Solution Quality Research Articles

An Effective Local Search Algorithm for Flexible Job Shop Scheduling in Intelligent Manufacturing Systems

As one of the most classical scheduling problems, flexible job shop scheduling problems (FJSP) find widespread applications in modern intelligent manufacturing systems. However, the majority of meta-heuristic methods for solving FJSP in the literature are population-based evolutionary algorithms, which are complex and time-consuming. In this paper, we propose a fast effective single-solution based local search algorithm with an innovative adaptive weighting technique (AWLS) for solving FJSP. The adaptive weighting technique assigns weights to each operation and adaptively updates them during the exploration. AWLS integrates a Tabu Search strategy and the adaptive weighting technique to smooth the landscape of the search space and enhance the exploration diversity. Computational experiments on 313 well-known benchmark instances demonstrate that AWLS is highly competitive with state-of-the-art algorithms in terms of both solution quality and computational efficiency, despite of its simplicity. Specifically, AWLS improves the previous best-known results in the literature on 33 instances and match the best-known results on the remaining ones except for only one under the same time limit of up to 300 s. As a strongly Non-deterministic Polynomia (NP)-hard problem which has been extensively studied for nearly half a century, breaking the records on these classic instances is an arduous task. Nevertheless, AWLS establishes new records on 8 challenging instances whose previous best records were established by a state-of-the-art meta-heuristic algorithm and a famous industrial solver.

A Clinically Immersive Medical Innovation Program for US MD Students: Curricular Description and Program Outcomes.

There is growing need for physician-innovators to address the mounting challenges within the US healthcare system. Despite this, there remains a significant gap in understanding of the efficacy of innovation programs for US MD candidates. We present initial program outcomes of a novel, clinically immersive medical innovation program offered to MD candidates at the David Geffen School of Medicine (DGSOM) at UCLA. A novel clinically immersive medical innovation curriculum was developed based on existing and reputable medical innovation frameworks and tailored for medical students. Curricular topics broadly included clinical ethnography, interviewing techniques, mind mapping, needs formulation and prioritization, quality improvement, intellectual property, reimbursement pathways, solution landscaping and prioritization, regulatory processes. The program was trialed during an unscheduled summer with voluntary enrollees from DGSOM Class of 2024. The traditional four-level Kirkpatrick model was employed to assess program outcomes. Program outcomes were positive on all four Kirkpatrick levels. Students rated enjoyment at 9.5/10 for lectures and 9.1/10 for clinical immersion. Student-perceived confidence in key skills increased by 43%, and 75% of faculty directly perceived improvement in ethnographic skills. Students were highly engaged in both didactics and clinical immersion, discovering on average 2.6 faculty-verified needs per week. Faculty largely felt their students discovered important unmet clinical needs and added value to their clinical practice. We developed and trialed a novel clinically immersive medical innovation curriculum tailored for medical students. This program achieved positive outcomes on all four levels of the Kirkpatrick model. Our findings have driven the local adoption of this program into our institution's medical school curriculum. We hope that the program efficacy demonstrated herein catalyzes more institutions to trial similar medical innovation programs.

Surrogate-assisted cooperative learning genetic programming for the resource-constrained project scheduling problem with stochastic activity durations and transfer times

For the project scheduling problem with transfer times under an uncertain environment, not only the activity durations are stochastic, but transfer times are often also stochastic. Therefore, we propose a resource-constrained project scheduling problem with stochastic activity durations and transfer times (RCPSP-SDT), which requires complex activity sequencing and resource transfer decisions with an activity priority rule (APR) and a resource transfer priority rule (RTPR) under unpredicted dynamic factors. However, manually designed combination rules of APRs and RTPRs are time-consuming and only for specific scenarios. Therefore, we develop a hyper-heuristic approach based on genetic programming (GP), which has been successfully applied to evolve activity priority rules for project scheduling problems. A new representation of GP individuals was designed to evolve the APR and the RTPR simultaneously. In order to improve the efficiency and solution quality of the approach, we propose surrogate-assisted cooperative learning genetic programming (SCLGP) based on GP. Based on the benchmark data set, computer experiments were conducted under nine variance levels of stochastic distributions. The results show that the proposed algorithm SCLGP performs significantly better than the classical priority rule (PR)-based heuristics. Furthermore, the effectiveness and efficiency of SCLGP were verified by comparing it to four other GP-based algorithms. Finally, the impact of the parameters on the algorithm was investigated, proving that these parameters affect the algorithm’s performance.

