eclectic model is equivalent to the spectrum of a simpler model, the hypereclectic spin chain. We provide further evidence for this conjecture, and introduce a generating function which fully characterises the Jordan block spectrum of the simplified model. This function is found by purely combinatorial means and is simply related to the q-binomial coefficient.

Using Solid Catalysts in Disulfide-Based Dynamic Combinatorial Solution- and Mechanochemistry.

It was shown for the first time that solid amines can act as catalysts for disulfide-based dynamic combinatorial chemistry (DCC) by ball mill grinding. The mechanochemical equilibrium for the two disulfide reactions studied was reached within 1-3 h using ten different amine catalysts. This contrasts with the weeks to months to achieve solution equilibrium for most solid amine catalysts at 2 %mol mol-1 concentration in a 2 mMolar disulfide dynamic combinatorial library in a suitable solvent. The final mechanochemical equilibrium was independent of the catalyst used but varied with other ball mill grinding factors such as the presence of traces of solvent. The different efficiencies of the amines tested were discussed.

Soliton solutions for the nonlocal reverse space Kundu–Eckhaus equation via symbolic calculation

The Kundu–Eckhaus (KE) equation describes the propagation of ultrashort femtosecond pulses in optical fibers. In this paper, the Hirota bilinear method is used to deal with nonlocal KE equation which is also called nonlocal integrable nonlinear Schrödinger equation with cubic and quintic nonlinearities. The N-soliton solution for the nonlocal KE equation is derived by virtue of symbolic calculation. Based on that, the exact solution expressions of two-soliton and three-soliton can be obtained. Several propagation situations are demonstrated and discussed for the combinatorial solutions of nonlocal KE equation under different parameters, including one periodic solitary wave evolution, two parallel, perpendicular and periodic solitary waves collision.

Minimizing Power Peaking Factor of BEAVRS-based Reactor Using Polar Bear Optimization Algorithms

Fuel loading pattern optimization is a complex problem because there are so many possibilities for combinatorial solutions, and it will take time to try it one by one. Therefore, the Polar Bear Optimization Algorithm was applied to find an optimum PWR loading pattern based on BEAVRS. The desired new fuel loading pattern is the one that has the minimum Power Peaking Factor (PPF) value without compromising the operating time. Operating time is proportional to the multiplication factor (k eff ). These parameters are usually contradictive with each other and will make it hard to find the optimum solution. The reactor was modelled with the Standard Reactor Analysis Code (SRAC) 2006. Fuel pins and fuel assemblies are modelled with the PIJ module for cell calculations. One-fourth symmetry was used with the CITATION X-Y module for core calculations. The optimization was done with 200 populations and 50 iterations. The PPF value for the selected solution should never exceed 2.0 in every burn-up step. Out of 28 solutions, the best optimal fuel loading pattern had a maximum value PPF of 1.458 and a k eff of 0.916 at day 760 of calculated time (corresponding to a cycle length of 479 days). Therefore, the maximum PPF value was 27.1% lower than the safety factor, and the same operating time as the standard loading pattern has been achieved.

COMBINATORIAL RECONSTRUCTION OF TWO-DIMENSIONAL WORDS IN THE HYPOTHESIS SHIFT 1

The article considers the formulation of the problem of reconstruction of two-dimensional words by a given multiset of subwords, under the hypothesis that this subset is generated by the displacement of a two-dimensional window of fixed size by an unknown two-dimensional word with a shift 1. A variant of the combinatorial solution of this reconstruction problem is proposed, based on a two-fold application of the one-dimensional word reconstruction method using the search for Eulerian paths or cycles in the de Bruyne multiorgraph. The efficiency of the method is discussed under the conditions of a square two-dimensional shift window one having a large linear size.