Sublevel stope layout planning through a greedy heuristic approach based on dynamic programming

The noisy intermediate-scale quantum (NISQ) devices that have just emerged in recent years provide an opportunity for the physical realization of quantum circuits. As the first step of mapping quantum circuits to these devices, qubit allocation imposes a great impact on the number of additional quantum operations required throughout the mapping. The global optimization of qubit allocation is NP-hard, but since many current NISQ devices have very few qubits, it is possible to solve this problem exactly. In this paper, we propose an exact approach for qubit allocation, which takes advantage of the branch and bound algorithm as the basic framework. In order to further prune the considerably huge state space, three techniques have been proposed and integrated into the exact approach, including an optimized lower bound for quadratic assignment problem, prioritization of logical qubits, and branch pruning by structural symmetry of physical qubits. Moreover, based on the multiple optimal solutions obtained by the exact approach, we give an error-aware qubit allocation method. For problems that are too large to be solved by the exact approach, we also give a heuristic qubit allocation approach with polynomial time complexity. Experimental evaluations show that the exact approach proposed in this paper is feasible for the qubit allocation of current NISQ architectures. For all benchmarks considered, this exact approach can find multiple optimal solutions to the qubit allocation problem on IBM Melbourne, a 16-qubit NISQ architecture, in no more than 20 min. It can serve as a evaluation baseline of any heuristic approach. Experimental evaluations also show that the proposed heuristic approach is near-optimal in terms of routing cost. Both the exact approach and the heuristic approach can be integrated into existing quantum circuit mapping approaches.

ABSTRACTA widely used unsupported underground mining technique is sublevel stoping, in which portions of ore-body within certain size constraints are extracted. In this article, a sequential approach is proposed to solve the sublevel determination problem, which is part of development and infrastructure planning, and the stope layout planning problem for polymetallic sublevel stope mining with pillars. First, a new algorithm is proposed to determine the sublevels, which focuses on minimizing the development costs while maintaining access to the profitable portions of the ore-body. Then, the stope layout is planned between the sublevels. A new mixed-integer linear programming formulation for determining the ultimate stope limits is introduced. A case study is conducted on a copper–molybdenum mine to demonstrate the proposed approaches. The results show that the output of the stope layout plan is within the optimal mining limits, which confirms the validity of the approach.

The Hiraki mine is situated in the southeastern part of the Hyogo prefecture, about 50km to the northwest of Osaka. Hiraki deposit is a large hydrothermal kaolin deposit in Japan, output of which is 5, 000-6, 000 tons/month. And Hiraki-Kaolin is mainly used for chinaware and glass-fiber.In the recent ten years, trackless underground mining have been adopted in Hiraki mine. Among underground mining methods, sublevel stoping, room and pillar method with underhand stoping supported by the rock bolts are working, and then mechanized cut and fill supported by the cable bolt is working too.This paper is described the underground mining method at Hiraki mine, under the following items.1. Sublevel stoping method.2. Underhand stoping supported by the rock bolts.3. Mechanized cut and fill.4. Measurements on the effect of rock bolting.5. Adopting reasons of cable bolting.6. Past records and Effects of cable bolting.

This paper first analyzes the characteristics and principles of the layout planning of emergency resources, explores the problems of emergency resource layout and distribution planning, and mentions the multi-constraint conditions of layout planning. Then, by describing the layout planning problem of emergency resources under multi-constraints and the related variable symbols, we constructed a two-layer layout planning model of emergency resources under multi-constraints, and after analyzing the particle swarm algorithm, we designed the layout planning model solving process based on particle swarm optimization. Finally, by constructing an emergency resource layout case, the centrality of the emergency resource layout network is explored, and the shortest distance and the best site selection of each emergency resource point corresponding to the demand point are divided. The results show that the structural degree centrality is between [0,0.78], the mileage degree centrality is between [0,1], the flow degree centrality is between [0.1,1], the structural median is between [0,0.32], the mileage median is between [0,2], and the structural proximity centrality and the mileage proximity centrality scores are both within the range of [0,1]. The shortest distribution distance of A, B, C, D, and E is selected to be only 393886m, and the error with the actual is around 0.009, which is able to carry out the layout planning effectively.

In the statistical literature, several large comparative studies have been conducted on the confidence intervals of proportions. However, few comparative studies have focused on the confidence intervals for extreme event proportions (e.g. zero-failure or all-success events) calculated using exact, approximate, and Bayesian methods. In this study, an extensive simulation with three-level nesting, comprising 980 million parameter space points, was designed based on the relationship between the binomial and beta distributions. After thoroughly examining three evaluation criteria – interval width, coverage, and oscillation – the exact method is recommended for estimating confidence intervals for extreme event proportions. The rationale for this recommendation is explained from four perspectives: exact vs. approximate methods, frequentist vs Bayesian methods, average coverage vs coverage oscillation, and the representativeness of the evaluated methods. Three real-world case studies further demonstrate the validity of this recommendation.

