Original Constraints Research Articles

Decision Diagram Decomposition for Quadratically Constrained Binary Optimization

In recent years the use of decision diagrams within the context of discrete optimization has proliferated. This paper continues this expansion by proposing the use of decision diagrams for modeling and solving binary optimization problems with quadratic constraints. The model proposes the use of multiple decision diagrams to decompose a quadratic matrix so that each individual diagram has provably limited size. The decision diagrams are then linked through channeling constraints to ensure that the solution represented is consistent across the decision diagrams and that the original quadratic constraints are satisfied. The resulting family of decision diagrams are optimized over by a dedicated cutting-plane algorithm akin to Benders decomposition. The approach is general, in that commercial integer programming solvers can readily apply the technique. A thorough experimental evaluation on both benchmark and synthetic instances exhibits that the proposed decision diagram reformulation provides significant improvements over current methods for quadratic constraints in state-of-the-art solvers.

Correction to: Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

In the article Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints, we claimed a worst-case runtime of and for the Multi-Objective Evolutionary Algorithm and the Multi-Objective Genetic Algorithm, respectively, on linear profit functions under dynamic uniform constraint, where denotes the difference between the original constraint bound B and the new one. The technique used to prove these results contained an error. We correct this mistake and show a weaker bound of for both algorithms instead.

Optimal management of pumped hydroelectric production with state constrained optimal control

We present a novel technique to solve the problem of managing optimally a pumped hydroelectric storage system. This technique relies on representing the system as a stochastic optimal control problem with state constraints, these latter corresponding to the finite volume of the reservoirs. Following the recent level-set approach presented in O. Bokanowski, A. Picarelli, H. Zidani, State-constrained stochastic optimal control problems via reachability approach, SIAM J. Control and Optim. 54 (5) (2016), we transform the original constrained problem in an auxiliary unconstrained one in augmented state and control spaces, obtained by introducing an exact penalization of the original state constraints. The latter problem is fully treatable by classical dynamic programming arguments.

Anomalies in Special Permutation Flow Shop Scheduling Problems

Recent researches show that there are some anomalies, which are not satisfied with common sense, appearing in some special permutation flow shop scheduling problems (PFSPs). These anomalies can be divided into three different types, such as changing the processing time of some operations, changing the number of total jobs and changing the number of total machines. This paper summarizes these three types of anomalies showing in the special PFSPs and gives some examples to make them better understood. The extended critical path is proposed and the reason why these anomalies happen in special PFSPs is given: anomalies will occur in these special PFSPs when the time of the operations on the reverse critical path changes. After that, the further reason for these anomalies is presented that when any one of these three types of anomalies happens, the original constraint in the special PFSPs is destroyed, which makes the anomalies appear. Finally, the application of these anomalies in production practice is given through examples and also with the possible research directions. The main contribution of this research is analyzing the intial reason why the anomalies appear in special PFSPs and pointing out the application and the possible research directions of all these three types of anomalies.

Realizable causal-consistent reversible choreographies for systems with first-in-first-out communication channels

We re-engineer a pomset-based abstract semantics (and the associated semantic constraints) recently proposed for compositionally specified choreographies for systems of components communicating over first-in-first-out channels. We prove that the original semantics over-specifies components' behaviour and that for this (but not only this) reason, the original semantic constraints are insufficient for the realizability of choreographies. We remove the problematic over-specification in the semantics, extend the semantics to explicitly specified interaction pomset sets, define an abstract syntax of choreographies and rephrase choreography semantics in terms of it, and newly provide a syntax-independent definition of choreography well-formedness. We prove that choreographies well-formed in the new sense are realizable and under a certain additional condition also causal-consistent reversible. Devising a set of rules for inferring well-formedness of choreographies compositionally, we correct the semantic constraints originally claimed sufficient for operands of individual composition operators. Our constraints and our definition of choreography well-formedness are in certain ways also less restrictive than the original ones. In particular, we newly allow also choreographies exploiting accidental event orderings.