Enhancing subsurface seismic profiling with distributed acoustic sensing and optimization algorithms

The distribution of shear-wave velocities in the subsurface is generally used to assess the potential for seismic liquefaction and soil amplification effects and to classify seismic sites. Newly developed distributed acoustic sensing (DAS) technology enables estimation of the shear-wave distribution as a high-density seismic observation system. This technology is characterized by low maintenance costs, high-resolution outputs, and real-time data transmission capabilities, albeit with the challenge of managing massive data generation. Rapid and efficient interpretation of data is the key to advancing application of the DAS technology. In this study, field tests were carried out to record ambient noise over a short period using DAS technology, from which the surface-wave dispersion curves were extracted. In order to reduce the influence of directional effects on the results, an unsupervised clustering method is used to select appropriate clusters to extract the Green's function. A combination of a genetic algorithm and Monte Carlo (GA-MC) simulation is proposed to invert the subsurface velocity structure. The stratigraphic profiles obtained by the GA-MC method are in agreement with the borehole profiles. Compared to other methods, the proposed optimization method not only improves the solution quality but also reduces the solution time.

Software can be The Differentiator

Zeiss Industrial Quality Solutions is taking a consultative approach to working with its UK customers and recently held an Inspect User Day at its excellence centre in Rugby. Zeiss is also gearing up to move into a new state-of-the-art facility in the early part of 2025 that will grow its capabilities

Railway alignment optimization in regions with densely-distributed obstacles based on semantic topological maps

Railway alignment development in a study area with densely-distributed obstacles, in which regions favorable for alignments are isolated (termed an isolated island effect, i.e., IIE), is a computation-intensive and time-consuming task. To enhance search efficiency and solution quality, an environmental suitability analysis is conducted to identify alignment-favorable regions (AFRs), focusing the subsequent alignment search on these areas. Firstly, a density-based clustering algorithm (DBSCAN) and a specific criterion are customized to distinguish AFR distribution patterns: continuously-distributed AFRs, obstructed effects, and IIEs. Secondly, a study area characterized by IIEs is represented with a semantic topological map (STM), integrating between-island and within-island paths. Specifically, between-island paths are derived through a multi-directional scanning strategy, while within-island paths are optimized using a Floyd-Warshall algorithm. To this end, the intricate alignment optimization problem is simplified into a shortest path problem, tackled with conventional shortest path algorithms (of which Dijkstra’s algorithm is adopted in this work). Lastly, the proposed method is applied to a real case in a mountainous region with karst landforms. Numerical results indicate its superior performance in both construction costs and environmental suitability compared to human designers and a prior alignment optimization method.

A Swarm Intelligence Solution for the Multi-Vehicle Profitable Pickup and Delivery Problem

Delivery apps are experiencing significant growth, requiring efficient algorithms to coordinate transportation and generate profits. One problem that considers the goals of delivery apps is the multi-vehicle profitable pickup and delivery problem (MVPPDP). In this paper, we propose eight new metaheuristics to improve the initial solutions for the MVPPDP based on the well-known swarm intelligence algorithm, Artificial Bee Colony (ABC): K-means-GRASP-ABC(C)S1, K-means-GRASP-ABC(C)S2, Modified K-means-GRASP-ABC(C)S1, Modified K-means-GRASP-ABC(C)S2, ACO-GRASP-ABC(C)S1, ACO-GRASP-ABC(C)S2, ABC(S1), and ABC(S2). All methods achieved superior performance in most instances in terms of processing time. For example, for 250 customers, the average times of the algorithms was 75.9, 72.86, 79.17, 73.85, 76.60, 66.29, 177.07, and 196.09, which were faster than those of the state-of-the-art methods that took 300 s. Moreover, all proposed algorithms performed well on small-size instances in terms of profit by achieving thirteen new best solutions and five equal solutions to the best-known solutions. However, the algorithms slightly lag behind in medium- and large-sized instances due to the greedy randomised strategy and GRASP that have been used in the scout bee phase. Moreover, our algorithms prioritise minimal solutions and iterations for rapid processing time in daily m-commerce apps, while reducing iteration counts and population sizes reduces the likelihood of obtaining good solution quality.

