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On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem

Ishara Hewa Pathiranage, Aneta Neumann

Year: 2026Venue: arXiv preprintArea: cs.NEType: PreprintEmbeddings: 61

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Summary

This paper addresses the Dynamic Chance-Constrained Open-Pit Mine Scheduling Problem (DCC-OPMSP) by proposing a bi-objective evolutionary formulation that maximizes expected profit while minimizing risk. To handle dynamic changes in resource capacities, the authors introduce a diversity-based change-response mechanism integrated into four multi-objective evolutionary algorithms (MOEAs), demonstrating superior performance over re-evaluation-based baselines across various mining instances.

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DCC-OPMSP · problem · 100%MOEA/D · algorithm · 100%NSGA-II · algorithm · 100%SMS-EMOA · algorithm · 100%SPEA2 · algorithm · 100%MineLib · dataset · 95%

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MOEA/D → isextendedby → diversity-based change response mechanism

confidence 90% · We integrate this mechanism into four MOEAs... resulting in MOEA/D-DIV

DCC-OPMSP → solvedby → MOEA/D

confidence 90% · We evaluate the effectiveness of this mechanism across four multi-objective evolutionary algorithms

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Abstract

Abstract:Open-pit mine scheduling is a complex real world optimization problem that involves uncertain economic values and dynamically changing resource capacities. Evolutionary algorithms are particularly effective in these scenarios, as they can easily adapt to uncertain and changing environments. However, uncertainty and dynamic changes are often studied in isolation in real-world problems. In this paper, we study a dynamic chance-constrained open-pit mine scheduling problem in which block economic values are stochastic and mining and processing capacities vary over time. We adopt a bi-objective evolutionary formulation that simultaneously maximizes expected discounted profit and minimizes its standard deviation. To address dynamic changes, we propose a diversity-based change response mechanism that repairs a subset of infeasible solutions and introduces additional feasible solutions whenever a change is detected. We evaluate the effectiveness of this mechanism across four multi-objective evolutionary algorithms and compare it with a baseline re-evaluation-based change-response strategy. Experimental results on six mining instances demonstrate that the proposed approach consistently outperforms the baseline methods across different uncertainty levels and change frequencies.

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ON THE USE OF EVOLUTIONARY OPTIMIZATION FOR THE DYNAMIC CHANCE CONSTRAINED OPEN-PIT MINE SCHEDULING PROBLEM Ishara Hewa Pathiranage Machine Learning and Optimisation, School of Computer Science and Information Technology, Adelaide University, Adelaide, Australia Aneta Neumann Machine Learning and Optimisation, School of Computer Science and Information Technology, Adelaide University, Adelaide, Australia ABSTRACT Open-pit mine scheduling is a complex real-world optimization problem that involves uncertain economic values and dynamically changing resource capacities. Evolutionary algorithms are partic- ularly effective in these scenarios, as they can easily adapt to uncertain and changing environments. However, uncertainty and dynamic changes are often studied in isolation in real-world problems. In this paper, we study a dynamic chance-constrained open-pit mine scheduling problem in which block economic values are stochastic and mining and processing capacities vary over time. We adopt a bi-objective evolutionary formulation that simultaneously maximizes expected discounted profit and minimizes its standard deviation. To address dynamic changes, we propose a diversity-based change response mechanism that repairs a subset of infeasible solutions and introduces additional feasible solutions whenever a change is detected. We evaluate the effectiveness of this mechanism across four multi-objective evolutionary algorithms and compare it with a baseline re-evaluation–based change-response strategy. Experimental results on six mining instances demonstrate that the pro- posed approach consistently outperforms the baseline methods across different uncertainty levels and change frequencies. Keywords Open-pit mine scheduling · Dynamic optimization · Multi-objective evolutionary algorithms · Chance constraints 1 Introduction The open-pit mine scheduling problem (OPMSP) is a large-scale combinatorial optimization problem that determines the optimal sequence of block extraction from a mining deposit to maximize the net present value (NPV), while satisfying geological and operational constraints. Over the years, OPMSP has been addressed using a variety of optimization approaches, including integer linear programming methods [1], heuristics [2], metaheuristics such as differential evolution (DE) [3], and evolutionary algorithms [4], as well as hybrid approaches [5]. However, real-world mining operations operate under multiple sources of uncertainty and dynamic changes, includ- ing stochastic ore grades, commodity price fluctuations, equipment downtime, weather conditions, and time-varying mining and processing capacities. Ignoring these factors can lead to infeasible or suboptimal production schedules, reduced economic returns, and compromised operational safety [6, 7]. Several approaches have been proposed to address OPMSP under uncertainty, including exact methods [6, 8] and metaheuristic techniques such as particle swarm optimization [9], differential