Specific Problem Instances Research Articles

A Perspective on Protein Structure Prediction Using Quantum Computers.

Despite the recent advancements by deep learning methods such as AlphaFold2, in silico protein structure prediction remains a challenging problem in biomedical research. With the rapid evolution of quantum computing, it is natural to ask whether quantum computers can offer some meaningful benefits for approaching this problem. Yet, identifying specific problem instances amenable to quantum advantage and estimating the quantum resources required are equally challenging tasks. Here, we share our perspective on how to create a framework for systematically selecting protein structure prediction problems that are amenable for quantum advantage, and estimate quantum resources for such problems on a utility-scale quantum computer. As a proof-of-concept, we validate our problem selection framework by accurately predicting the structure of a catalytic loop of the Zika Virus NS3 Helicase, on quantum hardware.

Automated Design of Affine Maximizer Mechanisms in Dynamic Settings

Dynamic mechanism design is a challenging extension to ordinary mechanism design in which the mechanism designer must make a sequence of decisions over time in the face of possibly untruthful reports of participating agents. Optimizing dynamic mechanisms for welfare is relatively well understood. However, there has been less work on optimizing for other goals (e.g., revenue), and without restrictive assumptions on valuations, it is remarkably challenging to characterize good mechanisms. Instead, we turn to automated mechanism design to find mechanisms with good performance in specific problem instances. We extend the class of affine maximizer mechanisms to MDPs where agents may untruthfully report their rewards. This extension results in a challenging bilevel optimization problem in which the upper problem involves choosing optimal mechanism parameters, and the lower problem involves solving the resulting MDP. Our approach can find truthful dynamic mechanisms that achieve strong performance on goals other than welfare, and can be applied to essentially any problem setting---without restrictions on valuations---for which RL can learn optimal policies.

A benchmark test suite for evolutionary multi-objective multi-concept optimization

For real-world design optimization, there may often exist multiple candidate concepts that may solve the problem at hand. The process of concurrently identifying the best concept and the corresponding variable values that optimize the design objective(s) is termed as a multi-concept optimization (MCO). While such problems are commonly encountered in practical domains such as engineering, transport, product design, there has been little focus on developing computationally efficient algorithms for MCO. One of the reasons contributing to this gap is the scarcity of benchmark problems with diverse challenges that could be used as a testbed for the development and systematic evaluation of advanced MCO algorithms. In this paper, we particularly focus on MCO problems with multiple conflicting objectives. We review the existing multi-objective MCO test problems and identify their shortcomings through preliminary numerical experiments. Then, we propose a methodology and provide a test problem generator for systematically constructing new multi-objective MCO instances with desired properties. We also propose 28 specific test problem instances using this generator to build a benchmark suite that poses a wide range of challenges to the prospective search strategies. Further, we conduct numerical experiments on the proposed test suite using multiple existing algorithmic strategies from the literature to demonstrate their performance. The results clearly highlight the challenges faced by the strategies for different types of problems. These observations emphasize the need for research efforts towards the development of more efficient and versatile MCO algorithms to tackle a wider range of MCO problems.

Measurement-Based Deterministic Imaginary Time Evolution.

We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by a Suzuki-Trotter decomposition, an evolution approximating imaginary time evolution can be realized. The randomness due to measurement is corrected using conditional unitary operations, making the evolution deterministic. Both the measurements required for the algorithm and the conditional unitary operations can be constructed efficiently. We show that the algorithm converges only below a specified energy threshold and the complexity is estimated for some specific problem instances.

A machine learning enhanced multi-start heuristic to efficiently solve a serial-batch scheduling problem

Serial-batch scheduling problems are widespread in several industries (e.g., the metal processing industry or industrial 3D printing) and consist of two subproblems that must be solved simultaneously: the grouping of jobs into batches and the sequencing of the created batches. This problem’s NP-hard nature prevents optimally solving large-scale problems; therefore, heuristic solution methods are a common choice to effectively tackle the problem. One of the best-performing heuristics in the literature is the ATCS–BATCS(β) heuristic which has three control parameters. To achieve a good solution quality, most appropriate parameters must be determined a priori or within a multi-start approach. As multi-start approaches performing (full) grid searches on the parameters lack efficiency, we propose a machine learning enhanced grid search. To that, Artificial Neural Networks are used to predict the performance of the heuristic given a specific problem instance and specific heuristic parameters. Based on these predictions, we perform a grid search on a smaller set of most promising heuristic parameters. The comparison to the ATCS–BATCS(β) heuristics shows that our approach reaches a very competitive mean solution quality that is only 2.5% lower and that it is computationally much more efficient: computation times can be reduced by 89.2% on average.

