Predecessor Operations Research Articles

Multiobjective Optimization for FJSP Under Immediate Predecessor Constraints Based OFA and Pythagorean Fuzzy Set

In the flexible job shop scheduling problem (FJSP), immediate predecessor operations have an explicit impact on the scheduling results, and are often ignored. To analyze the influence of immediate predecessor operations on machine tool manufacturing workshops, four forms of immediate predecessor operations with the consideration of uncertain transportation and preparation time are defined. Then, the four forms of immediate predecessor operations are integrated into the FJSP, and a multiobjective FJSP is constructed. An improved optimal foraging algorithm (OFA) and Pythagorean fuzzy set (PFS) are combined to establish a multiobjective optimization algorithm, named PFSOFA. This algorithm is then used to solve the multiobjective FJSP. In PFSOFA, the Pareto fronts are mapped into PFSs. The Pythagorean fuzzy numbers (PFNs) in a PFS are transformed into right triangles, and the distances between the PFNs and the reference PFNs are defined as the distances between their right triangle centroids. Then, all distances of a PFS are integrated by the distance prospect function to obtain a distance prospect value. This value is then used to lead the iteration of PFSOFA. Through extensive experiments, including a real factory application case, the performance of PFSOFA is verified to be better than four classical multiobjective optimization algorithms for solving the multiobjective FJSP constructed in this paper. And for the factory case, PFSOFA also obtained the better schemes.

Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness

We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any execution is strongly fair with respect to a specified set of live edges: whenever the source vertex of a live edge is visited infinitely often along a play, the edge itself is traversed infinitely often along the play as well. We show that, surprisingly, strong transition fairness retains the algorithmic characteristics of the fixpoint algorithms for $\omega$-regular games -- the new algorithms have the same alternation depth as the classical algorithms but invoke a new type of predecessor operator. For Rabin games with $k$ pairs, the complexity of the new algorithm is $O(n^{k+2}k!)$ symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption. Further, we show that GR(1) specifications with strong transition fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as the usual algorithm. In contrast, strong fairness necessarily requires increasing the alternation depth depending on the number of fairness assumptions. We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic $\omega$-regular games that runs in $O(n^{k+2}k!)$ symbolic steps, improving the state of the art. Finally, we have implemented a BDD-based synthesis engine based on our algorithm. We show on a set of synthetic and real benchmarks that our algorithm is scalable, parallelizable, and outperforms previous algorithms by orders of magnitude.

Koopman-Inspired Implicit Backward Reachable Sets for Unknown Nonlinear Systems

Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In this paper, we show how learned Koopman approximations can be used for state-feedback correct-by-construction control. To this end, we introduce the Koopman over-approximation, a (possibly hybrid) lifted representation that has a simulation-like relation with the underlying dynamics. Then, we prove how successive application of controlled predecessor operation in the lifted space leads to an implicit backward reachable set for the actual dynamics. Finally, we demonstrate the approach on two nonlinear control examples with unknown dynamics.

Computation of controlled invariant sets for discrete-time switched nonlinear systems with time-delay

We consider the concept of set invariance for discrete-time switched nonlinear systems with time-delays, referred to here as D-invariance. Specifically, the existence of controlled invariant sets for nonlinear switched systems with time-delay is proved by defining a suitable predecessor operator. As the main contribution, we use the interval analysis method to iteratively computing the inner-approximation of a controlled D-invariant set, which is a key step towards invariance control of switched nonlinear systems with time-delay. The sequence of the approximated controlled D-invariant sets are obtained by considering all possible delays within a given bounded region of the state space, so that a D-invariant set and controller that are independent of time-delay are obtained. Finally, two examples are given to show the performance of this method.

The doubling metric and doubling measures

We introduce the so-called doubling metric on the collection of non-empty bounded open subsets of a metric space. Given an open subset $\mathbb{U}$ of a metric space $X$, the predecessor $\mathbb{U}_\ast$ of $\mathbb{U}$ is defined by doubling the radii of all open balls contained inside $\mathbb{U}$, and taking their union. The predecessor of $\mathbb{U}$ is an open set containing $\mathbb{U}$. The directed doubling distance between $\mathbb{U}$ and another subset $\mathbb{V}$ is the number of times that the predecessor operation needs to be applied to $\mathbb{U}$ to obtain a set that contains $\mathbb{V}$. Finally, the doubling distance between open sets $\mathbb{U}$ and $\mathbb{V}$ is the maximum of the directed distance between $\mathbb{U}$ and $\mathbb{V}$ and the directed distance between $\mathbb{V}$ and $\mathbb{U}$.