evolution [10, 11], evolutionary algo- rithms [12], and hybrid methods [5]. Nevertheless, to the best of our knowledge, no prior work has simultaneously addressed stochastic profits and dynamically changing resource capacities within the OPMSP framework. Considering both aspects is essential to avoid operational bottlenecks, such as mill overloads or deviations between planned and arXiv:2604.13385v1 [cs.NE] 15 Apr 2026 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem actual ore grades. Addressing these issues early in the planning process ensures the development of robust, efficient, and operationally feasible mine plans. Evolutionary algorithms (EAs) are particularly effective for stochastic and dynamic optimization problems due to their flexibility and robustness [13, 14, 15, 16, 17]. To handle uncertainty explicitly, chance-constraints [18] can be used in optimization problems, ensuring that stochastic constraints are satisfied with a predefined confidence level α. In this context, multi-objective evolutionary algorithms (MOEAs) are particularly effective, as they enable the simultaneous optimization of multiple stochastic components, such as the expected value and variance [19, 20]. In this paper, we investigate the dynamic chance-constrained open-pit mine scheduling problem with stochastic profits and dynamically changing resource capacities. 1.1 Related Work The OPMSP has been extensively studied due to its economic importance and computational complexity. For instance, a DE-based approach was proposed in [3] for solving the deterministic OPMSP by reducing problem dimensionality via a single-period formulation. This method incorporates feasibility repair during reproduction and a local search method, achieving strong performance on instances with up to 112,687 blocks. While early studies typically assume deterministic geological models, more recent work adopts ensemble-based representations that capture spatial grade uncertainty through multiple equi-probable realizations generated via geostatistical simulation. Geological uncertainty has been explicitly modeled using ensemble block models with multiple realizations, often combined with chance constraints to limit downside risk [7, 12, 21]. For example, Xie et al. [11] formulated the stockpile blending problem under grade uncertainty as a single-objective nonlinear optimization problem with chance constraints, solved using DE with customized repair operators. Similarly, Stimson et al. [12] applied a single-objective EA to the chance-constrained OPMSP, where uncertainty is incorporated by discounting profits across multiple real- izations. However, both approaches rely on a fixed confidence level, α. Evolutionary algorithms have also shown strong performance on dynamic optimization problems. Dynamic knapsack, travelling thief problem and submodular optimization problems were studied in [17, 22, 23, 24, 25, 26], demonstrat- ing that MOEAs often outperform single-objective methods. Theoretical analysis of dynamic graph coloring with incremental changes [14] showed that EA-based re-optimization is more efficient than restarting from scratch. In real-world applications, NSGA-I and its variants have been successfully applied to dynamic hydro-thermal power scheduling [27], effectively tracking changing Pareto-optimal fronts. Only a limited number of studies address stochastic and dynamic optimization simultaneously using EAs. In [13], a bi-objective dynamic chance-constrained knapsack problem was introduced, where item weights follow independent uniform distributions and probabilistic constraints are estimated using Chebyshev’s inequality and the Chernoff bound. The results showed that MOEAs are particularly effective for dynamic chance-constrained optimization, although separate runs are required for different confidence levels. Hewa Pathiranage et al. [15] addressed this limitation using a three-objective formulation, which was independent of the chosen confidence level. Furthermore, Perera and Neumann [16] studied both bi-objective and three-objective formulations with stochastic profits using GSEMO with standard and sliding-window parent selection, and multi-objective approaches [28] showing clear advantages of these approaches. Recent work on stochastic and dynamic multiple knapsack problems [29] further demonstrates the effectiveness of MOEAs. These studies motivate the application of MOEAs to the dynamic chance-constrained OPMSP considered in this paper. 1.2 Our Contribution To the best of our knowledge, this is the first work to investigate the chance-constrained OPMSP in dynamic environ- ments using MOEAs. We assume that the economic value of each block follows a normal distribution, while mining and processing capacities vary randomly over time. To address this problem, we adopt a bi-objective formulation that simultaneously maximizes the expected net present value and minimizes its standard deviation. This formulation aims to find Pareto-optimal solutions that balance expected profit and risk, subject to chance constraints. By explicitly incorporating risk as a separate objective, the proposed approach eliminates the need to predefine a confidence level during optimization, enabling MOEAs to generate high-quality solutions across a range of confidence levels α in a single run. To handle dynamic changes in resource capacities, we introduce a diversity-increasing based change-response mech- anism. When a change is detected, a subset of infeasible solutions is repaired using hyper-mutation, and additional randomly generated feasible solutions are inserted to maintain population diversity. This mechanism is integrated into four MOEAs, mutation-only variants of MOEA/D, NSGA-I, SMS-EMOA, and