264 results about "Pareto optimal" patented technology

This invention belongs to the field of oil supply, lubrication, and cooling technology for aero-engine bearings. It provides a method for temperature control and parameter optimization design of under-ring lubricated bearings. The method includes: generating sample data on total heat generation, bearing element temperature, and oil slingering temperature of the bearing through experiments or simulations based on bearing structural parameters and operating condition parameters; constructing a predictive model with the parameters as input and thermal-fluid performance as output; quantifying the influence of input parameters using global sensitivity analysis, screening key design parameters, and constructing a multi-objective optimization model with the objectives of minimizing bearing element temperature control accuracy and total heat generation; solving the model to obtain the Pareto optimal solution set, and determining the optimal combination of structure and oil supply parameters that satisfies the oil slingering temperature safety constraint and bearing thermal reliability requirements while achieving optimal overall performance. This invention is applicable to the refined design of high-speed bearings in rotating machinery such as aero-engines, enabling precise temperature control and coordinated energy consumption optimization.

This invention belongs to the field of artificial intelligence hardware architecture design and discloses a method, system, device, and medium for cross-layer optimization of multi-core packaging and optical interconnect clusters for large language model training. The method includes: constructing a design space, including a core hardware architecture layer, an optical interconnect network layer, and a training parallel strategy layer; performing an outer-layer search to search for the architecture parameters of the multi-core modules within the core hardware architecture layer; for each outer-layer search sampling point, performing an inner-layer search to collaboratively optimize the optical interconnect network topology and training parallel strategy within the optical interconnect network layer and the training parallel strategy layer; and outputting the Pareto optimal design point on the training performance and cluster cost plane. The technical solution described in this invention can guide the design of related training clusters, thereby fully leveraging the advantages and potential of core technology and optical interconnect technology in large language model training.

This invention discloses a multi-objective optimization method for high-pile piers and abutments based on an improved Grey Wolf algorithm. The method includes the following steps: establishing a design variable with pile inclination and torsion angle as the design variables, and simultaneously minimizing the standard deviation of pile driving force, maximum pull-out force, and maximum pile bending moment as the optimization objective; designing an integer index discrete encoding strategy to map discrete inclination and torsion angle parameters in the project to integer indices; using an improved multi-objective Grey Wolf optimization algorithm for solving the problem, efficiently searching for Pareto optimal solutions by introducing a nonlinear convergence factor, external archive maintenance, and a leader selection mechanism based on crowding distance; and finally outputting a series of pile placement schemes that achieve a balance between pile driving force uniformity, pull-out force, and bending moment control. This invention achieves collaborative optimization of multiple engineering objectives, with strong algorithm adaptability and significant optimization effects, providing scientific and efficient design decision support for high-pile piers and abutments and other pile foundation projects.

Systems and methods for tuning hyperparameters of a model includes: receiving a multi-criteria tuning work request for tuning hyperparameters of the model of the subscriber to the remote tuning service, wherein the multi-criteria tuning work request includes: a first objective function of the model to be optimized by the remote tuning service; a second objective function to be optimized by the remote tuning service, the second objective function being distinct from the first objective function; computing a joint tuning func-tion based on a combination of the first objective function and the second objective function; executing a tuning opera-tion of the hyperparameters for the model based on a tuning of the joint function; and identifying one or more proposed hyperparameter values based on one or more hyperparam-eter-based points along a convex Pareto optimal curve.

The application provides a kind of instruction driving machine task planning method and system based on knowledge model, and the specific knowledge of field is structuredly represented by knowledge model, and the object of class level, instance level of field knowledge and its logical relationship are represented;Further, the semantics of instruction is understood, and then the task planning problem represented by instruction is normalized, specifically including task planning object and its mutual constraint relationship;On this basis, further consider the space-time constraint between task objects and the measurement and evaluation of task efficiency.Finally, through atlas and visual graph display, give the pareto optimal scheme under multi-dimension, support intelligent or man-machine interactive decision, realize man-machine interaction in task planning, and output field-specific reliable scheme based on natural language.

