Improving performance of open-pit mine production scheduling problem under grade uncertainty by hybrid algorithms

In mines planning, the long-term production scheduling problem (LTPSP) in open-pit mines is considered as a significant issue. It also specifies the distribution of cash flow during the course of the mine-life. Actually, LTPSP is a large-scale optimisation problem including large data-sets, multiple constraints, and uncertainty in the input factors that, has to be solved in a reasonable time. LTPSP, despite the valuable efforts of researchers, has not yet been well resolved. In this paper, hybrid models have been offered by the Lagrangian relaxation (LR) method with meta-heuristic methods, bat algorithm and particle swarm optimisation for solving the LTPSP due to the deterministic assumption and concerning the grade uncertainty. To bring update the Lagrange multipliers, the meta-heuristic algorithms have been applied. In terms of cumulative net present value, average ore grade, and computational time in a 12-year production period, the consequences achieved from the case studies point out that a solution close to optimisation can be presented by the LR-bat algorithm hybrid strategy in comparison with other methods. The results analysis has shown that the proposed method produces a near-optimal solution with a rational time that can be a good suggestion for utilising in the mining industry.

Due to the large size of open-pit mines’ long-term production scheduling (OPMPS) problem in large-scale deposits, it is challenging to solve that problem as the mixed integer linear programming (MILP) model. This study used an approach of the genetic algorithm (GA) to tackle this challenge. So, in a small hypothetical deposit, based on the blocks in the ultimate pit limit and scenarios with 2–6 phases, net present values (NPV) and computational times obtained from the GA and MILP model were compared to evaluate the GA. Also, the GA was applied to a large-scale deposit to determine the efficiency of the GA in real deposits. The maximum NPV was obtained for the four-phase scenario in the hypothetical deposit and the six-phase scenario in the large-scale deposit. Although the GA’s NPV decreased slightly compared to the global optimum solution from the MILP model, the computational time was significantly reduced.

Enhanced physics-informed neural networks with Augmented Lagrangian relaxation method (AL-PINNs)

Dynamic economic dispatch (DED) over multiple time periods is a large-scale coupled spatial-temporal optimization problem. Therefore, the Lagrangian relaxation method has been widely used to split the large-scale optimization problem with coupled structure into several small sub-problems. In order to bring robustness for updating the dual multipliers and yielding convergence without strong assumptions, the augmented Lagrangian relaxation method is introduced in this paper. However, the added penalty term in an augmented Lagrangian function is non-separable, which leads to the difficulty in achieving full decomposition for parallel computation. To address this problem, a diagonal quadratic approximation method is employed to yield an approximated block separation of the non-separable penalty term. Furthermore, the ramp rate constraints are relaxed in this paper, so that the DED model is decomposed into several single-period economic dispatch models that can be efficiently handled in parallel, called the parallel augmented Lagrangian relaxation method. Particularly, the proposed relaxation strategy has a high separability feature which theoretically leads to sound convergence property. Numerical results on the IEEE 118-bus and a practical Polish 2383-bus test system over a different number of time periods show the effectiveness of the proposed method. In addition, the proposed method can be extended to other coupled spatial-temporal scheduling problems in power systems, such as energy storage dispatch.

Hybrid Bat & Particle Swarm Algorithm for optimization of labyrinth spillway based on half & quarter round crest shapes

This study proposes an optimisation method for open pit mines that integrates economic and social impacts. Mine capacity, maximum production scale, mining life, resource endowment, among other factors, are used as intermediate links to associate social impacts with mine production scheduling, leading to the construction of a quantitative model of mining social benefits. A series of nested candidate mining fields (geological optimal pits) are used as chromosome genes to construct a genetic optimisation algorithm for open-pit mine production scheduling based on biological evolution theory, with a catastrophe algorithm incorporated to mitigate premature convergence to local optima during the optimisation search process. The results demonstrate that the economic-social integrated optimisation method can effectively enhance the social benefits of resource exploitation. Moreover, the social utility generated by resource exploitation significantly influences the production plan of open-pit mines, extending the mining life by 10 years and reducing the mining scale by 22.73%, thereby effectively curbing unsustainable exploitation and ensuring resource sustainability.

Optimization studies in high speed turning of Ti-6Al-4V

An Open-Pit Production Scheduling (OPPS) problem focuses on specifying block production scheduling to achieve the highest possible Net Present Value (NPV). This paper presents a new mathematical model for OPPS under uncertainty. To this end, a robust box and ellipsoidal counterpart approach was used. The proposed method was implemented in a hypothetical model. A Genetic Algorithm (GA) and an exact mathematical modeling approach were used to solve the model. It was shown that the scheduling of deterministic and robust models in various conditions is different. Considering the type of robust counterparts, different production plans under various conditions were scheduled. Furthermore, the price of robustness was determined for various levels of conservation.

The increasing adoption of solar energy as a clean and sustainable power source has intensified research efforts toward developing more efficient photovoltaic (PV) cells. These cells exhibit nonlinear characteristics that are significantly influenced by variations in irradiance and temperature. Accurate estimation of PV model parameters plays a crucial role in maximizing performance, particularly via precise maximum power point (MPP) tracking. This paper presents a new hybrid metaheuristic algorithm that combines the global exploration capability of the Bat Algorithm (BA) with local exploitation efficiency of the Crow Search Algorithm (CR) to optimize PV parameter estimation. The proposed approach is tested using Single-Diode (SDM), Double-Diode (DDM), and Triple-Diode (TDM) models based on the RTC France dataset. The hybrid model demonstrates better convergence behavior and robustness compared to conventional approaches. Qualitatively, it effectively manages parameter uncertainty; quantitatively, it achieves RMSE values of 0.00077299 (SDM), 0.0008215 (DDM), and 0.0008068 (TDM), outperforming traditional algorithms such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).