SPEA2, resulting in MOEA/D-DIV, 2 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem NSGA-I-DIV, SMS-EMOA-DIV, and SPEA2-DIV, respectively. The proposed approach is evaluated against corre- sponding re-evaluation–based baseline algorithms, MOEA/D-RE, NSGA-I-RE, SMS-EMOA-RE, and SPEA2-RE, which rely solely on re-evaluation after a change occurs. Experimental results across six mining instances show that the proposed method consistently outperforms the baselines under different uncertainty levels and dynamic change frequencies. The remainder of the paper is organized as follows. Section 2 presents the proposed method for solving the open-pit mine scheduling problem with stochastic profits and dynamic resource constraints. Section 3 describes the multi- objective evolutionary algorithms we used and the experimental setup. Next, Section 4 presents and analyzes the results. Finally, Section 5 concludes the paper with key findings. 2 Open Pit Mine Scheduling Problem with Stochastic Profits and Dynamic Resource Constraints This section defines the dynamic chance-constrained OPMSP, its bi-objective fitness function, and the dynamic change-response mechanism. 2.1 Problem Definition We consider a dynamic chance-constrained open-pit mine scheduling problem, referred to as the DCC-OPMSP, in which block economic values are stochastic, and resource capacities vary over time. LetB denote the set of mineable blocks, andT =1,...,T denote the planning periods. A schedule is represented by binary decision variables x = x t b | b ∈ B, t ∈ T, where x t b = 1 if block b is mined in period t, and x t b = 0 otherwise. LetP denote the set of precedence constraints, where (a,b)∈P means that block a must be mined before block b. Let R be the set of resources. For each resource r ∈ R, block b consumes r b units, and R t r denotes the available capacity of resource r in period t. Each block b ∈ B is associated with a stochastic profit p b , modeled as a normally distributed random variable, p b ∼ N (μ b ,σ 2 b ), where μ b and σ 2 b denote the expected value and variance of block b, respectively. Block profits are spatially correlated, reflecting geological dependencies within the orebody. A mining schedule is represented using binary decision variables x t b , where x t b = 1 if block b is extracted in period t, and x t b = 0 otherwise. For a given solution x, the total discounted NPV is a random variable defined as p(x) = P t∈T 1 (1+d) t P b∈B p b x t b , where d denotes the discount rate per annum. Since p(x) is a linear combination of (possibly correlated) normally distributed random variables, it also follows a normal distribution. The DCC-OPMSP is formulated as follows: Maximize P, Subject toPr(p(x)≥ P )≥ α,(1) t X τ=1 x τ a ≥ t X τ=1 x τ b , ∀(a,b)∈P, t∈T ,(2) X t∈T x t b ≤ 1, ∀b∈B,(3) X b∈B r b x t b ≤ R t r , ∀r ∈R, t∈T ,(4) x t b ∈0, 1, ∀b∈B, t∈T .(5) The objective is to find a schedule x such that the probability of achieving a discounted NPV of at least P is no less than a confidence level α. Constraint (1) enforces the chance constraint, while Constraints (2)–(4) ensure prece- dence feasibility, single extraction of blocks, and compliance with mining and processing capacity limits, respectively. Constraint (5) ensures the binary nature of the decision variables. We assume α∈ [1/2, 1) in this paper. In addition to stochastic block profits, we incorporate dynamic changes in resource capacities over time. Every τ fitness evaluations, we randomly select a subset of periods and apply capacity variations. For each selected period, we sample a scaling factor γ ∼ U (1− η, 1 + η) and scale the baseline capacities of all resources in that period by γ. Figure 1 illustrates an example of such dynamic capacity variations for the Newman1 instance [30], where mining 3 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem Figure 1: Dynamic changes in mining and processing capacities over six periods under 30 dynamic changes. Each subplot represents one period, showing deviations from the baseline capacity limits (dashed lines) for the Newman1 instance. and processing capacities are shown in blue and orange, respectively. Solid lines represent modified capacity limits following dynamic changes, while dashed lines indicate the baseline capacities. 2.2 Chance-Constrained Profit Modeling We now describe how the chance constraint in Constraint (1) is modeled and evaluated. We adopt the chance- constrained optimization framework for the knapsack problem with normally distributed profits proposed in [31], which allows the probabilistic constraint to be reformulated as a deterministic, risk-adjusted objective. Accordingly, the objective function takes the following form: f (x) =E[p(x)]− K α · p Var[p(x)],(6) where K α = Φ −1 (α) denotes the α-quantile of the standard normal distribution. The expected discounted profit is given by E[p(x)] = X t∈T 1 (1 + d) t X b∈B μ b x t b . LetB ore ⊆ B denote the set of ore blocks, i.e., blocks that generate stochastic processing profit. Since each block is extracted at most once and its uncertainty is block-specific, the variance of the total discounted profit is defined as Var[p(x)] = X t∈T 1 (1 + d) 2t Var t (x), where Var t (x) denotes the variance of the total profit obtained in period t. Following [12], the period-wise variance is computed as Var t (x) = X b∈B ore σ 2 b x t b + max     0, X b,b ′ ∈B ore b̸=b ′ Cov(b,b ′ )x t b x t b ′     ,(7) where σ 2 b denotes the variance of the profit of ore block b, and Cov(b,b ′ ) denotes the covariance between the profits of ore blocks b and b ′ . The variance and covariance terms are estimated using ensemble-based profit realizations following [12]. To remain consistent with the modeling