Optimization with uncertainty – A case study for controller recalibration

Although Advanced Process Control (APC) applications have a very attractive economic return, they are often turned off after a year or so because changes in the process or operating conditions create a mismatch between the process and the original models and constraints. Periodic recalibration of the models can restore function, and substantially extend the useful life of an APC project. Through optimization of a stochastic simulation, this work shows that the recalibration schedule is important, and as well, relatively insensitive to a precise date. This case study also reinforces a general methodology for optimizing stochastic processes.

Joint source coding rate allocation and flow scheduling for data aggregation in collaborative sensing networks

In collaborative sensing networks such as WSNs (Wireless Sensor Networks), due to overlapping converge areas among neighbor nodes, they may percept a large number of similar or identical data, which incurs sensing data redundancy and unnecessary energy consumption. Slepian-wolf theorem based source coding is an effective method to reduce redundancy in data aggregation. However, the exponential growth of constraints prevent the method from practical application. Therefore, in this paper, we propose a cross-layer optimization framework to solve data aggregation problem by jointly considering optimal source encoding rate and flow scheduling. By proving the convex of constraints of Spelian-Wolf theorem, we relax original constraints so that the optimal encoding rate scheme can be adopted. The relaxation makes the optimization problem feasible. Furthermore, we employ dual decomposition to separate the original problem into two sub-problems. By solving the two subproblem distributedly, we provide optimal encoding rate allocation for each node and flow scheduling for each link. Simulation results demonstrate that our framework can reduce data redundancy and network traffic significantly compared to the exiting algorithms.

Redesign of reverse logistics network with managerial decisions on the minimum quality level and remanufacturing policy

In reverse logistic networks, end-of-use products are collected and transported to the factory for remanufacturing. The economic and environmental values of a reverse network depend significantly on the quality of the end-of-use products and the remanufacturing policies. Therefore, it is desirable to consider the minimum quality level of the remanufacturing and the remanufacturing policy during the initial design stage. A redesign of the reverse logistics network is addressed based on decisions made regarding the location of the collection facility, the allocation, the minimum quality level and the remanufacturing policies. Based on the known continuous distribution for the quality of an end-of-use product, a bi-objective mathematical model was developed. A mathematical model was then transformed into mixed integer programmes using quadratic terms in the constraints through the development of a discretisation method. To obtain Pareto solutions of a bi-objective model, a quality constraint method was developed by relaxing the non-linearity and complexity of the original epsilon constraint method. The proposed mathematical model and algorithm were able to redesign reverse logistics network throughout the entire processes of collection, transportation and remanufacturing. The validity of the model and accessibility for a large size problem demonstrated through numerical experiments are described herein.

RT-trust: automated refactoring for trusted execution under real-time constraints

Real-time systems must meet strict timeliness requirements. These systems also often need to protect their critical program information (CPI) from adversarial interference and intellectual property theft. Trusted execution environments (TEE) execute CPI tasks on a special-purpose processor, thus providing hardware protection. However, adapting a system written to execute in environments without TEE requires partitioning the code into the regular and trusted parts. This process involves complex manual program transformations that are not only laborious and intellectually tiresome, but also hard to validate and verify for the adherence to real-time constraints. To address these problems, this paper presents novel program analyses and transformation techniques, accessible to the developer via a declarative meta-programming model. The developer declaratively specifies the CPI portion of the system. A custom static analysis checks CPI specifications for validity, while probe-based profiling helps identify whether the transformed system would continue to meet the original real-time constraints, with a feedback loop suggesting how to modify the code, so its CPI can be isolated. Finally, an automated refactoring isolates the CPI portion for TEE-based execution, communicated with through generated calls to the TEE API. We have evaluated our approach by successfully enabling the trusted execution of the CPI portions of several microbenchmarks and a drone autopilot. Our approach shows the promise of declarative meta-programming in reducing the programmer effort required to adapt systems for trusted execution under real-time constraints.

