Deterministic Programming Research Articles

Tachis: Higher-Order Separation Logic with Credits for Expected Costs

We present Tachis, a higher-order separation logic to reason about the expected cost of probabilistic programs. Inspired by the uses of time credits for reasoning about the running time of deterministic programs, we introduce a novel notion of probabilistic cost credit. Probabilistic cost credits are a separation logic resource that can be used to pay for the cost of operations in programs, and that can be distributed across all possible branches of sampling instructions according to their weight, thus enabling us to reason about expected cost. The representation of cost credits as separation logic resources gives Tachis a great deal of flexibility and expressivity. In particular, it permits reasoning about amortized expected cost by storing excess credits as potential into data structures to pay for future operations. Tachis further supports a range of cost models, including running time and entropy usage. We showcase the versatility of this approach by applying our techniques to prove upper bounds on the expected cost of a variety of probabilistic algorithms and data structures, including randomized quicksort, hash tables, and meldable heaps. All of our results have been mechanized using Coq, Iris, and the Coquelicot real analysis library.

A Modal Type Theory of Expected Cost in Higher-Order Probabilistic Programs

The design of online learning algorithms typically aims to optimise the incurred loss or cost , e.g., the number of classification mistakes made by the algorithm. The goal of this paper is to build a type-theoretic framework to prove that a certain algorithm achieves its stated bound on the cost. Online learning algorithms often rely on randomness, their loss functions are often defined as expectations, precise bounds are often non-polynomial (e.g., logarithmic) and proofs of optimality often rely on potential-based arguments. Accordingly, we present pλ-amor, a type-theoretic graded modal framework for analysing (expected) costs of higher-order probabilistic programs with recursion. pλ-amor is an effect-based framework which uses graded modal types to represent potentials, cost and probability at the type level. It extends prior work (λ-amor) on cost analysis for deterministic programs. We prove pλ-amor sound relative to a Kripke step-indexed model which relates potentials with probabilistic coupling. We use pλ-amor to prove cost bounds of several examples from the online machine learning literature. Finally, we describe an extension of pλ-amor with a graded comonad and describe the relationship between the different modalities.

Maximizing virtual power plant profit: A two-level optimization model for energy market participation

Managing dispersed generation via virtual power plants (VPPs) is crucial for maximizing profits in electricity markets. This paper presents a model aimed at maximizing VPP profit through participation in the energy market. The proposed model addresses grid and security constraints of units using deterministic programming, formulated as an equilibrium-constrained, two-level mathematical optimization model. The first level focuses on maximizing VPP profit, while the second optimizes social welfare. Applying duality theory transforms this two-level model into a mixed-integer linear programming model, further refined using Karush–Kuhn–Tucker (KKT) optimality conditions. Given the inherent conflict in these objectives, a novel algorithm employing water flow dynamics is proposed for solving the model. To enhance method performance, the Pareto criterion and fuzzy decision-making are incorporated. Model tests are conducted on a standard 24-bus IEEE grid, demonstrating its efficiency. For the single-objective problem without line congestion, the solving time was 12 s. Introducing line congestion increased the profit by 13.4 %, from $40,413.21 to $45,837.32. In the two-objective problem without congestion, the profit ranged between $36,928.72 and $42,813.28, and emissions ranged from 275.21 to 2,916.32 pounds. With congestion, the profit range increased by a maximum of 8.7 %, and emissions were reduced by up to 4.6 %.

Disentangling Parallelism and Interference in Game Semantics

Game semantics is a denotational semantics presenting compositionally the computational behaviour of various kinds of effectful programs. One of its celebrated achievement is to have obtained full abstraction results for programming languages with a variety of computational effects, in a single framework. This is known as the semantic cube or Abramsky's cube, which for sequential deterministic programs establishes a correspondence between certain conditions on strategies (''innocence'', ''well-bracketing'', ''visibility'') and the absence of matching computational effects. Outside of the sequential deterministic realm, there are still a wealth of game semantics-based full abstraction results; but they no longer fit in a unified canvas. In particular, Ghica and Murawski's fully abstract model for shared state concurrency (IA) does not have a matching notion of pure parallel program-we say that parallelism and interference (i.e. state plus semaphores) are entangled. In this paper we construct a causal version of Ghica and Murawski's model, also fully abstract for IA. We provide compositional conditions parallel innocence and sequentiality, respectively banning interference and parallelism, and leading to four full abstraction results. To our knowledge, this is the first extension of Abramsky's semantic cube programme beyond the sequential deterministic world.