assumptions in [12] and to avoid underestimating risk due to sampling noise, negative covariance values are truncated to zero. 4 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem Algorithm 1 Dynamic Change Response Mechanism with Diversity Increase Require: Population P of size N , mutation operator M 1: P ←Evaluate(s)| s∈ P 2: F ←s∈ P | v(s) = 0, I ← P \ F 3: if|F| < N then 4: S ← RandomSelect(I, min0.2N,|I|) 5: F ← F ∪Repair(s,M )| s∈ S 6: k ← min0.2N, N −|F| 7: F ← F ∪s 1 ,...,s k where s i ∼ RandomFeasible 8:while|F| < N do 9: F ← F ∪arg min u∈I v(u) 10:end while 11: end if 12: P ← F 2.3 Bi-Objective Fitness Function We employ a bi-objective formulation for the DCC-OPMSP, defined as g 2D (x) = f 1 (x),f 2 (x) ,(8) where f 1 (x) maximizes the expected discounted net present value, while f 2 (x) minimizes its standard deviation. The objectives are defined as follows. f 1 (x) = E[p(x)], if v(x) = 0, −v(x),otherwise, (9) f 2 (x) = p Var[p(x)],if v(x) = 0, Var[p(x)] + M · v(x), otherwise, (10) whereE[p(x)] denotes the expected discounted NPV and Var[p(x)] is the total variance of the discounted NPV across all periods. The constant M is a large penalty, and v(x) represents the total penalty due to resource vi- olations. The total violation is computed as v(x) = P T t=1 v t (x), where the violation in period t is defined as v t (x) = max r∈R max 0, y t r − R t r , where y t r = P b∈B r b x t b denotes the usage of resource r in period t and R t r is its corresponding capacity limit. This bi-objective formulation avoids fixing a confidence level α during optimization because both objectives, f 1 (x) and f 2 (x), are independent of α. As a result, the evolutionary algorithm explores a range of risk-return trade-offs in a single run. After optimization, we can evaluate the risk-adjusted discounted objective value (Eq. (6)) at different confidence levels and select appropriate schedules without re-optimizing. 2.4 Dynamic Change Response Mechanism with Diversity Increase We modify the resource capacities of a randomly selected subset of periods every τ iterations. When a change oc- curs, the population is re-evaluated under the updated constraints. However, re-evaluation alone is often insufficient, especially when the population has already converged to locally optimal or infeasible regions [32]. We propose a diversity-increasing change response mechanism for the DCC-OPMSP (Algorithm 1). After a dynamic change, the population is re-evaluated and partitioned into a feasible set F and an infeasible set I . If|F| < N , feasi- bility and diversity are restored in two steps. First, up to 20% of the population is selected from I for repair, bounded by |I|, using the hypermutation-based operator (Algorithm 2). In this process, solutions are accepted based on fea- sibility and lexicographic comparison, prioritizing f 1 over f 2 , or by minimizing constraint violation when infeasible. Second, up to 20% of the population is replaced with randomly generated feasible solutions, bounded by the remaining capacity N −|F|. 3 Multi-Objective Evolutionary Algorithms and Experimental Setting In this section, we present the multi-objective evolutionary algorithms used and the experimental setting. 5 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem Algorithm 2 Repair Mechanism with Hypermutation Require: Initial solution s, mutation operator M , mutation probability P m 1: s best ← s, P m ← 2P m 2: while stopping criterion not met do 3: y ← Evaluate(M (s best )) 4:if v(y) = 0 and v(s best ) > 0∨ (f 1 (y),f 2 (y))≺ lex (f 1 (s best ),f 2 (s best )) then 5: s best ← y 6:else if v(y) > 0 and v(y) < v(s best ) then 7: s best ← y 8:end if 9: end while 10: return s best Table 1: Summary of problem instances from MineLib [30]. InstanceTBlocksPredec.Vars.Res.Disc. Newman161 0603 9226 36020.08 Zuck Small209 400145 640188 00020.10 KD1214 153219 778169 83610.15 Zuck Medium1529 2771 271 207439 15520.10 P4HD1040 947738 609409 47020.00 Marvin2053 271650 6311 065 42020.10 3.1 Multi-Objective Evolutionary Algorithms We evaluate the proposed DCC-OPMSP using four widely used multi-objective evolutionary algorithms: the Multi- Objective Evolutionary Algorithm based on Decomposition (MOEA/D) [33], the Non-dominated Sorting Genetic Algorithm I (NSGA-I) [34], the S-Metric Selection Evolutionary Multi-Objective Algorithm (SMS-EMOA) [35], and the Strength Pareto Evolutionary Algorithm 2 (SPEA2) [36]. These algorithms have different selection and diver- sity preservation mechanisms and are commonly used as baselines in multi-objective optimization under uncertainty and dynamic environments. MOEA/D decomposes the multi-objective problem into scalar subproblems using a set of weight vectors. Each solu- tion is associated with a weight vector, and neighborhoods are defined based on the distances between weight vectors. We use the Tchebycheff aggregation function g te (x | λ,z ∗ ) = max i λ i |f i (x)− z ∗ i |, where λ = (λ 1 ,...,λ m ) is the weight vectors, satisfying λ i ≥ 0 and P m i=1 λ i = 1, f i (x) denotes the i-th objective function, and z ∗ denotes the current reference (ideal) point. NSGA-I maintains a population of size N and applies non-dominated sorting and crowding distance to rank solutions in the population. At each generation, an offspring population of size N is generated using binary tournament selection and mutation, and the best N solutions from the combined parent and offspring populations are selected. SPEA2 maintains a population and an external archive of non-dominated solutions. Fitness values are computed using dominance strength and a density estimate based on the k-th nearest neighbor. The archive is updated at each generation to preserve high-quality and