Influence of bit design on the stability of a rotary drilling system

This paper extends the RGD model originally proposed by Richard et al. (J Sound Vib 305(3):432–456, 2007, https://doi.org/10.1016/j.jsv.2007.04.015) to investigate drilling-induced vibrations, by considering idealized drag bits characterized either by multiple angular offsets between the blades or by a combination of full and partial blades, a departure from the symmetric bit of the RGD model consisting of multiple continuous blades. The RGD model is built on a two-degrees of freedom discrete representation of the drillstring combined with a rate-independent bit/rock interaction law. By relaxing the original constraints on the bit geometry, the coupled state-dependent delay differential equations governing the angular and axial motions of the bit now contain multiple state-dependent time delays. A linear stability analysis leads to explicit expressions for the critical rotational speed(s) defining two different regimes of stability of the coupled dynamics. Stability maps indicate that both groups of bits have a better axial stability than their RGD counterparts. It is also found that multiple critical rotation speeds exist for certain bit geometries, in contrast to the single axial stability boundary of the original RGD model. Time simulations confirm the predictions of the linear stability analysis and show evidence of the existence of different types of quasi-periodic responses before the establishment of a limit cycle characterized by both axial and torsional stick-slip events.

An improved constrained predictive functional control for industrial processes: A chamber pressure process study

An improved constrained predictive functional control for the pressure of a coke furnace is proposed in this article. In conventional constrained model predictive control, a quadratic programming problem is usually constructed to replace the original cost function and constraints to obtain the optimal control law. Under strict constraints, however, the relevant quadratic programming problem may have no feasible solutions. Unlike conventional approaches, there are several effective relaxations introduced for the constraints in the proposed scheme; then, a new cost function and the new transformed constraints are generated. With the improved constraints and cost function, there are always acceptable solutions for the quadratic programming problem under various conditions. The validity of the presented constrained model predictive control algorithm is evaluated through the regulation of the pressure of the coke furnace.

A randomized relaxation method to ensure feasibility in stochastic control of linear systems subject to state and input constraints

We consider a linear system affected by an additive stochastic disturbance and address the design of a finite horizon control policy that is optimal according to some cost criterion and accounts also for probabilistic constraints on both the input and state variables. The resulting policy can be implemented over a receding horizon according to the model predictive control strategy. Such a possibility, however, is hampered by the fact that a feasibility issue may arise when recomputing the policy. Infeasibility indeed can occur if the disturbance has unbounded support and the state is required to remain in a bounded set. In this paper, we propose a solution to this issue that is based on the introduction of a constraint relaxation that becomes effective only when the original problem turns out to be unfeasible. This is obtained via a cascade of two probabilistically-constrained optimization problems where, in the first one, performance is neglected and the policy is designed to fully recover feasibility or – if this is not possible – to determine the minimum level of relaxation which is needed to recover feasibility; in the second step, such a minimum relaxation level is imposed while optimally (re-)tuning the control policy parameters. Both problems are solved through a computationally tractable scenario-based scheme using a finite number of disturbance realizations and providing an approximate solution that satisfies with high confidence the original probabilistic constraints of the cascade.

Stochastic Successive Convex Approximation for General Stochastic Optimization Problems

One key challenge for solving a general stochastic optimization problem with expectations in the objective and constraint functions using ordinary stochastic iterative methods lies in the infeasibility issue caused by the randomness over iterates. This letter aims to address this main challenge. First, we obtain an equivalent stochastic optimization problem which is to minimize the weighted sum of the original objective and the penalty for violating the original constraints. Then, we propose a stochastic successive convex approximation (SSCA) method to obtain a stationary point of the original stochastic optimization problem. Using similar techniques, we propose a parallel SSCA method to obtain a stationary point of a special case of the general stochastic optimization problem which has decoupled constraint functions. We also provide application examples of the proposed methods in power control for interference networks. The proposed SSCA and parallel SSCA methods achieve empirically higher convergence rates and lower computational complexities than existing ones, benefiting from the elegant way of balancing the objective minimization and constraint satisfaction over random iterates.