The Hampered [formula omitted]-Median Problem with Neighbourhoods

This paper deals with facility location problems in a continuous space with neighbours and barriers. Each one of these two elements, neighbours and barriers, makes the problems harder than their standard counterparts. Combining all together results in a new challenging problem that, as far as we know, has not been addressed before, but has applications for inspection and surveillance activities and the delivery industry assuming uniformly distributed demand in some regions. Specifically, we analyse the k-Median problem with neighbours and polygonal barriers in two different situations. None of these problems can be seen as a simple incremental contribution since in both cases the tools required to analyse and solve them go beyond any standard overlapping of techniques used in the separated problems. As a first building block, we deal with the problem assuming that the neighbourhoods are not visible from one another and therefore there are no rectilinear paths that join two of them without crossing barriers. Under this hypothesis, we derive a valid mixed-integer linear formulation. Removing that hypothesis leads to a more general and realistic problem, but at the price of making it more challenging. Adapting the elements of the first formulation, we also develop another valid mixed-integer bilinear formulation. Both formulations rely on tools borrowed from computational geometry that allow to handle polygonal barriers and neighbours that are second-order cone (SOC) representable, which we preprocess and strengthen with valid inequalities. These mathematical programming formulations are also instrumental to derive an adapted matheuristic algorithm that provides good quality solutions for both problems in short computing time. The paper also reports extensive computational experience, counting 2400 experiments, showing that our exact and heuristic approaches are useful: the exact approach can solve optimally instances with up to 50 neighbourhoods and different number of barriers within one hour of CPU time, whereas the matheuristic approach always returns good feasible solutions in less than 300 s.

A cooperative learning-aware dynamic hierarchical hyper-heuristic for distributed heterogeneous mixed no-wait flow-shop scheduling

The distributed heterogeneous mixed scheduling mode in the manufacturing systems emphasizes the cooperation between factories for the entire production cycle, which poses enormous challenges to the processing and assignment of jobs. Discrepancies in the processing environment and types of machines of each factory during various production stages cause diverse processing paths and scheduling. The distributed heterogeneous mixed no-wait flow-shop scheduling problem with sequence-dependent setup time (DHMNWFSP-SDST), abstracted from the industrial scenarios, is addressed in this paper. The mathematical model of DHMNWFSP-SDST is established. A cooperative learning-aware dynamic hierarchical hyper-heuristic (CLDHH) is proposed to solve the DHMNWFSP-SDST. In CLDHH, a cooperative initialization method is developed to promote diversity and quality of solutions. A hierarchical hyper-heuristic framework with reinforcement learning (RL) is designed to select the algorithm component automatically. Estimation of Distribution Algorithm (EDA) guides the upper-layer RL to select four neighborhood structures. A dynamic adaptive neighborhood switching constructs the lower-layer RL to accelerate exploitation with the dominant sub-neighborhoods. An elite-guided hybrid path relinking achieves local enhancement. The experimental results of CLDHH and six state-of-the-art algorithms on instances indicate that the proposed CLDHH is superior to the state-of-the-art algorithms in solution quality, robustness, and efficiency.

Методика для решения задачи выбора признаков в регрессионной модели Кокса

The technique based on the use of a hybrid optimization method to solve the feature selection problem for the Cox regression model is proposed. The hybrid optimization method includes two metaheuristic methods: the ant colony optimization and the genetic algorithm. The ant colony optimization used as the basic algorithm that solves the main optimization problem. The genetic algorithm solves the problem of finding the optimal set of parameters for the ant algorithm improving its performance. The method is modified and adapted to solve the problem under consideration. The key feature of adaptation is the deposition of pheromones on the vertices rather than on the edges of the graph, as well as the method for calculating the assessment of heuristic information about each vertex. A fitness target function was constructed that determines the quality of solutions to the feature selection problem and is based on an assessment of the performance of the Cox model with a selected set of parameters. The concordance index (c-index) was used to evaluate the Cox model. The efficiency of the methodology is shown using the implemented program using the example of a database of recidivism. For the database used, the most significant sets of features were obtained that have the greatest impact on the quality of training of the survival analysis model.