This invention relates to the field of resource scheduling, and proposes a task scheduling optimization method and system based on dynamic task profile modeling. The method includes the following steps: real-time collection of task metadata of the target task and computing node operation data of the intelligent computing center, and standardization processing; extraction of discriminative features from the standardized task metadata; input of the discriminative features into the dynamic task profile modeling model to generate a dynamic task profile; wherein the dynamic task profile modeling model is configured with a spatiotemporally coupled tensor model for multi-dimensional representation of the target task, and an online non-negative matrix factorization algorithm for dynamically updating the feature matrix of the discriminative features; based on the standardized computing node operation data and the dynamic task profile, a Pareto optimal solution set is generated based on a multi-objective optimization algorithm, and the task scheduling optimization scheme is output.

This invention relates to a deep learning-based autonomous obstacle avoidance and path planning system and method for unmanned aerial vehicles (UAVs). The system includes: a perception simulation module, which uses multi-sensor joint modeling to achieve dynamic environmental reconstruction; a decision control and dynamics modeling module, which generates a series of control commands after acquiring fused perception data; and a scene interaction module, which realizes dynamic obstacle behavior modeling and multi-scene library access. The perception simulation module, decision control and dynamics modeling module, and scene interaction module are integrated with a ROS-MATLAB joint interface platform to achieve real-time synchronization and visualization analysis of multi-source heterogeneous data. This invention proposes a dynamic obstacle prediction model driven by multimodal data, using attention weights to dynamically allocate sensor confidence, reducing obstacle velocity prediction error to 0.12 m / s; and designs a hierarchical reward function and a priority experience replay strategy, improving the DRL training convergence speed to 40% and achieving a Pareto optimal state for path length and energy consumption.

This invention provides an energy-saving clustering routing method for wireless sensor networks based on improved multi-target ant colony optimization, comprising: Step 1, initialization; Step 2, determining the set of active sensor nodes in the current round; Step 3, completing network clustering; Step 4, maintaining the Pareto optimal path solution set; Step 5, repeating steps 2 to 4 until the maximum number of iterations is reached or the solution set converges, outputting the Pareto optimal path solution set as the routing scheme for network data transmission. This invention improves network energy efficiency and extends network lifetime by constructing a globally collaborative energy management framework that integrates sleep scheduling, cluster head election, and routing optimization, while ensuring the real-time performance and reliability of data transmission.

The application provides an engineering education system and method fusing explainable multi-objective intelligent optimization, and relates to the technical fields of intelligent education and artificial intelligence optimization. The method comprises the following steps: obtaining an initial engineering design scheme of a user, and obtaining a standardized multi-dimensional index vector through physical simulation analysis and logical analysis; configuring weights with structured reasons for each index, identifying critical weight values leading to decision reversal through sensitivity analysis, and then determining optimization objectives and constraint conditions; performing multi-objective optimization search using an explainable multi-objective optimizer, generating a Pareto optimal solution set and outputting explainable data; simultaneously generating a behavior interaction sequence of the user; generating a capability evaluation report of the user according to the behavior interaction sequence; and adjusting a preset teaching logic sequence according to the capability evaluation report to form a closed-loop teaching process. The application is suitable for cultivating and evaluating the decision-making ability of students in balancing technical performance and environmental sustainability in engineering design.

The invention relates to a low-carbon park optimal scheduling method based on dynamic carbon flow tracking, and the method comprises the steps: constructing and describing a park integrated energy system multi-energy flow coupling model, and building a dynamic carbon flow calculation model based on a dynamic carbon flow tracking mechanism; carrying out carbon constraint based on a dynamic carbon flow calculation result by using a park integrated energy system hour-level rolling optimization scheduling model with operation cost and carbon emission minimization as a target; and converting the optimal scheduling model into a mixed integer linear programming problem, and obtaining a Pareto optimal solution set by using an epsilon-constraint method and taking the minimum operation cost as a target and carbon emission as a constraint. Compared with the prior art, the method provided by the invention overcomes the defect that the traditional static accounting method cannot reflect the spatial-temporal dynamic characteristics of the carbon flow, and provides an accurate carbon measurement basis for implementing low-carbon scheduling in a park.