Hyperspectral Imaging Applications to Geometallurgy: Utilizing Blast Hole Mineralogy to Predict Au-Cu Recovery and Throughput at the Phoenix Mine, Nevada

Abstract The Phoenix mine and predecessor operations in north-central Nevada have produced an aggregate of 5.2 Moz of gold and 550 million pounds of copper from an Eocene-aged Au-Cu porphyry-related skarn. The complex skarn mineralogy intimately associated with ore-grade mineralization poses significant challenges to blasting, mining, comminution, and process operations. These challenges are rooted in highly variable silicate mineralogy, which manifests as fine-grained, submillimeter grain-size, generally green colored rocks that inhibit accurate identification in the field. Prior to this study, all mineralogical data utilized in Phoenix mine ore control were sourced from blast hole cuttings mapped by ore control geologists in the field—the standard practice at many modern mine sites. At Phoenix, a direct link between mineralogy and mill performance was recognized; however, mineralogical data captured in the field was not sufficient to optimize process operations. To address this, it was determined that analytical work was necessary to quantify fine-grained mineralogy of variable ore types. A visible-near and short-wave infrared (VNIR-SWIR) hyperspectral imaging system provided the ideal tool, as it allows near real-time mineralogical data acquisition and semiquantitative determination of mineral abundances. Multiple iterative studies were conducted to prove that hyperspectral imaging of Phoenix ore types provides results suitable for process optimization. This six-month study described here included hyperspectral imaging of 3,008 blast hole cuttings samples from three pits, and 877 crusher feed, rougher feed, and rougher tails samples. Hyperspectral feature extractions derived from mill samples were paired with associated mill performance data and used to build predictive Au-Cu recovery, grade, and throughput models using multiple linear regression, partial least squares, and deep learning techniques with R-correlation values to observed data of 0.56 to 0.71. Blast hole hyperspectral data were then applied to recovery, grade, and throughput models to calculate predicted recoveries and throughputs that were spatially kriged with excellent correlations to geologic features. The application of VNIR-SWIR hyperspectral imaging to blast hole cuttings is a powerful predictive and diagnostic geometallurgical tool in operations where silicate mineralogy has a strong impact on process operations.

Automatic Generation of Communication Requirements for Enforcing Multi-Agent Safety

Distributed controllers are often necessary for a multi-agent system to satisfy safety properties such as collision avoidance. Communication and coordination are key requirements in the implementation of a distributed control protocol, but maintaining an all-to-all communication topology is unreasonable and not always necessary. Given a safety objective and a controller implementation, we consider the problem of identifying when agents need to communicate with one another and coordinate their actions to satisfy the safety constraint. We define a coordination-free controllable predecessor operator that is used to derive a subset of the state space that allows agents to act independently, without consulting other agents to double check that the action is safe. Applications are shown for identifying an upper bound on connection delays and a self-triggered coordination scheme. Examples are provided which showcase the potential for designers to visually interpret a system's ability to tolerate delays when initializing a network connection.

IRAQ 2003 (PART 2): THE ROAD TO BAGHDAD

The operational plans The attack on Iraq, or Operation Iraqi Freedom as it was called, would be very different from its predecessor Operation Desert Storm, 12 years before. The main strategic difference was, of course, the fact that Desert Storm encompassed an enormous international military coalition, with ground, air and naval forces being supplied by America, Britain, France, Italy, Australia, Argentina, Saudi Arabia, Egypt and Syria. Iraqi Freedom was shouldered by only two countries, the US and the UK, with Australia supplying a small contingent of SAS troops, the Czech Republic a platoon of chemical warfare troops and Spain a hospital ship. To drive the Iraqi occupying forces out of Kuwait in 1991, an enormous force of 15 divisions had been amassed. These had been organised into 3 American corps (XVIII Airborne Corps, consisting of two airborne divisions, a mechanised infantry division, as well as a French light armoured division; VII Corps, consisting of three US and one UK armoured divisions and one US mechanised infantry division; and a US Marine corps, consisting of two Marine divisions), a Saudi Arabian corps of two divisions, an Egyptian corps of two divisions, and a Syrian division.3 For Iraqi Freedom, only a single army corps (V), consisting of two mechanised infantry divisions and an airborne division, together with a marine division, an understrength composite British armoured division, and some smaller independent units, was available. And because of political wrangling, one mechanised infantry division arrived far too late on the battlefield to participate in the fighting. So, compared to 15 divisions in 1991, the job would now have to be done by only four. Nevertheless, with the new American weapons of precision and the extremely able Abrams tank, a repeat of Gulf War I was not really necessary.