Integer factorization as subset-sum problem

This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer factorization to a specific instance of the multiple choice subset-sum problem. As an application, we will improve upon special purpose factorization algorithms for integers composed of divisors with small difference. In particular, we will refine the runtime complexity of Fermat's factorization algorithm by a large subexponential factor. Our first procedure is deterministic, rigorous, easy to implement and has negligible space complexity. Our second procedure is heuristically faster than the first, but has non-negligible space complexity.

A conceptual framework for Digital Twins in production scheduling and control

The interest in enhancing decision-making using Digital Twins in production systems is increasing in the recent years. However, most of the scientific contributions in the field lack of generality as they focus on specific problem instances, overburdening the search for a common thread. To help overcoming this issue, the authors propose a conceptual framework in order to analyze the role of Digital Twins in applications in different production environments, with specific concern on production scheduling and control. The analysis is achieved by responding to three main questions, which focus on the application, the integration, and the functionality of the Digital Twin. The framework is applied to describe six relevant use cases of Digital Twins within this research area.

Navigation Among Movable Obstacles via Multi-Object Pushing Into Storage Zones

With the majority of mobile robot path planning methods being focused on obstacle avoidance, this paper, studies the problem of Navigation Among Movable Obstacles (NAMO) in an unknown environment, with static (i.e., that cannot be moved by a robot) and movable (i.e., that can be moved by a robot) objects. In particular, we focus on a specific instance of the NAMO problem in which the obstacles have to be moved to predefined storage zones. To tackle this problem, we propose an online planning algorithm that allows the robot to reach the desired goal position while detecting movable objects with the objective to push them towards storage zones to shorten the planned path. Moreover, we tackle the challenging problem where an obstacle might block the movability of another one, and thus, a combined displacement plan needs to be applied. To demonstrate the new algorithm’s correctness and efficiency, we report experimental results on various challenging path planning scenarios. The presented method has significantly better time performance than the baseline, while also introducing multiple novel functionalities for the NAMO problem.

A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian

<abstract><p>We derive the equations of motion of an action-dependent version of the Einstein-Hilbert Lagrangian as a specific instance of the Herglotz variational problem. Action-dependent Lagrangians lead to dissipative dynamics, which cannot be obtained with the standard method of Lagrangian field theory. First-order theories of this kind are relatively well understood, but examples of singular or higher-order action-dependent field theories are scarce. This work constitutes an example of such a theory. By casting the problem in clear geometric terms, we are able to obtain a Lorentz invariant set of equations, which contrasts with previous attempts.</p></abstract>

Host-graph-sensitive RETE nets for incremental graph pattern matching with nested graph conditions

BackgroundEfficient querying of large graph structures is a problem at the heart of several application domains such as social networks and model driven engineering. In particular in the context of model driven engineering, where the same query is executed frequently over an evolving graph structure, incremental techniques based on RETE nets are a popular solution. However, the construction of adequate RETE nets for a specific problem instance is a challenge in and of itself. MethodsIn this article, we propose an approach to RETE net construction for queries in the form of graph patterns equipped with nested graph conditions that considers not only the structure of the query, but also the structure of the host graph to improve the net's performance regarding execution time and memory consumption. Furthermore, we suggest a technique for adapting the net structure to changing host graph characteristics. We evaluate the presented concepts empirically based on queries and data from two independent benchmarks, using a mature tool for incremental graph pattern matching as a reference. ResultsOur evaluation results indicate that considering host graph structure during RETE net construction can improve performance of the resulting net. The experiments also demonstrate that adapting the net structure to changing host graph characteristics can be performed with an acceptable execution time overhead for our examples and may yield more adequate RETE nets. Overall, our approach never performed worse than the reference by more than factor 1.2 regarding execution time and achieved an improvement by up to factor 20.