The present application belongs to the field of military command control and combat simulation, and relates to a local rapid reconstruction method for a killing network based on a complementary network strategy. The method acquires current state information of the killing network and detects failed nodes or edges, constructs a local repair area centered on the failed nodes, establishes a multi-objective optimization model in the repair area aiming to maximize task recovery benefits, minimize resource use costs and minimize task completion delays, solves to obtain a Pareto optimal solution set by using a TM-NSGA-III algorithm guided by a conversion matrix, and finally screens and executes a reconstruction scheme according to a battlefield situation. The present application reduces the search space by localized modeling, combines the conversion matrix to inherit the effective information of the original network, realizes rapid and high-quality reconstruction of the killing network, and improves the resilience and self-healing ability of the killing network in a dynamic battlefield environment.

This invention provides an intelligent experimental decision-making method and device for foamed lightweight soil mix proportions, relating to the field of building material design technology. The method includes: acquiring experimental data of multi-source foamed lightweight soil and preprocessing it to obtain a standardized tabular dataset; using the standardized tabular dataset as context input to a pre-trained tabular prior data fitting network model to obtain performance prediction values; employing the SHAP value analysis method to calculate the contribution value of input features to the performance prediction values, thus obtaining the contribution relationship between input features and performance prediction values; using the tabular prior data fitting network model as the performance prediction model, establishing a multi-objective optimization model by combining material cost and material density, and setting constraints based on the contribution relationship; and using a non-dominated sorting genetic algorithm to solve the multi-objective optimization model, searching for a set of Pareto optimal mix proportion schemes. This invention can automatically search for Pareto optimal mix proportion schemes, improving the efficiency of mix proportion design.

This invention discloses a heat sink structure optimization design method based on a non-dominated sorting genetic algorithm, belonging to the field of heat sink optimization design technology. The method first determines the structural parameters to be optimized (heat sink length, width, height, fin thickness, fin spacing, substrate thickness) and the optimization objective function (maximum junction temperature of power devices, heat sink mass, heat sink entropy productivity). Then, Latin hypercube sampling is used to sample parameters and establish a geometric model. Sample data is constructed through thermal simulation, and a surrogate model is established using response surface methodology. Finally, multi-objective optimization is performed based on the non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set, and the best solution is selected through comprehensive performance evaluation indicators. This invention effectively reduces heat sink mass and cost while ensuring heat dissipation performance, shortens the R&D cycle, and is applicable to the heat dissipation optimization design of power devices in power electronic systems.

This invention belongs to the field of high-performance thermoplastic composite granule preparation and process optimization technology. Specifically, it relates to a method and system for determining the optimal process for twin-screw extrusion preparation of carbon fiber / polyetheretherketone (PEEK) granules based on numerical simulation and multi-objective optimization. A three-dimensional model of the internal flow channel of the twin-screw extruder is established, and discretization is performed using a mesh stacking method. Multiple simulation conditions are constructed within a preset temperature and extrusion speed range, and process safety constraints are established. The analytic hierarchy process (AHP) – approximation of ideal solution ranking method is used for index standardization, weight allocation, and comprehensive scoring. With process temperature and extrusion speed as decision variables, a non-dominated sorting genetic algorithm is used for multi-objective global search to obtain the Pareto optimal solution set, which is then ranked and optimized to output recommended process parameter combinations. This invention's method can reduce the risk of thermal degradation and fiber damage while considering the mixing effect, and reduces the cost and cycle time of trial and error.