Study on the effects of accident-tolerant fuels on the safety of CPR1000 nuclear power plants

Abstract In this paper, CPR1000 Nuclear power plant was taken as the reference unit. According to CPR1000 Probabilistic Safety Analysis (PSA), the Large Break loss of coolant accident (LOCA), Medium Break LOCA, Small Break LOCA, Station Blackout (SBO), Total Loss of Feed water (TLOFW) and Anticipated transient without trip (ATWT) with Loss of Main Feed water (LOMF) were selected as the representative accident scenarios. The house holding deterministic programs LOCUST were used to analyze each of the above selected scenarios for five different accident tolerant fuels (ATF). The effects on accident process, reactor core damage time, system success criteria and personnel response time were analyzed under the above scenarios. The above results for the five ATF materials were compared to those for standard UO2-Zr in the same scenarios, then some useful conclusions were obtained which can be used to support ATF material selection. In the end, based on the deterministic calculations, the effects of different ATF materials on CPR1000 PSA results such as core damage frequency (CDF) were evaluated in detail with traditional PSA software Risk Spectrum. According to the results, ATFs have some advantages on core damage time, success criteria or operators’ action time window. But the CDF was changed little compared to standard UO2-Zr system. Through the studies, it is found the most important thing is that due to the much longer time windows some new plant modifications can be provided to mitigate the accidents which can contribute to the plant safety and decrease risk more.

A deterministic, c-di-GMP-dependent program ensures the generation of phenotypically similar, symmetric daughter cells during cytokinesis

Phenotypic heterogeneity in bacteria can result from stochastic processes or deterministic programs. The deterministic programs often involve the versatile second messenger c-di-GMP, and give rise to daughter cells with different c-di-GMP levels by deploying c-di-GMP metabolizing enzymes asymmetrically during cell division. By contrast, less is known about how phenotypic heterogeneity is kept to a minimum. Here, we identify a deterministic c-di-GMP-dependent program that is hardwired into the cell cycle of Myxococcus xanthus to minimize phenotypic heterogeneity and guarantee the formation of phenotypically similar daughter cells during division. Cells lacking the diguanylate cyclase DmxA have an aberrant motility behaviour. DmxA is recruited to the cell division site and its activity is switched on during cytokinesis, resulting in a transient increase in the c-di-GMP concentration. During cytokinesis, this c-di-GMP burst ensures the symmetric incorporation and allocation of structural motility proteins and motility regulators at the new cell poles of the two daughters, thereby generating phenotypically similar daughters with correct motility behaviours. Thus, our findings suggest a general c-di-GMP-dependent mechanism for minimizing phenotypic heterogeneity, and demonstrate that bacteria can ensure the formation of dissimilar or similar daughter cells by deploying c-di-GMP metabolizing enzymes to distinct subcellular locations.

System reliability analysis of geogrid reinforced retaining wall using random finite element method

Stabilizing earthwalls is extremely important in geotechnical engineering projects and has become an integral part of transportation infrastructures. Meanwhile, geogrid reinforced retaining walls have been the attention of designers due to their advantages. On the other hand, the soil heterogeneity and the requirement of investigating the internal (geogrid rupture and geogrid pullout) and external (global and lateral displacement) stability modes of these structures have necessitated performing system reliability analysis. In this study, finite element in conjunction with random fields is used to evaluate the reliability of these walls. For this purpose, a finite element program is coded in MATLAB to obtain internal and external safety factors considering staged construction. The deterministic program is extended to a stochastic framework to account for spatial variability of soil parameters in retained backfill, foundation soil, and reinforced fill. In the last part of this study, reliability indices of stability modes are calculated to obtain the series system reliability index, utilizing the Sequential Compounding Method (SCM). The results indicated that the effect of soil heterogeneity is more significant on internal stability modes compared to external stability modes especially geogrid pullout. The results of the system reliability analysis demonstrated more critical conditions thus the reliability index of the system was less than the reliability index of individual components.