The dial-a-ride problem with private fleet and common carrier

Dial-a-ride problems aim to design the least-costly door-to-door vehicle routes for transporting individual users, subject to several service constraints like time windows, service and route durations, and ride-time. In some cases, providers cannot meet the demand and may outsource some requests. In this paper, we introduce, model, and solve the dial-a-ride problem with private fleet and common carrier (DARP-PFCC) that makes it possible to transfer the demand unmet by the provider to mobility-on-demand services and taxis. All outsourced vehicles are assumed to be available at any instant of the day and have unlimited capacity, enabling to satisfy all user requests, particularly during peak times. We implement a branch-and-cut (B&C) algorithm based on an exact method from the literature to solve the DARP-PFCC, and we develop a near parameter-free parallel metaheuristic to handle large instances. Our metaheuristic combines the Biased Random-key Genetic Algorithm (BRKGA) and the Q-learning (QL) method into the same framework (BRKGA-QL), in which an agent helps to use feedback information to dynamically choose the parameters of BRKGA during the search to select the most appropriate configuration to solve a specific problem instance. Both algorithms are flexible enough to solve the classical DARP, and extensive computational experiments demonstrate the efficiency of our methods. For the DARP instances, the B&C proved optimality for 41 of the 42 instances tested in a reasonable computational time, and the BRKGA-QL found the best-known solution for these instances within a matter of seconds. These results indicate that our metaheuristic performs equally well than state-of-the-art DARP algorithms. In the DARP-PFCC experiments on a set of 504 small-size instances, B&C proved optimality for 497 instances, while BRKGA-QL found 452 optimal solutions, totaling 90.94% of the instances solved to optimality. Finally, we present the results for a real case study for the DARP-PFCC, where BRKGA-QL solved very large problem instances containing up to 713 transportation requests. We also derive some managerial analyses to assess the effects of vehicle capacity reduction, for example due to the COVID-19 pandemic, on shared transportation. The results point to the benefits of combining the private fleet and common carriers in dial-a-ride problems, both for the provider and for the users.

Learning algorithms to deal with failures in production planning

New technologies and the advancement of Industry 4.0 have led to significant changes in production processes, e.g., increased use of data for decision making, faster production speed due to automation, and shorter planning horizons. Soon, the resolution methods and scenarios consolidated in the literature may not adapt to this situation. Therefore, decision-makers must consider this new context in the production planning phase. This work proposes approaches to solve production planning problems in uncertain environments and introduces a framework that predicts the best strategy for implementation according to the specific problem instance. We incorporate characteristics of Industry 4.0 into our study, considering that the delivery of products at their due dates to customers will be more relevant than minimizing costs. The proposed proactive approaches use machine learning algorithms to predict disruptions on the shop floor. We compare strategies considering feedback information on real failures to modify the planning of future periods. Further, we propose a proactive-online approach integrating proactive and real-time decisions, comparing the results with a corrective strategy. Based on computational tests performed with a proposed benchmark, we conclude that the proactive and proactive-online approaches resulted in lower total weighted tardiness in comparison to the corrective method. Regarding the proactive and proactive-online approaches, we observe that their results depend on the set of analyzed instances, justifying the proposition of the framework. Lastly, for most cases, the strategies predicted by the framework achieved lower total weighted tardiness when compared with the average results obtained by all the strategies studied in this work.

On the design of shell-and-tube heat exchangers under uncertain operating conditions

This paper addresses the problem of designing shell and tube heat exchangers operating under uncertain conditions. Traditional design methods assume constant process conditions and known value of thermal design factors. Thus may fail to meet specifications when operational conditions change. Use of safety factors or worst-case design often leads to conservative design and equipment oversizing. No guideline is available in the literature for choosing a design approach. In order to provide designers better awareness on this issue, we investigate when uncertainty should be taken into account, what are the advantages and drawbacks of available approaches for design under uncertainty, and which is the preferred method to be applied in specific problem instances. To answer the above research questions, comparative sizing of equipment is carried out under consistent assumptions adopting five alternative design methods; namely design for nominal reference condition with verification of off-design performances, worst case design, use of safety margins, design to optimize a prescribed objective function, and robust design. Either random uncertainty in external process conditions, and epistemic uncertainty in heat transfer coefficients and fouling resistances are considered. Different types of specifications (more/less is better or nominal is better) are accounted for. Probability of meeting specifications and resulting geometrical characteristics are compared. It is the first time that a similar comparison is carried out, and results discussion allows to identify merits and limitations of the considered approaches. It is found that no single approach is superior, as any method can be suited to a design situation but perform poorly in other cases. Justification for explaining the observed behaviour is used in order to provide guidance to designers in choosing the preferable design method for a specific instance resulting in more cost-effective equipment configuration with higher probability of meeting specifications.

Fast Rates for Contextual Linear Optimization

Incorporating side observations in decision making can reduce uncertainty and boost performance, but it also requires that we tackle a potentially complex predictive relationship. Although one may use off-the-shelf machine learning methods to separately learn a predictive model and plug it in, a variety of recent methods instead integrate estimation and optimization by fitting the model to directly optimize downstream decision performance. Surprisingly, in the case of contextual linear optimization, we show that the naïve plug-in approach actually achieves regret convergence rates that are significantly faster than methods that directly optimize downstream decision performance. We show this by leveraging the fact that specific problem instances do not have arbitrarily bad near-dual-degeneracy. Although there are other pros and cons to consider as we discuss and illustrate numerically, our results highlight a nuanced landscape for the enterprise to integrate estimation and optimization. Our results are overall positive for practice: predictive models are easy and fast to train using existing tools; simple to interpret; and, as we show, lead to decisions that perform very well. This paper was accepted by Hamid Nazerzadeh, data science.

Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures

This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantelli (zeroth partial moment) inequalities, Scarf and Lo (first partial moment) bounds, and semideviation (second partial moment) in one dimension are investigated. The infinite dimensional primal problems are formulated and the simpler finite dimensional dual problems are derived. A principal motivating question is how does data-driven distributional ambiguity affect the moment bounds. Towards answering this question, some theory is developed and computational experiments are conducted for specific problem instances in inventory control and portfolio management. Finally some open questions and suggestions for future research are discussed.

Empirical performance bounds for quantum approximate optimization

The quantum approximate optimization algorithm (QAOA) is a variational method for noisy, intermediate-scale quantum computers to solve combinatorial optimization problems. Quantifying performance bounds with respect to specific problem instances provides insight into when QAOA may be viable for solving real-world applications. Here, we solve every instance of MaxCut on non-isomorphic unweighted graphs with nine or fewer vertices by numerically simulating the pure-state dynamics of QAOA. Testing up to three layers of QAOA depth, we find that distributions of the approximation ratio narrow with increasing depth while the probability of recovering the maximum cut generally broadens. We find QAOA exceeds the Goemans-Williamson approximation ratio bound for most graphs. We also identify consistent patterns within the ensemble of optimized variational circuit parameters that offer highly efficient heuristics for solving MaxCut with QAOA. The resulting data set is presented as a benchmark for establishing empirical bounds on QAOA performance that may be used to test on-going experimental realizations.

Resource estimate for quantum many-body ground-state preparation on a quantum computer

We estimate the resources required to prepare the ground state of a quantum many-body system on a quantum computer of intermediate size. This estimate is made possible using a combination of quantum many-body methods and analytic upper bounds. Our routine can also be used to optimize certain design parameters for specific problem instances. Lastly, we propose and benchmark an improved quantum state preparation procedure. We find that it reduces the circuit T-depth by a factor as large as $10^6$ for intermediate-size lattices.

Vanishing of All Equivariant Obstructions and the Mapping Degree

Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group $${\mathfrak {S}}_n$$ , there exists an $${\mathfrak {S}}_n$$ -equivariant map $$X \rightarrow {{\mathbb {R}}}^n$$ whose image avoids the diagonal $$\{(x,x,\dots ,x)\in {{\mathbb {R}}}^n\mid x\in {{\mathbb {R}}}\}$$ . Previously, the special cases of this statement for certain X were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of $$\mathfrak S_n$$ -equivariant maps from the boundary $$\partial \Delta ^{n-1}$$ of $$(n-1)$$ -simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.

Density deconvolution under general assumptions on the distribution of measurement errors

In this paper, we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically, deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the characteristic function of the measurement errors does not have zeros on the real line. This assumption is rather strong and is not fulfilled in many cases of interest. In this paper, we develop a methodology for constructing optimal density deconvolution estimators in the general setting that covers vanishing and nonvanishing characteristic functions of the measurement errors. We derive upper bounds on the risk of the proposed estimators and provide sufficient conditions under which zeros of the corresponding characteristic function have no effect on estimation accuracy. Moreover, we show that the derived conditions are also necessary in some specific problem instances.

A Scalable Reinforcement Learning Algorithm for Scheduling Railway Lines

This paper describes an algorithm for scheduling bidirectional railway lines (both single- and multi-track) using a reinforcement learning (RL) approach. The goal is to define the track allocations and arrival/departure times for all trains on the line, given their initial positions, priority, halt times, and traversal times, while minimizing the total priority-weighted delay. The primary advantage of the proposed algorithm compared to exact approaches is its scalability, and compared to heuristic approaches is its solution quality. Efficient scaling is ensured by decoupling the size of the state-action space from the size of the problem instance. Improved solution quality is obtained because of the inherent adaptability of reinforcement learning to specific problem instances. An additional advantage is that the learning from one instance can be transferred with minimal re-learning to another instance with different infrastructure resources and traffic mix. It is shown that the solution quality of the RL algorithm exceeds that of two prior heuristic-based approaches while having comparable computation times. Two lines from the Indian rail network are used for demonstrating the applicability of the proposed algorithm in the real world.