This paper concerns a disassembly line balancing problem (DLBP) in remanufacturing that aims to allocate a set of tasks to workstations to disassemble a product. We consider two objectives in the same time, i.e., minimising the number of workstations required and minimising the operating costs. A common approach to such problems is to covert the multiple objectives into a single one and solve the resulting problem with either exact or heuristic methods. However, the appropriate weights must be determined a priori, yet the results provide little insight on the trade-off between competing objectives. Moreover, DLBP problems are proven NP-complete and thus the solvable instances by exact methods are limited. To this end, we formulate the problem into a multi-objective dynamic program and prove the monotonicity property of both objective functions. A backward recursive algorithm is developed to efficiently generate all the non-dominated solutions. The numerical results show that our proposal is more efficient than alternative exact algorithms proposed in the literature and can handle much larger problem instances.

Flight schedule design for a charter airline

Many real-world optimization problems can be modelled as combinatorial optimization problems. Often, these problems are characterized by their large size and the presence of multiple, conflicting objectives. Despite progress in solving multi-objective combinatorial optimization problems exactly, the large size often means that heuristics are required for their solution in acceptable time. Since the middle of the nineties the trend is towards heuristics that “pick and choose” elements from several of the established metaheuristic schemes. Such hybrid approximation techniques may even combine exact and heuristic approaches. In this chapter we give an overview over approximation methods in multi-objective combinatorial optimization. We briefly summarize “classical” metaheuristics and focus on recent approaches, where metaheuristics are hybridized and/or combined with exact methods.


 Allied Indo Coal Jaya is one of the mining companies with types of coal mining materials. Mining methods used by PT. Allied Indo Coal Jaya is an open-pit mining and underground mining method. In the underground mining method, the adding system used is a room and pillar where coal extraction activities are carried out semi-conventionally and detonation. Blasting is carried out to support coal production activities to achieve the targets set by the company. However, the problem faced today is the non-achievement of the production target in Tunnel 9, which is 33 tons of coal while the actual production is 18.70 tons of coal. The non-achievement of production targets due to the geometry of blasting is inadequate for the dismantling of coal with the desired target. Based on the calculation of the dimensions of mine progress, it was found that the coal production yield was 17.03 tons of coal, while for blasting activities using the theory of R. L. Ash, it was found that the blasting result was 12.60 tons of coal. With blasting activities that were able to dismantle 12.60 tons of coal and the number of workers as many as 6 people, a mining profit of Rp.52,435,619.27 was obtained. Increased blasting twice daily and the addition of 8 personnel in Tunnel 9 are the answers to raising coal productivity. The addition of blasting activities and the number of workers can increase coal products to 35.20 tons of coal with a mining profit of Rp. 108,407,142,864.

Multi-compartment vehicles (MCVs) can deliver several product segments jointly. Separate compartments are necessary as each product segment has its own specific characteristics and segments cannot be mixed during transportation. The size and position of the compartments can be adjusted for each tour with the use of flexible compartments. However, this requires that the compartments can be accessed for loading/unloading. The layout of the compartments is defined by the customer and segment sequence, and it needs to be organized in a way that no blocking occurs during loading/unloading processes. Routing and loading layouts are interdependent for MCVs. This paper addresses such loading/unloading issues raised in the distribution planning when using MCVs with flexible compartments, loading from the rear, and standardized transportation units. The problem can therefore be described as a two-dimensional loading and multi-compartment vehicle routing problem (2L-MCVRP). We address the problem of obtaining feasible MCV loading with minimal routing, loading and unloading costs. We define the loading problem that configures the compartment setup. Consequently, we develop a branch-and-cut (B&C) algorithm as an exact approach and extend a large neighborhood search (LNS) as a heuristic approach. In both cases, we use the loading model in order to verify the feasibility of the tours and to assess the problem as a routing and loading problem. The loading model dictates the cuts to be performed in the B&C, and it is used as a repair mechanism in the LNS. Numerical studies show that the heuristic reaches the optimal solution for small instances and can be applied efficiently to larger problems. Additionally, further tests on large instances enable us to derive general rules regarding the influence of loading constraints. Our results were validated in a case study with a European retailer. We identified that loading constraints matter even for small instances. Feasible loading can often be achieved only through minor changes to the routing solution and therefore with limited additional costs. Further, the importance to integrate loading constraints grows as the problem size increases, especially when a heterogeneous mix of segments is ordered.