Integrated optimization of pilot and pilot carrier routing in seaports

Pilotage is an important service for vessels to enter and leave seaports. When vessels entering or leaving their berths, pilots are assigned to provide assistance on board to maneuver the vessels. Pilot carriers, such as pilot boats and helicopters are utilized to transport pilots from the pilot station to the vessels at appointed ground. With the increasing number of calling vessels, the pilotage plan should be made properly considering the limited pilots and carriers resources in seaports to enhance timing reliability, which is a key port performance indicator. This paper studies the pilot and pilot carrier routing problem arising in seaports, where both the routes of pilots and carriers are determined jointly to achieve the lowest pilotage costs. The required service time intervals of vessels, the synchronization between pilots and carriers and the limited working duration for both pilots and carriers are considered. The problem is formulated as an arc-flow model, and a hybrid multi-start adaptive large neighborhood search and local search algorithm (mALNS-LS) is developed. Efficient departure time and cost computation methods are designed based on a set of forward and backward functions, and a model-based post optimization is applied. Computational experiments verify the performance of the proposed mALNS-LS in terms of solution quality and efficiency.

An improved particle swarm optimisation algorithm for optimum placement and sizing of biogas-fuelled distributed generators for seasonal loads in a radial distribution network

Optimal allocation is critical for effective planning and operation of grid connected distributed generator(s) (DGs) subject to efficient optimisation approach(es). In this paper, an improved particle swarm optimisation (IPSO) algorithm based on weighted randomised acceleration coefficients and adaptive inertia weight for dynamic movement of the particles towards an optimal solution is proposed. The technique is expected to determine optimal placement, sizing and power factor of biogas-fuelled distributed generators (B-DGs such as internal combustion engine (ICE) and fuel cells (FC)) in a radial distribution network. The proposed IPSO is applied to simultaneously optimise three technical objectives namely total active power loss (TAPL), voltage deviation (VD) and voltage stability index (VSI) considering load growth and seasonal voltage dependence. The proposed IPSO is validated using an IEEE 33 bus radial distribution network to evaluate its effectiveness through various combinations of B-DGs for different scenarios and cases with a maximum of 3 B-DGs. Some of the key findings indicate that operating 3 ICEs at optimal power factor reduces TAPL by 93.52 %, reduces VD by 99.62 % and improves VSI by 23.32 % compared to 61.80 % TAPL reduction, 94.77 % VD reduction and 17.89 % VSI improvement for 3 FCs operating at unity power factor. The proposed IPSO gives better results than the standard PSO in terms of solution quality, convergence speed and statistical results. It is also perceived to be better compared to most of the recent state-of-the-art optimization algorithms found in literature.

Vivid-persona: customizable persona tool with interactive and immersive experiences

In the design field, persona is widely used to help design teams understand their target users. However, existing persona tools have limitations such as insufficient interactivity, inability to arouse designers’ empathy, and inability to finely segment users. We developed Vivid-Persona, which is a customisable persona tool offering an interactive and immersive experience. Designers can set the demographics and scenarios of the target user to customise a persona. The tool generates a realistic image of the persona using a Diffusion model. Embedded with the ChatGPT and SadTalker models, the persona can engage in real-time video chats with designers. The persona is augmented with facial expressions, based on the analysis of the emotions in utterances. A user study showed that Vivid-Persona effectively solves the problem of user segmentation, significantly enhancing the designer’s perception of persona in terms of authenticity, clarity, empathy and willingness to use, as well as the quality of the output design solutions.

Two-stage knowledge-assisted coevolutionary NSGA-II for bi-objective path planning of multiple unmanned aerial vehicles

This paper focuses on the bi-objective path planning problem of multiple unmanned aerial vehicles (UAVs) under the complex environment with numerous obstacles and threat areas, where the UAVs need to be kept as far away as possible from threat areas during flight. Based on the integrated energy reduction perspective, a bi-objective model is subtly constructed by minimizing the total energy consumption of each path (including flight altitude, horizontal turns, and path length), and minimizing the costs of the total threats (including ground radar, anti-aircraft gun, missile and geological hazard threat areas). Moreover, a two-stage knowledge-assisted coevolutionary NSGA-II algorithm is novelly proposed to enhance collaboration and avoid collision. The first stage is designed for population convergence, where the considered constrained problem is solved with the help of the designed problem without the constraints of threats and obstacles. The second stage emphasizes the quality and diversity of solutions. In this stage, a double-population coevolution approach is developed. Additionally, a multi-mode strategy is introduced for the inferior population, leveraging reinforcement learning. This strategy aids in selecting the optimal mode from random swing, directed guidance, and potential dominance exploration. Furthermore, experimental results in two different environments show that the proposed algorithm can better solve the collaborative path planning problem for multiple UAVs compared with other five classical or recent proposed algorithms.