well-distributed solutions. SMS-EMOA directly maximizes the hypervolume indicator. At each iteration, one offspring solution is generated and inserted into the population, and the solution with the smallest hypervolume contribution is removed. For dynamic environments, we extend each algorithm with the proposed diversity-based change response mechanism, resulting in MOEA/D-DIV, NSGA-I-DIV, SMS-EMOA-DIV, and SPEA2-DIV. As dynamic baselines, we also con- sider a re-evaluation-based change-response method, denoted as MOEA/D-RE, NSGA-I-RE, SMS-EMOA-RE, and SPEA2-RE. 3.2 Experimental Setting We use six standard benchmark instances based on real-world mining projects and simulated data from the MineLib library [30]. Specifically: Newman1, Zuck Small, Zuck Medium, Marvin are conceptually simulated mines, KD represents a copper deposit in Arizona, USA, and P4HD is a gold and copper deposit located in Nevada, USA. Table 1 summarizes the main characteristics of these instances. 6 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem We model the block economic values as normally distributed random variables, consistent with prior work [12, 37]. Geological uncertainty is represented using 50 spatially correlated ensemble realizations, indexed by e ∈ E = 1,..., 50. For the Newman1 and Marvin instances, we generate grade ensembles to represent uncertainty. For the remaining instances, where explicit grade data is unavailable, we generate ensemble profit realizations p be for each block b∈B and ensemble member e∈E . The standard deviation of each block profit distribution is set to 20% of its mean value. Chance constraints are evaluated at confidence levels α∈0.60, 0.90, 0.99. In dynamic settings, we consider different numbers of dynamic changes during optimization, ν ∈20, 10, 5, 2, where larger values of ν correspond to more frequent changes. Dynamic changes are introduced periodically every τ fitness evaluations, where τ is determined by the total evaluation budget E max as τ = E max /ν. The magnitude of each dynamic change is controlled by η = 0.4 through the scaling factor γ. We set the population size to 20 for all algorithms. Following [11], we allocate 10,000 fitness evaluations per run. We use a greedy–randomized heuristic for initial feasible solution generation that assigns high-value blocks and their predecessors to earlier periods while respecting precedence and resource constraints, and then improve it using a domain-specific period swap mutation with probability P m = 0.1 that reassigns blocks across periods, favoring early extraction of ore and delayed removal of waste, without violating feasibility [37]. For MOEA/D-RE and MOEA/D-DIV, we use the neighborhood size 8, neighborhood selection probability 0.9, and replacement of up to 12 neighboring solutions per iteration. NSGA-I-RE, NSGA-I-DIV, SPEA2-RE, and SPEA2- DIV employ equal-sized parent and offspring populations, while SMS-EMOA-RE and SMS-EMOA-DIV generate a single offspring per iteration. We evaluate the performance of algorithms using the offline error, which measures the deviation between the best so- lution found after each change and the deterministic upper bound p(x ∗ ), obtained by solving the relaxed deterministic OPMSP using the Gurobi Optimizer [38]. For each change i, let x i denote the best solution obtained after the i-th change. If x i is feasible, the offline error is defined as e i = p(x ∗ )− p(x i ). Otherwise, we penalize infeasibility by setting e i = p(x ∗ )+v(x i ), where v(x i ) is the total resource-violation measure defined in Section 2. The overall offline error is computed as E = 1 ν P ν i=1 e i . We use the Kruskal–Wallis test with a 95% confidence level and Bonferroni post-hoc correction [39] to evaluate the statistical significance. 4 Experimental Results This section evaluates the proposed change response mechanism on the DCC-OPMSP against re-evaluation baselines. Tables 2 and 3 present the mean, standard deviation, and statistical comparisons of offline error across six mining instances under stochastic and dynamic settings. Lower mean offline error values correspond to better performance, indicating that the solutions achieve profits closer to the optimal profit p(x i ∗ ). All algorithms with the diversity-based change response method (-DIV) consistently show lower mean offline error than their baseline counterparts (-RE), indicating that they adapt more effectively to the changes. This suggests that re-evaluation-based algorithms often struggle to recover feasibility quickly after a change, particularly when dynamic changes are frequent. For all settings, it is shown that when the confidence level of the chance constraint becomes tighter, the offline error increases. Higher confidence levels restrict feasible solutions, requiring more risk-averse extraction sequences. Therefore, the best obtained profit decreases, which tends to increase the offline error. When ν = 20, MOEA/D-DIV outperforms other algorithms with a diversity-based mechanism for all the mining instances, while SPEA2-DIV underperforms other -DIV algorithms. However, when ν = 2, almost all the -DIV variants perform similarly. In this setting, MOEA/D-RE also performs similarly to MOEA/D-DIV for the Zuck Small instance. Overall, the offline error decreases as the number of dynamic changes ν decreases, since less frequent changes allow the algorithms more time to adapt and converge to feasible solutions. Additionally, Table 3 reports the statistical comparison of total offline error for all eight algorithms on the Newman1, P4HD, and Marvin instances under different confidence levels and dynamic change frequencies. Pairwise statistical tests confirm that the diversity-based variants (–DIV) significantly