This invention discloses a method for architecture generation and hierarchical alignment-based precise aggregation for heterogeneous federated learning, comprising the following steps: 1) initializing a global supernet; 2) constructing an architecture exploration environment based on reinforcement learning; 3) performing offline generative exploration in the supernet search space; 4) constructing a Pareto optimal candidate architecture pool; 5) determining the set of clients participating in training and dividing resource levels according to resource budget; 6) selecting the optimal nested subnet for each resource level; 7) distributing the selected subnet architecture and parameters to clients for local training; 8) generating parameter masks for each client; 9) performing precise aggregation of gradients uploaded by clients based on the masks and updating the global supernet weights; 10) iterating through communication rounds until the model converges or reaches a preset number of rounds. This invention solves the suboptimal performance problem caused by traditional heuristic architecture generation methods, as well as the parameter space mismatch and aggregation interference problems caused by incompatibility of heterogeneous subnet structures.

This invention relates to a dynamic simulation and optimization decision-making method for low-carbon policies in industrial parks based on energy-carbon-economic synergy. It falls within the technical field of low-carbon policy formulation and evaluation for industrial parks, and includes the following steps: park boundary identification and carbon emission responsibility unit division; multi-source data collection and construction of an energy-carbon-economic synergy database; construction of a dynamic coupling simulation model of energy flow, carbon flow, and economic flow; construction of an energy-carbon-economic synergy evaluation model; construction of a policy net economic effect model; establishment of a policy tool variable set and policy scenario library; and construction of a multi-objective optimization model to solve for the Pareto optimal frontier. This invention establishes a multi-dimensional synergistic evaluation index system and a full-lifecycle policy net economic effect accounting model that includes the systemic cost of the power grid. Combined with a multi-objective optimization algorithm and a policy sandbox intelligent recommendation mechanism, it achieves full-process dynamic simulation, multi-dimensional effect evaluation, multi-constraint compliance verification, and global optimization decision-making for low-carbon policies in industrial parks.

This invention provides a method for improving water conditions based on current status assessment and multi-objective synergy, relating to the field of water environment management technology. The invention comprehensively evaluates the current status of water areas to form an evaluation result table, identifies advantageous and disadvantageous indicators, determines the conflict relationships and optimization potential of engineering measures, constructs a mathematical response function between control indicators and engineering measures, establishes a multi-objective optimization model, and uses the NSGA-III algorithm to obtain the Pareto optimal solution set. Combined with multivariate criteria, it outputs optimized engineering combinations and expected results applicable to different management scenarios. This invention can transform static evaluation into dynamic decision support, improving the scientific rigor and accuracy of water management decisions.

This invention relates to a method and system for optimizing train operation schemes for Y-shaped lines operating across different rail systems. The method includes: designing a flexible cross-system transportation organization mechanism; establishing a dataset of interconnected cross-system rail transit routes; constructing a bi-objective optimization model for flexible train formation across lines; and constructing the NSGA-II algorithm for solving the bi-objective optimization model, outputting the train operation optimization scheme corresponding to the Pareto optimal solution set. This invention aims to solve key problems in cross-line operation, such as the difficulty of adapting fixed routes and train formation patterns to the spatiotemporal imbalance of passenger flow between main and branch lines, low train occupancy rates on cross-lines, and excessively long departure intervals due to the occupation of capacity on each line. This allows for efficient coordinated scheduling of flexible train formations and multiple routes.

This invention relates to the field of geotechnical engineering monitoring and slope stability analysis technology, specifically to a method and system for the layout of slope monitoring points throughout the entire construction and operation cycle. The method acquires multi-source monitoring data and constructs a unified data warehouse through cleaning, format conversion, and spatiotemporal registration. Based on this unified data warehouse, a dynamic risk assessment model coupled with the limit equilibrium method and the finite element method is used to identify target risk areas, and key monitoring variables are identified through global sensitivity analysis. Finally, a multi-objective optimization algorithm is used to solve for the Pareto optimal solution set to determine the location and density of monitoring points. This invention achieves adaptive matching of the monitoring network to changes in geological conditions and dynamic engineering needs throughout the entire cycle, improving the targeting of monitoring and the efficiency of resource allocation.