Design of an iterative method for environmental-sustainable development: Integrating bioinspired computing techniques

The need for sustainable development has grown in response to global environmental, social, and economic challenges. Conventional computational methods frequently struggle to address the complex nature of the Sustainable Development Goals (SDGs), lacking the ability to balance global search with local optimization and failing to prioritize goals related to sustainability. To address these restrictions, this work introduces the Integrated Bioinspired Computing Model for Sustainable Development (IBCMSD). By combining Genetic Algorithms (GAs), Artificial Neural Networks (ANNs), and Ant Colony Optimization (ACO), a cohesive hybrid model is developed that improves exploration and exploitation, balance for increased efficiency, and solution quality. It is implemented on High-Performance Computing (HPC) clusters to ensure scalability and resilience when dealing with complicated optimization challenges. Furthermore, using a multidisciplinary co-design method completes the model with multiple views, increasing its relevance and applicability in real-world circumstances. IBCMSD makes a significant contribution to computational sustainability by leveraging bioinspired computing, potentially enabling informed decision-making and SDG accomplishment across multiple domains.

Long-Term Mine Planning: A Survey of Classical, Hybrid and Artificial Intelligence-Based Methods

The aim of long-term mine planning (LTMP) is two-fold: to maximize the net present value of profits (NPV) and determine how ores are sequentially processed over the lifetime. This scheduling task is computationally complex as it is rife with variables, constraints, periods, uncertainties, and unique operations. In this paper, we present trends in the literature in the recent decade. One trend is the shift from deterministic toward stochastic problems as they reflect real-world complexities. A complexity of growing concern is also in sustainable mine planning. Another trend is the shift from traditional operational research solutions — relying on exact or (meta) heuristic methods — toward hybrid methods. They are compared through the scope of the problem formulation and discussed via solution quality, efficiency, and gaps. We finally conclude with opportunities to incorporate artificial intelligence (AI)-based methods due to paucity, multiple operational uncertainties simultaneously, sustainability indicator quantification, and benchmark instances.

Memetic discrete differential evolution with domain knowledge for blocking scheduling distributed flow shop with lot-streaming constraints

This article addresses the blocking distributed flow shop scheduling problem with lot-streaming (BDFSPL) with the objective of minimizing the maximum completion time, or makespan. In many realistic conditions, a job is divided into multiple continuous processed sublots. This pattern achieves operation overlap on consecutive machines and decreases the completion time of the whole job. Moreover, there are no buffers between machines, potentially causing finished sublots to be blocked on the current machine until the downstream machine is available. This is the first study to consider distributed production, blocking constraints, and lot-streaming together. To address this problem, we formulate a mathematical model for BDFSPL and propose a memetic discrete differential evolution (MDDE) algorithm. First, the MDDE algorithm partitions the entire population into three subpopulations based on solution quality, and each subpopulation evolves independently through adaptive scale and parameter adjustment. Second, four discrete mathematical operators are proposed to generate new individuals, and based on these operators, discrete mutation, crossover, and selection operations of MDDE are designed. Additionally, a crucial path-based local search strategy, informed by the domain knowledge of the best individual, is embedded into MDDE to enhance the exploitation capacity. To validate MDDE’s effectiveness, comprehensive experiments with several related algorithms on extensive testing instances are carried out, and the parameters of the MDDE algorithm are calibrated by employing a design of experiments. The comparison results demonstrate the effectiveness and efficiency of the proposed MDDE algorithm for the BDFSPL.