outperform their corresponding re-evaluation-based baselines (–RE). Similar performance trends are observed for the remaining mining instances. Our results indicate that the diversity-based method significantly outperforms the corresponding re-evaluation–based baselines across different frequencies of dynamic changes and confidence levels in mining instances with up to 53,271 blocks. Moreover, the proposed bi-objective formulation produces a set of solutions for any confidence level within the considered range in a single run. As a result, solutions for new confidence levels can be obtained directly from the same non-dominated set without requiring additional optimization runs. Overall, these findings demonstrate that the proposed bi-objective formulation and the dynamic diversity-based change response mechanism are well-suited for large-scale open-pit mine scheduling in stochastic and dynamic environments. 7 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem Table 2: Mean and standard deviation of offline error (×10 6 ) under different dynamic change frequencies (ν) and confidence levels (α). The best mean across all algorithms is highlighted in gray, and pairwise comparisons between (–RE) and (–DIV) variants are highlighted in bold. Inst.να MOEA/D-RE (1) MOEA/D-DIV (2) NSGA-I-RE (3) NSGA-I-DIV (4) SPEA2-RE (5) SPEA2-DIV (6) SMS-EMOA-RE (7) SMS-EMOA-DIV (8) meanstdmeanstdmeanstdmeanstdmeanstdmeanstdmeanstdmeanstd Newman1 2 0.607.031.120.740.0512.880.001.140.0112.880.011.150.0212.880.001.140.01 0.907.611.101.410.0513.210.001.800.0113.210.011.810.0213.210.001.810.01 0.998.191.082.080.0513.550.002.470.0113.550.002.480.0213.550.002.480.01 5 0.6011.661.710.840.0415.370.011.260.0119.990.001.560.3015.370.011.250.01 0.9012.161.67 1.500.0415.640.011.920.0120.120.002.220.3015.640.011.910.01 0.9912.661.632.170.0415.910.012.580.0120.260.002.890.3015.910.012.580.01 10 0.6017.321.180.930.0415.410.021.360.0119.660.862.180.5815.410.021.350.01 0.9017.671.161.590.0415.680.022.020.0119.800.842.830.5715.670.022.010.01 0.9918.031.132.260.0415.940.022.680.0119.940.813.490.5715.940.022.680.01 20 0.6020.190.610.950.0516.430.401.350.0217.620.462.330.3816.510.281.340.01 0.9020.460.591.620.0516.670.392.010.0217.830.452.980.3816.740.272.000.01 0.9920.720.572.290.0516.910.382.670.0218.030.443.640.3716.980.262.660.01 Zuck Small 2 0.6027.510.7927.460.7430.210.4930.190.4430.090.5330.320.2830.090.4430.250.46 0.9031.260.7931.210.7433.960.4933.940.4433.840.5334.070.2733.840.4434.000.46 0.9935.050.7935.000.7337.750.4937.720.4337.620.5337.860.2737.630.4337.780.46 5 0.60461.9036.5029.280.99542.780.5630.260.43542.560.5332.9611.73542.580.5430.240.33 0.90463.8536.2933.030.99544.280.5634.010.42544.060.5336.7111.70544.080.5433.990.33 0.99465.8236.0836.820.98545.790.5637.810.42545.580.5340.5011.67545.600.5437.780.33 10 0.60611.9127.7029.360.47702.660.4630.130.20702.780.4151.2825.98697.2720.5930.210.23 0.90613.2827.5333.080.46703.410.4633.850.20703.530.4154.9425.90698.0520.4933.940.23 0.99614.6727.3636.830.46704.170.4637.610.20704.290.4158.6325.83698.8320.4037.700.23 20 0.60693.0112.8430.200.33749.147.3630.580.18750.4810.15155.0322.83750.6010.3430.590.19 0.90694.0712.77 33.920.33749.697.3234.300.18751.0310.11158.3822.75751.1510.2934.320.19 0.99695.1512.6937.680.33750.267.2938.060.18751.5910.06161.7722.68751.7010.2538.070.19 KD 2 0.60111.056.9958.130.62237.340.1059.190.20237.380.0859.170.21237.350.1059.110.13 0.90112.226.9759.390.62237.970.1060.450.20238.010.0860.430.21237.980.1060.370.13 0.99113.396.9660.660.62238.600.1061.720.20238.640.0861.700.21238.610.1061.640.13 5 0.60214.508.6461.551.09339.230.0459.844.99339.240.0460.416.16339.230.0458.220.07 0.90215.428.6262.791.08339.480.0461.084.98339.490.0461.656.15339.480.0459.470.07 0.99216.358.5964.031.08339.730.0462.344.98339.750.0462.916.14339.730.04 60.730.07 10 0.60277.3313.3659.480.57375.850.0391.8622.47375.850.0394.5618.56375.840.03 57.800.10 0.90278.1013.3160.720.57375.970.0393.0422.43375.970.0395.7418.52375.970.0359.050.10 0.99278.8813.2661.970.57376.100.0394.2422.38376.100.0396.9318.48376.100.0360.310.10 20 0.60295.9220.0760.050.24340.190.06131.9432.13340.180.08134.6624.73340.160.0659.180.06 0.90296.6420.0261.290.24340.440.06133.0432.06340.430.08135.7724.68340.410.0660.430.06 0.99297.3619.9762.550.23340.700.06134.1631.99340.690.07136.8824.63340.670.06 61.690.06 Zuck Medium 2 0.60384.191.36 85.431.99384.760.9886.441.58384.690.8388.111.76385.000.9686.491.86 0.90385.411.35 87.781.98385.980.9888.791.58385.920.8390.451.76386.210.9588.841.85 0.99386.641.3490.151.97387.220.9791.161.57387.160.8392.821.75387.440.9491.221.85 5 0.60585.000.4788.591.05586.370.4489.501.20586.510.44120.2554.00586.280.5389.311.10 0.90585.490.4790.971.05586.860.4491.881.19586.990.44122.5253.83586.770.5391.681.09 0.99585.980.4793.361.04587.350.4394.281.19587.490.44124.8253.67587.260.5394.081.09 10 0.60651.440.2887.200.86646.0918.5387.030.79655.420.23242.6963.79655.320.23 86.700.64 0.90651.690.2889.590.85646.3618.4689.420.78655.660.23244.6363.59655.570.2389.110.64 0.99651.930.2792.010.85646.6318.3891.830.78655.910.23246.5863.39655.810.2391.540.64 20 0.60686.750.2985.600.56653.997.8385.600.58652.1910.35206.6833.66652.1510.4685.600.48 0.90686.870.2988.010.56654.247.8088.020.58652.4410.31208.7533.57652.4110.4288.010.48 0.99686.990.2990.440.55654.507.7690.460.58652.7010.27210.8433.47652.6710.3890.450.48 P4HD 2 0.60119.521.7659.720.41154.420.1160.010.33154.400.1060.100.35154.410.1259.980.35 0.90120.121.75 60.460.41154.800.1160.750.33154.780.1060.850.35154.780.1260.730.35 0.99120.731.74 61.220.41155.180.1161.500.33155.160.1061.600.35155.170.1261.480.35 5 0.60164.132.5561.052.98213.160.0662.994.25213.140.0561.092.16213.150.0560.300.25 