(Un)Solvable loop analysis

AbstractAutomatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the problem is in general undecidable, the goal is settled for restricted classes of loops. For the class of solvable loops, introduced by Rodríguez-Carbonell and Kapur (in: Proceedings of the ISSAC, pp 266–273, 2004), one can automatically compute invariants from closed-form solutions of recurrence equations that model the loop behaviour. In this paper we establish a technique for invariant synthesis for loops that are not solvable, termed unsolvable loops. Our approach automatically partitions the program variables and identifies the so-called defective variables that characterise unsolvability. Herein we consider the following two applications. First, we present a novel technique that automatically synthesises polynomials from defective monomials, that admit closed-form solutions and thus lead to polynomial loop invariants. Second, given an unsolvable loop, we synthesise solvable loops with the following property: the invariant polynomials of the solvable loops are all invariants of the given unsolvable loop. Our implementation and experiments demonstrate both the feasibility and applicability of our approach to both deterministic and probabilistic programs.

Fourth Party Logistics Routing Problem Under Uncertain Time and Random Demand

With the rapid development of the economy, the fourth party logistics (4PL) has become an indispensable part of economic development, and the path optimization is an important topic in the research of 4PL routing problem. This paper studies the fourth party logistics routing problem with random demand and uncertain transportation time and transfer time by considering the randomness and uncertainty of the environment. In order to solve the path optimization strategy that minimizes the total transportation cost, this paper establishes an uncertain random programming model under the constraints of the total transportation time, the carrying capacity of the logistics provider, the transfer capacity of the transfer station, and the demand of the distributor. Subsequently, this paper transforms the uncertain random programming model into an equivalent deterministic programming model based on the distribution functions of random demand and uncertain time, and verifies the effectiveness of the model through two examples. The results show that the uncertain random programming model can give a reasonable path optimization strategy.

Enhancing neutrosophic fuzzy goal programming approach for solving multi-objective probabilistic linear programming problems

This article considers a stochastic multi-objective linear programming problem in a neutrosophic framework. The right-hand sides of the constraints are random variables associated with their means and variances, and the single-valued trapezoidal neutrosophic numbers are included in the coefficients of the objective functions to investigate the problem. The problem is successfully converted into the related deterministic programming model based on the formulation of the scoring function and several distributions, such as the Uniform, Exponential, and Gama distributions. Applying fuzzy goal programming, the deterministic problem is solved. An example is then solved to demonstrate the solution methodology.

Chronic back pain prevalence at small area level in England - the design and validation of a 2-stage static spatial microsimulation model

Spatially disaggregated estimates provide valuable insights into the nature of a disease. They highlight inequalities, aid public health planning and identify avenues for further research. Spatial microsimulation is advantageous in that it can be used to create large microdata sets with intact microlevel relationships between variables, which allows analysis of relationships between variables locally. This methodological paper outlines the design and validation of a 2-stage static spatial microsimulation model for chronic back pain prevalence across England, suitable for policy modelling. Data used was obtained from the Health Survey for England and the 2011 Census. Microsimulation was performed using SimObesity, a previously validated static deterministic program, and the synthetic chronic back pain microdataset was internally validated. The paper also highlights modelling considerations for researchers embarking on similar work, as well as future directions for research in this area of microsimulation.

A neurodynamic algorithm for dependent joint chance constrained geometric programs

This research studies the use of copula theory to model dependencies in joint probabilistic constrained geometric programs with dependent rows. The row vectors are assumed to follow an elliptical distribution, and their dependencies are modeled through a Gumbel–Hougaard copula. We use a log transformation to convert the chance-constrained geometric program into a deterministic optimization problem. Then we solve the resulting deterministic program using a dynamical neural network. The stability and convergence of the proposed neural network approach are demonstrated. The primary characteristic of our framework is its ability to solve the dependent joint chance constrained geometric programs without resorting to any convex approximation methods. This feature sets our approach apart from the current state-of-the-art solving techniques. The neurodynamic algorithm is finally applied to solve three geometric optimization problems.