One of the challenging problems in the field of structural engineering is designing cost-efficient structures with improved performance subject to earthquake loading conditions. Structural optimization procedures can be effectively employed for performance-based optimal design of structures. In this study, bat algorithm (BA) is utilized to implement performance-based optimum seismic design of steel dual braced frames for various performance levels. The required structural seismic responses are evaluated by performing nonlinear pushover analysis. The results found by BA are then compared with those of obtained by other popular meta-heuristics such as firefly algorithm (FA) and particle swarm optimization (PSO) to provide an insight about its computational performance. Two numerical examples are presented and the numerical results reveal that the BA outperforms PSO and FA.

The corona virus search optimizer for solving global and engineering optimization problems

Most optimization problems in engineering are nonlinear, with many constraints. Consequently, finding optimal solutions to such nonlinear problems requires efficient optimization methods. Most of the methods used so far are gradient-based methods. In gradient-based methods, the objective function must be differentiable, and the search for the optimum solution usually starts with a guess-point. For multimodal objectives, the search will likely get stuck at a local optimum. Nowadays, new metaheuristic methods are being developed for solving nonlinear optimization problems. Metaheuristic methods neither require a guess-point nor a derivative of the objective function. Metaheuristic methods, called Bat Algorithm and Spiral Dynamic Method, have been developed for solving optimization problems. Each of the methods has the strength to solve the problem. We propose combining Bat Algorithm (BA) and Dynamic Spiral Method (DSM) for solving mixed integer optimization. The bat Algorithm is used for the exploration stage to find some candidate solutions. Meanwhile, the dynamic spiral method is used in local search to find the best optimum solution. The result obtained by Bat Algorithm-Dynamic Spiral Method (BA-DSM) were more effective than the standard Bat Algorithm in solving the problem.

Production planning and scheduling problems emphasize the need for the availability of management tools that can help to assure proper service levels to customers, maintaining, at the same time, the production costs at acceptable levels and maximizing the utilization of the production facilities. In this case, a production scheduling problem that arises in the context of the activities of a company dedicated to the manufacturing of furniture for children and teenagers is addressed. Two bicriteria metaheuristic procedures are proposed to solve the sequencing problem in a production equipment that constitutes the bottleneck of the production process of the company. The production scheduling problem can be characterized as a general flow shop with sequence dependant setup times and additional inventory constraints. Two objectives are simultaneously taken into account when the quality of the candidate solutions is evaluated: the minimization of completion time of all jobs, or makespan, and the minimization of the total flow time of all jobs. Both procedures are based on a local search strategy that responds to the structure of the simulated annealing metaheuristic. In this case, both metaheuristic approaches generate a set of solutions that provides an approximation to the optimal Pareto front. In order to evaluate the performance of the proposed techniques a series of experiments was conducted. After analyzing the results, it can be said that the solutions provided by both approaches are adequate from the viewpoint of the quality as well as the computational effort involved in their generation. Nevertheless, a further refinement of the proposed procedures should be implemented with the aim of facilitating a quasi‐automatic definition of the solution parameters.

Power versus voltage curves of partial shading photovoltaic (PV) systems contain several local peaks (LPs) and one global peak (GP). Most conventional maximum power point tracker (MPPT) techniques may not follow the GP under partial shading conditions (PSC). The use of metaheuristic techniques such as the bat algorithm (BA) and particle swarm optimization (PSO) can overcome these obstacles. All problems inherent in the using of BA as MPPT of PV systems has been discussed and solved in this paper. The first problem is the random initial values of bats that may cause premature convergence. Therefore, the initial values of bats were modified to be close to the anticipated positions of peaks to reduce the convergence time and improve the chance of capturing the GP. The second problem occurs when shading pattern changes the value and position of the GP which is not configurable because all bats are concentrated at the previous GP; this can be resolved by BA re-initialization. The the third problem is the GP memorized in the execution of the BA code forces the PV system to work at the duty ratio of the highest GP ever seen, which may not be the real GP. This problem is solved by updating the memorized GP. This paper also proposes a new criterion for selecting the optimal swarm size against number of peaks to reduce the convergence time and improve the chance of capturing the GP. To the authors' knowledge, most of these problems inherent in the BA have hitherto not been addressed in the literature. The simulation and experimental results obtained from the proposed modified BA (MBA) with re-initialization have been compared to the PSO and grey wolf optimization (GWO) techniques which show the superiority of using MBA strategy in the MPPT of partial shading PV systems.

ABSTRACTSimultaneous stochastic optimisation manages risk and capitalises on the unique interactions that occur in a mining complex, where materials are transferred between mines, processors, stockpiles, and waste facilities to achieve a marketable product. Typically, when optimising the production schedule, the primary focus is to deliver valuable products to the market. However, this tends to ignore the environmental and economic impact of simplifying waste management requirements, including the storage and disposal of waste material. Stricter regulations and engineering requirements are transforming past mining practices to develop more sustainable operations. These transformations increase the financial cost of waste management and identify the requirement to integrate waste management into the production schedule. Additionally, misrepresenting the material uncertainty and variability associated with the amount of waste produced can impact, both, the stakeholders and the profitability of a mining complex. In this case study, a simultaneous stochastic optimisation approach is applied in a gold mining complex that integrates waste management into the long-term production schedule. The resulting schedule leads to a 6% increase in the net present value when compared to a conventional approach, while minimising the likelihood of deviating from production targets and ensuring permit constraints are satisfied.