0.90164.552.5461.782.97213.310.0663.724.24213.290.0561.822.15213.310.0561.040.25 0.99164.982.5362.522.96213.460.0664.464.23213.440.0562.562.15213.460.05 61.780.25 10 0.60184.414.8063.758.73231.410.0362.596.50231.420.0377.955.96231.420.0360.270.17 0.90184.784.7864.498.71231.490.0363.336.48231.500.0378.665.95231.490.0361.010.17 0.99185.154.7565.238.69231.560.0364.086.47231.580.0379.375.93231.570.0361.760.17 20 0.60173.623.8463.685.21222.900.1076.9610.17222.870.0997.9210.67222.860.1060.630.11 0.90174.043.8364.425.20223.010.0977.6810.15222.980.0998.5910.64222.970.1061.380.11 0.99174.473.8265.175.19223.120.0978.4010.12223.100.0999.2610.61223.090.1062.140.11 Marvin 2 0.60414.5388.6744.212.15459.131.2247.531.53459.391.1548.652.69459.520.9247.231.37 0.90417.2087.9648.872.14461.451.2252.191.52461.711.1453.312.67461.840.9151.891.36 0.99419.9087.2453.572.12463.791.2156.891.51464.061.1358.012.66464.180.9156.601.36 5 0.60579.8987.7045.831.36709.644.4648.200.88539.711.5650.421.38711.034.5048.130.85 0.90581.9087.0550.441.35710.574.4652.800.88541.561.5655.011.37711.964.5052.730.85 0.99583.9386.3955.091.35711.514.4657.440.87543.421.5559.651.36712.894.5057.380.85 10 0.60618.5952.3945.880.81712.372.6547.860.69628.371.61112.7862.70711.742.6748.030.92 0.90620.6152.10 50.510.80713.292.6552.490.69629.761.61117.1962.48712.672.6752.660.92 0.99622.6551.8155.190.80714.232.6557.170.68631.151.61121.6462.25713.602.6757.330.91 20 0.60694.7045.2145.370.67792.821.8646.490.63635.302.31279.2179.79792.601.7346.460.49 0.90696.3744.9150.000.67793.281.8651.120.63636.682.31283.1079.51793.061.7351.090.48 0.99698.0444.6154.680.67793.751.8655.800.63638.072.31287.0379.22793.531.7355.760.48 5 Conclusion In this paper, we investigated the dynamic chance-constrained approach to solve the open-pit mine scheduling problem with stochastic block economic values and dynamically changing resource capacities. We formulated the problem as a bi-objective optimization model that simultaneously maximizes the expected net present value and minimizes its stan- dard deviation, providing a risk-aware framework for long-term mine planning. Unlike traditional chance-constrained approaches that require a fixed confidence level, the proposed formulation generates a Pareto front that captures a 8 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem Table 3: Statistical comparison of total offline error. X (+) indicates the column algorithm is significantly worse than X , X (−) indicates it is significantly better, and X (∗) denotes no significant difference. Inst. ν αMOEA/D-RE (1) MOEA/D-DIV (2) NSGA-I-RE (3) NSGA-I-DIV (4) SPEA2-RE (5) SPEA2-DIV (6) SMS-EMOA-RE (7) SMS-EMOA-DIV (8) Newman1 2 0.602 − 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 − 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 + 7 ∗ 0.902 − 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 − 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 + 7 ∗ 0.992 − 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 − 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 + 7 ∗ 5 0.602 ∗ 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 − 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 + 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 ∗ 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 − 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 + 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 ∗ 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 − 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 + 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 10 0.602 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 − 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 + 4 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 ∗ 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 + 4 + 5 + 6 + 7 + 8 + 1 − 2 ∗ 3 − 4 ∗ 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 + 4 + 5 + 6 + 7 + 8 + 1 − 2 ∗ 3 − 4 ∗ 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 20 0.602 + 3 ∗ 4 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 ∗ 3 − 4 ∗ 6 + 7 ∗ 8 ∗ 1 − 2 ∗ 3 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 + 3 ∗ 4 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 ∗ 3 − 4 ∗ 6 + 7 ∗ 8 ∗ 1 − 2 ∗ 3 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 + 3 ∗ 4 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 ∗ 3 − 4 ∗ 6 + 7 ∗ 8 ∗ 1 − 2 ∗ 3 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ Zuck Small 2 0.602 − 3 − 4 − 5 − 6 ∗ 7 − 8 − 1 ∗ 2 − 3 − 4 − 5 − 7 − 8 − 1 + 3 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 5 ∗ 6 + 8 ∗ 1 + 2 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 0.902 − 3 − 4 − 5 − 6 ∗ 7 − 8 − 1 ∗ 2 − 3 − 4 − 5 − 7 − 8 − 1 + 3 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 5 ∗ 6 + 8 ∗ 1 + 2 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 0.992 − 3 − 4 − 5 − 6 ∗ 7 − 8 − 1 ∗ 2 − 3 − 4 − 5 − 7 − 8 − 1 + 3 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 5 ∗ 6 + 8 ∗ 1 + 2 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 ∗ 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 4 ∗ 5 ∗ 6 + 7 ∗ 5 0.602 − 3 ∗ 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 − 3 ∗ 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 − 3 ∗ 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 10 0.602 − 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 − 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 − 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 20 0.602 − 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 − 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 − 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ KD 2 0.602 − 3 − 4 − 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 − 3 − 4 − 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 − 3 − 4 − 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 5 0.602 − 3 − 4 − 5 + 6 ∗ 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 7 ∗ 8 + 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 − 7 ∗ 0.902 − 3 − 4 − 5 + 6 ∗ 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 7 ∗ 8 + 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 − 7 ∗ 0.992 − 3 − 4 − 5 + 6 ∗ 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 7 ∗ 8 + 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 − 7 ∗ 10 0.602 − 3 − 4 − 5 ∗ 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 + 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 − 0.902 − 3 − 4 − 5 ∗ 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 + 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 − 0.992 − 3 − 4 − 5 ∗ 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 + 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 − 20 0.602 − 3 − 4 ∗ 5 ∗ 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 + 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 − 0.902 − 3 − 4 ∗ 5 ∗ 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 + 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 − 0.992 − 3 − 4 ∗ 5 ∗ 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 + 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 − Zuck Medium 2 0.602 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 5 0.602 ∗ 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 ∗ 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 ∗ 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 10 0.602 ∗ 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 + 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 0.902 ∗ 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 + 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 0.992 ∗ 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 + 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 20 0.602 + 3 + 4 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 8 ∗ 1 − 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 ∗ 3 − 4 − 6 + 7 + 8 + 1 − 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 0.902 + 3 + 4 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 8 ∗ 1 − 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 ∗ 3 − 4 − 6 + 7 + 8 + 1 − 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 0.992 + 3 + 4 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 8 ∗ 1 − 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 ∗ 3 − 4 − 6 + 7 + 8 + 1 − 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ P4HD 2 0.602 − 3 − 4 − 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 − 3 − 4 − 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 − 3 − 4 − 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 5 0.602 − 3 ∗ 4 − 5 + 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 − 3 ∗ 4 − 5 + 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 − 3 ∗ 4 − 5 + 6 + 7 ∗ 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 10 0.602 ∗ 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 0.902 ∗ 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 0.992 ∗ 3 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 ∗ 7 ∗ 8 + 1 + 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 20 0.602 − 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 + 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 0.902 − 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 + 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ 0.992 − 3 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 + 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 ∗ 2 − 3 − 4 − 6 + 7 ∗ 8 + 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 6 ∗ 7 ∗ Marvin 2 0.602 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 7 ∗ 8 ∗ 1 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 6 ∗ 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 5 0.602 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 10 0.602 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 ∗ 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 ∗ 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 − 3 ∗ 4 ∗ 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 + 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 ∗ 5 ∗ 6 + 7 + 8 + 1 ∗ 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 20 0.602 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.902 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ 0.992 ∗ 3 ∗ 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 − 7 ∗ 8 ∗ 1 ∗ 3 + 4 ∗ 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 8 ∗ 1 ∗ 2 − 4 − 5 ∗ 6 + 7 + 8 + 1 − 2 − 3 ∗ 4 − 6 + 7 ∗ 8 ∗ 1 ∗ 2 ∗ 3 + 5 + 6 + 7 + 8 + 1 − 2 − 3 − 4 − 5 ∗ 6 ∗ 7 ∗ range of confidence levels in a single run. To address time-varying resource capacities, we employed a diversity-based change response mechanism that combines solution repair with the introduction of randomly generated feasible so- lutions. We evaluated the proposed method against re-evaluation–based baseline change response mechanisms using four multi-objective evolutionary algorithms. Experimental results demonstrate that the proposed dynamic variants consistently outperform the baselines across all mining instances, confidence levels, and dynamic change frequencies, with MOEA/D-DIV and SMS-EMOA-DIV achieving the strongest performance. Overall, these results show that the proposed approach effectively handles stochastic and dynamic variations by producing high-quality, risk-aware mine schedules. 9 On the Use of Evolutionary Optimization for the Dynamic Chance Constrained Open-Pit Mine Scheduling Problem 6 Acknowledgement This work has been supported by the CNRS-Adelaide Mobility Scheme Award through grant 6021521. 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