Pointing probability Driven semi-analytic Monte Carlo Method (PDMC) – Part I: Global variance reduction for large-scale radiation transport analysis

We propose a Pointing Probability Driven Semi-Analytic Monte Carlo Method (PDMC) to replace the traditional Monte Carlo method for reactor physics analysis and radiation transport analysis. This paper describes the calculation principle and acceleration effect of the PDMC method in radiation transport analysis, highlighting its advantages in dealing with the deep-penetration problem. The PDMC method no longer requires particles to be transported to the detector. During the particle transport process, the global response of each particle state is calculated with a pointing probability to construct global information quickly. The statistical unbiasedness of the global response of a single particle state is demonstrated through rigorous mathematical derivation. The PDMC method does not rely on a deterministic program or iterative calculation, ensuring its universality and efficiency of global variance reduction (GVR). The PDMC method is tested in the China Fusion Engineering Test Reactor (CFETR) and the HBR2 benchmark. The results show that the PDMC method can significantly improve the efficiency of Monte Carlo deep-penetration simulation and is helpful for the GVR for large-scale radiation analysis.

ADEV: Sound Automatic Differentiation of Expected Values of Probabilistic Programs

Optimizing the expected values of probabilistic processes is a central problem in computer science and its applications, arising in fields ranging from artificial intelligence to operations research to statistical computing. Unfortunately, automatic differentiation techniques developed for deterministic programs do not in general compute the correct gradients needed for widely used solutions based on gradient-based optimization. In this paper, we present ADEV, an extension to forward-mode AD that correctly differentiates the expectations of probabilistic processes represented as programs that make random choices. Our algorithm is a source-to-source program transformation on an expressive, higher-order language for probabilistic computation, with both discrete and continuous probability distributions. The result of our transformation is a new probabilistic program, whose expected return value is the derivative of the original program’s expectation. This output program can be run to generate unbiased Monte Carlo estimates of the desired gradient, that can be used within the inner loop of stochastic gradient descent. We prove ADEV correct using logical relations over the denotations of the source and target probabilistic programs. Because it modularly extends forward-mode AD, our algorithm lends itself to a concise implementation strategy, which we exploit to develop a prototype in just a few dozen lines of Haskell (https://github.com/probcomp/adev).

Deterministic programming of human pluripotent stem cells into microglia facilitates studying their role in health and disease

Microglia, the resident immune cells of the central nervous system (CNS), are derived from yolk-sac macrophages that populate the developing CNS during early embryonic development. Once established, the microglia population is self-maintained throughout life by local proliferation. As a scalable source of microglia-like cells (MGLs), we here present a forward programming protocol for their generation from human pluripotent stem cells (hPSCs). The transient overexpression of PU.1 and C/EBPβ in hPSCs led to a homogenous population of mature microglia within 16 d. MGLs met microglia characteristics on a morphological, transcriptional, and functional level. MGLs facilitated the investigation of a human tauopathy model in cortical neuron-microglia cocultures, revealing a secondary dystrophic microglia phenotype. Single-cell RNA sequencing of microglia integrated into hPSC-derived cortical brain organoids demonstrated a shift of microglia signatures toward a more-developmental invivo-like phenotype, inducing intercellular interactions promoting neurogenesis and arborization. Taken together, our microglia forward programming platform represents a tool for both reductionist studies in monocultures and complex coculture systems, including 3D brain organoids for the study of cellular interactions in healthy or diseased environments.

Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm

The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.