This paper presents an efficient heuristic approach for scheduling residential smart home appliances. Using available hourly prices for electricity, the starting times of a supplied set of appliances are optimized so that the economic cost of the energy consumed is reduced, while satisfying the operational and peak power constraints. The algorithm schedules appliances one after the other based on a greedy strategy. The heuristic (c.f. exact) approach is taken to reduce the computational burden to a level allowing re-optimization to take place at regular intervals by a modest computing device without specialized software, which could be embedded in a smart meter. The proposed algorithm is evaluated through a preliminary experimental study comparing the obtained costs and computation times with an exact algorithm. Results indicate that the obtained cost was within 5% of the optimal cost, while the computation time reduced by exponential factors.

Leakage power consumption is an increasingly serious problem in very large-scale integration circuits, especially for portable applications. Two novel approaches to leakage power minimization in static complementary metal-oxide-semiconductor circuits that employ input vector control (IVC) are investigated. The authors model leakage effects by means of pseudo-Boolean functions. These functions are linearized and incorporated into an exact (optimal) integer linear programming (ILP) model, called virtual-gate ILP, which analyzes leakage variation with respect to a circuit's input vectors. A heuristic mixed-integer linear programming (MLP) method is also proposed, which has several advantages: it is faster, its accuracy can be quickly estimated, and tradeoffs between runtime and optimality can easily be made. Furthermore, the MLP model also provides a way to estimate a lower bound on circuit leakage current. The proposed methods are used to generate an extensive set of experimental results on leakage reduction. It is shown that average leakage currents are usually 1.25 times the minimum, confirming the effectiveness of IVC. The heuristic MLP approach is shown to be approximately 13.6 times faster than the exact ILP method, whereas finding input vectors whose power consumption is only a few percent above the optimum. In addition, the lower bound estimated by the MLP model is also within a few percent of the optimal value

Exact inference for the logistic regression model is based on generating the permutation distribution of the sufficient statistics for the regression parameters of interest conditional on the sufficient statistics for the remaining (nuisance) parameters. Despite the availability of fast numerical algorithms for the exact computations, there are numerous instances where a data set is too large to be analyzed by the exact methods, yet too sparse or unbalanced for the maximum likelihood approach to be reliable. What is needed is a Monte Carlo alternative to the exact conditional approach which can bridge the gap between the exact and asymptotic methods of inference. The problem is technically hard because conventional Monte Carlo methods lead to massive rejection of samples that do not satisfy the linear integer constraints of the conditional distribution. We propose a network sampling approach to the Monte Carlo problem that eliminates rejection entirely. Its advantages over alternative saddlepoint and Markov Chain Monte Carlo approaches are also discussed.

The paper discusses the main disadvantages of strip and underground mining methods and possibilities of eliminating the disadvantages through introducing a combined technology of coal deposit mining. Combined coal mining technology is the method comprising elements of several geotechnologies, for example, underground and strip mining, as well as, possibly, underwater mining, borehole and other techniques of deposit mining. The combined coal mining technology provides for unified layout for opening, development, production and processing of reserves for the whole LoM on the basis of general technological solutions made in advance. Such complex solutions for opening and development of deposit reserves within the opencast and underground mining contour allows minimizing the volume of openings and reducing the time for commissioning, investment costs, as well as decreasing the costs for aerage, drainage, rock mass hauling and land reclamation. Substantiation of deposit opening options should comprehensively take into account technical, organizational, and economic factors [34–37]. Analysis of the options as exemplified by the Makar’evskoe coal deposit development in Kuzbass allows to conclude that the combined method is promising and promotes increasing optimal volumes of coal production, while reducing the deposit development time by about 15 %, and increase the net present value compared to underground and opencast mining options more than 5 times.

Combinatorial optimization problems have very important applications in information technology, transportation, economics, management, network communication, and other fields. Since the problem size in real-scenario application is in large-scale, the demand for real-time and efficient solving approaches increases rapidly. The traditional exact methods guarantee the optimality of the final solution, but these methods can hardly solve the problem in acceptable time due to extremely high computational costs. Heuristic approaches can find feasible solutions in a limited time, while these approaches cannot meet the demand of solution quality. In recent years, hybrid algorithms based on exact methods and heuristic algorithms show outstanding performance in solving large-scale combinatorial optimization problems. The hybridization not only overcomes the shortcomings from single algorithm but also fully utilizes the search ability for population-based approaches as well as the interpretability in exact methods, which promotes the application of combinatorial optimization in real-world problems. This paper reviews existing studies on hybrid algorithms combining exact method and evolutionary computation, summarizes the characteristics of the existing algorithms, and directs the future research.