The convex hull heuristic for nonlinear integer programming problems with linear constraints and application to quadratic 0–1 problems

The convex hull heuristic is a heuristic for mixed-integer programming problems with a nonlinear objective function and linear constraints. It is a matheuristic in two ways: it is based on the mathematical programming algorithm called simplicial decomposition, or SD (von Hohenbalken in Math Program 13:49–68, 1977), and at each iteration, one solves a mixed-integer programming problem with a linear objective function and the original constraints, and a continuous problem with a nonlinear objective function and a single linear constraint. Its purpose is to produce quickly feasible and often near optimal or optimal solutions for convex and nonconvex problems. It is usually multi-start. We have tested it on a number of hard quadratic 0–1 optimization problems and present numerical results for generalized quadratic assignment problems, cross-dock door assignment problems, quadratic assignment problems and quadratic knapsack problems. We compare solution quality and solution times with results from the literature, when possible.

Research on urban new energy repeated conversion method oriented to municipal planning

In order to overcome the waste of energy in the utilisation of traditional urban new energy sources, a new urban renewable energy conversion method oriented to municipal planning is proposed. Based on the energy purchase cost, equipment operation cost and penalty cost of the new energy conversion system, the new energy conversion objective function is set up. The original constraints and lower optimisation problems are combined by KKT condition. Fortuny - A mat McCarl method is selected to transform the combined problems. For linear constraints, all models in the system are solved, and the unified and coordinated planning of multi-energy forms such as electricity, natural gas and heat energy is completed. The experimental results show that the method can transform the new urban energy, alleviate the pressure of transmission network and achieve energy optimisation; at the same time, it can effectively store energy and realise the repeated conversion of new energy; and the average conversion cost is only 200,100 Yuan, with high economic benefits.

A Convex Programming Method for Rocket Powered Landing With Angle of Attack Constraint

Real time trajectory planning is vital in rocket precision powered landing guidance. Due to the nonconvex angle of attack (AOA) constraint and other constraints, including nonlinear dynamics and thrust constraint, the powered landing trajectory planning problem is highly nonconvex, which makes it difficult to be solved in real time via existing nonconvex optimization algorithms. As the main contribution of this paper, the AOA constraint is taken into account in the problem. A convex feasible set method is presented to handle it, in which a quadratic concave function is introduced to find a convex feasible subset in the original AOA constraint and the second order term of this function is estimated by Gersgorin disc theorem. For the remaining nonconvexities, the lossless convexification is employed to address the thrust constraint, and the successive linearization is performed to handle the nonlinear dynamics. Thus, a convex optimization problem with AOA constraint for landing trajectory planning is built. The optimal solution to the original problem is obtained by iteratively solving convex problems. Numerical simulations show that the proposed method can find a feasible landing trajectory where the AOA constraint is satisfied and has a better convergence performance compared with the traditional linearization method.

Modeling spectral lags in active galactic nucleus flares in the context of Lorentz invariance violation searches

Context. High-energy photons emitted by flaring active galactic nuclei (AGNs) have been used for many years to constrain modified dispersion relations in vacuum encountered in the context of quantum gravity phenomenology. In such studies, done in the GeV–TeV range, energy-dependent delays (spectral lags) are searched for, usually neglecting any source-intrinsic time delay. Aims. With the aim being to distinguish Lorentz invariance violation (LIV) effects from lags generated at the sources themselves, a detailed investigation into intrinsic spectral lags in flaring AGNs above 100 GeV is presented in the frame of synchrotron-self-Compton scenarios for their very-high-energy (VHE) emission. Methods. A simple model of VHE flares in blazars is proposed, allowing to explore the influence of the main physical parameters describing the emitting zones on intrinsic delays. Results. For typical conditions expected in TeV blazars, significant intrinsic lags are obtained, which can dominate over LIV effects, especially at low redshifts, and should therefore be carefully disentangled from any extrinsic lags. Moreover, two main regimes are identified with characteristic spectral lags, corresponding to long-lasting and fast particle acceleration. Conclusions. Such intrinsic spectral lags should be detected with new-generation instruments at VHE such as the Cherenkov Telescope Array which begins operation in a few years. This will provide original constraints on AGN flare models and open a new era for LIV searches in the photon sector.