An extensive operational law for monotone functions of LR fuzzy intervals with applications to fuzzy optimization

The operational law proposed by Zhou et al. (J Intell Fuzzy Syst 30(1): 71–87, 2016) contributes to developing fuzzy arithmetic, while its applicable conditions are confined to strictly monotone functions and regular LR fuzzy numbers, which are hindering their operational law from dealing with more general cases, such as problems formulated as monotone functions and problems with fuzzy variables represented as fuzzy intervals (e.g., trapezoidal fuzzy numbers). In order to handle such cases we generalize the operational law of Zhou et al. in both the monotonicity of function and fuzzy variables in this paper and then apply the extensive operational law to the cases with monotone (but not necessarily strictly monotone) functions with regard to regular LR fuzzy intervals (LR-FIs) (of which regular LR fuzzy numbers are special cases). Specifically, we derive the computational formulae for expected values (EVs) of LR-FIs and monotone functions with regard to regular LR-FIs, respectively. On the other hand, we develop a solution scheme to dispose of fuzzy optimization problems with regular LR-FIs, in which a fuzzy programming is converted to a deterministic equivalent one and a newly devised solution algorithm is utilized to get the deterministic programming solved. The numerical experiments are conducted using our proposed solution scheme and the traditional fuzzy simulation-based genetic algorithm in the context of a purchasing planning problem. Computational results show that our method is much more efficient, yielding high-quality solutions.

Multi-Product Productions from Malaysian Oil Palm Empty Fruit Bunch (EFB): Selection for Optimal Process and Transportation Mode

In Malaysia, palm oil industries have played significant roles in the economic sectors and the nation’s developments. One aspect of these industries that is gaining growing interest is oil palm residue management and bio-based product generations. EFB has been identified to be a feasible raw material for the production of bio-energy, bio-chemicals, and bio-materials. In this paper, our previous deterministic mathematical programming model was extended to include decisions for selecting optimal transportation modes and processes at each level of the processing stage in the supply chain. The superstructure of alternatives was extended to show states of produced products whether solid, liquid, or gaseous, and for which truck, train, barge, or pipeline would be possible modes of transportation. The objective function was to maximize profit which accounts for associated costs including the emission treatment costs from production and transportation. The optimal profit was USD 1,561,106,613 per year for single ownership of all facilities in the supply chain.

Optimisation of Airline Dynamic Multileg Capacity Control Problem considering Competition from High-Speed Rail

This paper develops an optimisation model to address the dynamic multileg capacity control problem for the airline, taking into account the competition from the high-speed rail (HSR). Conventional capacity control models assume that the passenger demand is independent and that airlines control capacity independently. The proposed model considers the semi-independent demand, i.e., a customer of certain fare class arrives and makes choices from available alternatives provided by both airline and HSR. If the customer’s first option is rejected, their booking request will be diverted both horizontally to the other operator and vertically to parallel flights within the same operator. Making use of this assumption, the customer’s second and third choices are captured. With this model, airlines can control the sales process to determine whether or not to accept an initial booking request or diverted booking request to maximise their revenue. The deterministic linear programming (DLP) method is proposed as a model solution, enabling the computation of partitioned allocation and the bid price of each product. The optimal capacity control strategy is then obtained based on bid price control. To validate the model, numerical experiments are conducted to simulate customers' actual arrival and to show that the model is capable of producing better revenue, especially in the event that demand exceeds supply. Moreover, the demand diversion effect brings more revenue for both airline and HSR, and this potential revenue source has been ignored by previous research studies.

Multiperiod stochastic programming for biomass supply chain design under spatiotemporal variability of feedstock supply

Spatiotemporal uncertainties in the collection of crop residues pose great challenges to the development of a long-term and economic biomass-to-biofuel supply chain network (BSCN). A multiperiod stochastic programming (SP) model considering uncertain collectible corn stover removal and farmer participation rates is developed. The SP model is compared with the deterministic programming for the expected scenario (DPES) model to provide decision-making support for BSCN in two different periods. With the statistical results of separate deterministic programming models for each scenario generated randomly based on the normal distribution as a reference, the economic performance of the SP and DPES models is compared in the model development period and then confirmed in the model validation period. A county-level case study with a 10-year development and a 3-year validation period is applied. The economic performance of the SP model is comparable to that of the DPES model in the development period, and the SP model achieves much higher cost savings in the validation period. Although biomass transportation cost is the most unstable cost component, the variation in bioethanol production cost is largely consistent with that in biomass purchase cost. The SP model demonstrates stronger robustness to uncertainty than the DPES model.