Adaptive machine learning surrogate based multiobjective optimization for scavenging residual saltwater behind subsurface dams

High-fidelity physically based groundwater flow and solute transport models have been limited for seawater intrusion remediation design because of computationally intensive evolutionary algorithms. Data-driven machine learning approaches are promising to substitute expensive-cost groundwater numerical models within optimization due to computing efficiency. However, machine learning surrogates may accumulate error of forecasting and thereby result in infeasible optimal solutions. To achieve desired fidelity level, this study proposes a novel adaptive machine learning surrogate based multiobjective optimization method for coastal aquifer desalination. An adaptive modeling algorithm is newly introduced to iteratively retrain poorly-performed machine learning models and enhance predicting accuracy. The method is demonstrated to seek optimal extraction and injection strategies for scavenging residual saltwater trapped in an upstream aquifer behind a subsurface dam. Two conflicting objectives of minimizing the total extraction-injection rate and maximizing saltwater removal effectiveness are considered. Three machine learning models including artificial neural network (ANN), Gaussian process (GP) and response surface regression model (RSR) are developed to replace a high-fidelity seawater intrusion model for predicting chloride concentration and salinity mass. Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to derive Pareto fronts. Pareto optimal solutions obtained from machine learning models are compared against those from the seawater intrusion model. Results indicate that the developed machine learning models do not only have strong predicting capability, but also maintain good quality of Pareto optimal solutions, while achieving substantial computational saving up to 95%. Especially, the adaptively retrained RSR model inhibits error accumulation of forecasting and accelerates correct convergence to the true Pareto front. The proposed method is found superior performance in accurate convergence, widely-spread diversity as well as high computing efficiency than conventional methods.

Bayesian expectation maximization-maximization for robust estimation in proton exchange membrane fuel cells: A comparative study

In this paper, we present a novel approach based on Bayesian Expectation Maximization-Maximization (BEMM) to address this challenge. Unlike traditional optimization methods, which may struggle with high-dimensional and nonlinear optimization problems, BEMM offers a robust framework that combines the benefits of Bayesian inference with the flexibility of expectation maximization and maximization techniques. By iteratively updating parameter estimates based on observed data and maximizing the likelihood of the model, BEMM effectively navigates the solution space to converge on accurate estimates of the unspecified variables in Proton Exchange Membrane Fuel Cells (PEMFCs)models. Through extensive experimentation and comparison with other metaheuristic techniques, including Arithmetic Optimization Algorithm (AOA), Gravitational Search Algorithm (GSA), Flower Pollination Algorithm (FPA), and Biogeography-Based Optimization (BBO), we demonstrate the superior performance of our BEMM approach. Our results show that BEMM outperforms these alternative methods in terms of precision, convergence speed, and stability across various scenarios involving different numbers of unspecified variables. The implications of our findings are significant for both researchers and practitioners in the field of PEMFC modeling and optimization. By providing a more efficient and reliable method for estimating model parameters, our approach can facilitate more accurate predictions of PEMFC performance, leading to better-informed decision-making in the design, operation, and optimization of PEMFC systems. Furthermore, the robustness and versatility of BEMM make it well-suited for a wide range of optimization problems beyond PEMFC modeling, highlighting its potential impact across various domains of engineering and scientific research. In the sensitivity analysis, as the population size increases from 10 to 40, there is a significant improvement in solution quality by approximately 100 %. However, beyond a population size of 40, the marginal gains diminish, with only marginal improvements of less than 1 % observed despite further increases in population size up to 200.

Co-evolution genetic programming-based hyper-heuristics for the stochastic project scheduling problem with resource transfer and idle costs

In this paper, we study the stochastic resource-constrained project scheduling problem with transfer and idle costs (SRCPSP-TIC) under uncertain environments, where the resource transfer and idle take time and costs. Priority rule (PR) based heuristics are the most commonly used approaches for project scheduling under uncertain environments due to their simplicity and efficiency. For PR-based heuristics of the SRCPSP-TIC, activity priority rules (APRs) and transfer priority rules (TPRs) are necessary to decide the activity sequence and resource transfer. Traditionally, APRs and TPRs need to be manually designed, which is time-consuming and difficult to adapt to different scheduling scenarios. Therefore, based on two individual representation methods, we propose two co-evolution genetic programming (CGP) based hyper-heuristics to evolve APRs and TPRs automatically. Furthermore, a fitness function surrogate-assisted method and a transfer learning mechanism are designed to improve the efficiency and solution quality of the CGP. Based on the instances with different stochastic activity duration distributions, we test the performance of different CGP-based hyper-heuristics and compare the evolved PRs with the classical PRs to demonstrate the effectiveness of evolved PRs. Experimental results show that the proposed algorithms can automatically evolve efficient PRs for the SRCPSP-TIC.