RT-Trust: Automated refactoring for different trusted execution environments under real-time constraints

Abstract Real-time systems must meet strict timeliness requirements. These systems also often need to protect their critical program information (CPI) from adversarial interference and intellectual property theft. Trusted execution environments (TEE) execute CPI tasks on a special-purpose processor, thus providing hardware protection. However, adapting a system written to execute in environments without TEE requires partitioning the code into untrusted and trusted parts. This process involves complex manual program transformations that are not only laborious and intellectually tiresome, but also hard to validate and verify adherence to real-time constraints. To address these problems, this paper presents novel program analyses and transformation techniques, accessible to the developer via a declarative meta-programming model. The developer declaratively specifies the CPI portion of the system. A custom static analysis checks CPI specifications for validity, while probe-based profiling helps identify whether the transformed system would continue to meet the original real-time constraints, with a feedback loop suggesting how to modify the code, so its CPI can be isolated. Finally, an automated refactoring isolates the CPI portion for TEE-based execution, communicated with through generated calls to the TEE API. The reference implementation of our approach profiles and transforms real-time systems to isolate their CPI functions to execute on two different TEE platforms: OP-TEE and SGX. Although these platforms substantially differ in terms of their respective APIs and performance characteristics, our refactoring completely hides these differences from the developer by automatically synthesizing the correct CPI functionality required for these dissimilar TEE implementations. We have evaluated our approach by successfully enabling the trusted execution of the CPI portions of several microbenchmarks and a drone autopilot. Our approach shows the promise of declarative meta-programming in reducing the programmer effort required to adapt systems for trusted execution under real-time constraints.

Prescribed performance fault tolerant control for uncertain nonlinear systems with input saturation

This paper investigates the problem of adaptive fault tolerant tracking control for uncertain nonlinear systems in the event of external disturbances, actuator faults and input saturation. In order to guarantee the transient and steady-state control performance, the prescribed performance function is employed to impose the anticipant performance criterion on the output tracking error. By using the error transformation, the original inequality error constraint is converted to an unconstrained issue. For the conversion systems, the negative effect resulting from the external disturbances is restrained via the adaptive control approach. The radial basis function neural network (RBFNN) is adopted to handle the unknown nonlinear functions. The Nussbaum gain technique is utilised to deal with the nonlinear terms arising from the actuator faults and input saturation. Combining with the backstepping control strategy, an adaptive neural fault tolerant control (FTC) scheme is developed for the uncertain nonlinear systems. It is rigorously proved that the proposed controller is capable of ensuring the boundness of all closed-loop signals as well as the specified tracking performance. Simulation results on two examples are given to illustrate the effectiveness of the presented control approach.

Rectum Dose Constraints for Carbon Ion Therapy: Relative Biological Effectiveness Model Dependence in Relation to Clinical Outcomes.

The clinical application of different relative biological effectiveness (RBE) models for carbon ion RBE-weighted dose calculation hinders a global consensus in defining normal tissue constraints. This work aims to update the local effect model (LEM)-based constraints for the rectum using microdosimetric kinetic model (mMKM)-defined values, relying on RBE translation and the analysis of long-term clinical outcomes. LEM-optimized plans of treated patients, having suffered from prostate adenocarcinoma (n = 22) and sacral chordoma (n = 41), were recalculated with the mMKM using an in-house developed tool. The relation between rectum dose-volume points in the two RBE systems (DLEM|v and DMKM|v) was fitted to translate new LEM-based constraints. Normal tissue complication probability (NTCP) values, predicting late rectal toxicity, were obtained by applying published parameters. No late rectal toxicity events were reported within the patient cohort. The rectal toxicity outcome was confirmed using dosimetric analysis: DMKMVHs lay largely below original constraints; the translated DLEM|v values were 4.5%, 8.3%, 18.5%, and 35.4% higher than the nominal DMKM|v of the rectum volume, v—1%, 5%, 10% and 20%. The average NTCP value ranged from 5% for the prostate adenocarcinoma, to 0% for the sacral chordoma group. The redefined constraints, to be confirmed prospectively with clinical data, are DLEM|5cc ≤ 61 Gy(RBE) and DLEM|1cc ≤ 66 Gy(RBE).