A classification of symbolic transition systems

We define five increasingly comprehensive classes of infinite-state systems, called STS1--STS5, whose state spaces have finitary structure. For four of these classes, we provide examples from hybrid systems.STS1 These are the systems with finite bisimilarity quotients. They can be analyzed symbolically by iteratively applying predecessor and Boolean operations on state sets, starting from a finite number of observable state sets. Any such iteration is guaranteed to terminate in that only a finite number of state sets can be generated. This enables model checking of the μ-calculus.STS2 These are the systems with finite similarity quotients. They can be analyzed symbolically by iterating the predecessor and positive Boolean operations. This enables model checking of the existential and universal fragments of the μ-calculus.STS3 These are the systems with finite trace-equivalence quotients. They can be analyzed symbolically by iterating the predecessor operation and a restricted form of positive Boolean operations (intersection is restricted to intersection with observables). This enables model checking of all ω-regular properties, including linear temporal logic.STS4 These are the systems with finite distance-equivalence quotients (two states are equivalent if for every distance d , the same observables can be reached in d transitions). The systems in this class can be analyzed symbolically by iterating the predecessor operation and terminating when no new state sets are generated. This enables model checking of the existential conjunction-free and universal disjunction-free fragments of the μ-calculus.STS5 These are the systems with finite bounded-reachability quotients (two states are equivalent if for every distance d , the same observables can be reached in d or fewer transitions). The systems in this class can be analyzed symbolically by iterating the predecessor operation and terminating when no new states are encountered (this is a weaker termination condition than above). This enables model checking of reachability properties.

Covering sharing trees: a compact data structure for parameterized verification

The control state reachability problem is decidable for well-structured infinite-state systems like (Lossy) Petri Nets, Vector Addition Systems, and broadcast protocols. An abstract algorithm that solves the problem is the backward reachability algorithm of [1, 21 ]. The algorithm computes the closure of the predecessor operator with respect to a given upward-closed set of target states. When applied to this class of verification problems, symbolic model checkers based on constraints like [7, 26 ] suffer from the state explosion problem.In order to tackle this problem, in [13] we introduced a new data structure, called covering sharing trees, to represent in a compact way collections of infinite sets of system configurations. In this paper, we will study the theoretical complexity of the operations over covering sharing trees needed in symbolic model checking. We will also discuss several optimizations that can be used when dealing with Petri Nets. Among them, in [14] we introduced a new heuristic rule based on structural properties of Petri Nets that can be used to efficiently prune the search during symbolic backward exploration. The combination of these techniques allowed us to turn the abstract algorithm of [1, 21 ] into a practical method. We have evaluated the method on several finite-state and infinite-state examples taken from the literature [2, 18 , 20 , 30 ]. In this paper, we will compare the results we obtained in our experiments with those obtained using other finite and infinite-state verification tools.

HIERARCHICAL CONTROL FOR A CLASS OF UNCERTAIN PIECEWISE LINEAR HYBRID DYNAMICAL SYSTEMS

In this paper, we consider the hierarchical control problem for a class of uncertain hybrid dynamical systems. The continuous dynamics of this class of uncertain hybrid systems are described by linear difference state equations, whose right side functions are unknown but lie within some convex hulls of known functions. Our control objective is for the closed loop system to exhibit a desired behavior under the dynamic uncertainty, continuous disturbances and uncontrollable events. One of the main questions is the existence of appropriate controllers. We will focus on this question here, and present a novel methodology for the analysis of uncertain piecewise linear hybrid dynamical systems (PLHDS) based on backward reachability analysis. For this purpose, we derive the predecessor operator for this class of uncertain PLHDS. Then both static control specifications such as safety and reachability, and dynamic control specifications are considered. A temperature control system is used for illustration.

A partially ordered extention of the integers

This paper presents a monotonic system of Post algebras of order ω+ω* whose chain of Post constans is isomorphic with 0≤1≤2≤ ... ≤-3≤-2≤-1. Besides monotonic operations, other unary operations are considered; namely, disjoint operations, the quasi-complement, succesor, and predecessor operations. The successor and predecessor operations are basic for number theory.

Linear realization of finite automata

This paper presents a method for linear realization of automata when such exists.The basic tools employed are indexed partitions (as a way of writing certain mappings) and predecessor operations. The indexed partitions are studied in some detail and their connection to codes is explained. The method itself is simple and straightforward and contains no search steps. Only standard techniques of linear algebra, such as solving linear equations, are used. Examples are given to show the advantage of our method compared with previously known ones.

Predecessor machines

A predecessor machine is a random-access machine with a predecessor operation (i.e., an instruction which subtracts 1 from the contents of a memory cell), but with no operation which can increase the contents of a cell. A regressing function is a partial function which never yields an output larger than the maximum of its inputs and a constant. Unlike the situation for random-access machines with a successor operation, it does not matter whether or not predecessor machines with loop control also have conditional transfer instructions. Furthermore, the class of functions computable by predecessor loop machines consists of exactly those regressing functions which are computable by deterministic linear-bounded automata.