This invention discloses an intelligent project scheduling method and system based on multi-constraint optimization, relating to the field of smart project management. It constructs a multi-dimensional constraint model for the project, including task sequence relationships, resource skill matrices, construction space grids and capacity, and personnel risk coefficients. An initial feasible plan is generated based on the critical path method and heuristic resource balancing. The initial plan is then iteratively optimized using a multi-objective optimization algorithm to obtain the Pareto optimal plan. This invention improves the rationality and feasibility of project scheduling by constructing a multi-dimensional constraint model that comprehensively integrates various constraints such as tasks, resources, space, and personnel risks. By combining the critical path method and multi-objective optimization algorithms, a globally optimal plan is generated, achieving synergistic optimization of schedule, cost, resource balance, and personnel risk, thereby improving project construction efficiency.

The application belongs to the technical field of unmanned aerial vehicle operation control, and discloses a plant protection unmanned aerial vehicle intelligent path planning method and system based on multi-target optimization, which comprises the following steps: collecting multi-source data and processing the same to obtain processed data; constructing an energy consumption-pesticide efficacy multi-target optimization model according to the processed data, including a maximum prevention and treatment effect objective function and a minimum energy consumption objective function; solving the energy consumption-pesticide efficacy multi-target optimization model by using an improved NSGA-II algorithm, and generating a Pareto optimal solution set according to a constraint condition; and selecting a plurality of optimal solutions from the Pareto optimal solution set to obtain a three-dimensional flight path and corresponding flight parameters. The application realizes differentiated and accurate pesticide application for plant diseases and insect pests, solves the problems of uneven pesticide application, high energy consumption and poor adaptability of the traditional bow-shaped full coverage path, and significantly improves the accuracy, economy and environmental friendliness of plant protection operation.

The application discloses a kind of carbon dioxide foam fracturing fluid gas injection parameter multi-objective optimization method and device, wherein, method includes: obtaining target formation geologic parameter and engineering constraint parameter and carrying out normalization processing;Normalize geologic parameter is converted into dynamic constraint condition associated with equipment pressure resistance capacity, to dynamically adjust gas injection pressure upper limit;Multi-objective function is constructed with fracture complexity, flowback rate and carbon emission as optimization target;With dynamic constraint and engineering constraint as boundary, improved multi-objective evolutionary algorithm is used to solve function, which generates uniformly distributed reference points in target space and uses reference point correlation strategy for population evolution, to generate Pareto optimal solution set;According to engineering constraint, the solution set is filtered to obtain the feasible optimal solution set, and the gas injection pressure, discharge capacity and carbon dioxide phase proportion are real-time closed-loop controlled according to the optimal solution set.The application realizes collaborative optimization, and significantly improves fracturing effect and low-carbon performance.

This paper presents a sparse grid polynomial-based orbital game situation analysis method, belonging to the field of aerospace orbital adversarial and intelligent decision analysis technology. Addressing the problems of lack of systematic representation of multi-source uncertainties, low computational efficiency of traditional quantification methods, and difficulty in achieving multi-objective equilibrium optimization in existing high-orbit multi-to-multi dynamic adversarial scenarios, this paper constructs a POMDP multi-to-multi dynamic game model incorporating uncertainties in high-orbit dynamics and control execution, strategy behavior, and communication delay. A surrogate model is established using sparse grid sampling and polynomial chaotic expansion, and global sensitivity analysis is performed. Based on this, a multi-objective optimization model is constructed, and the Pareto optimal policy set is solved. This achieves game strategy generation that balances performance, robustness, and economy, and is applicable to spacecraft strategy optimization and space situation analysis in high-orbit multi-to-multi dynamic adversarial missions.

The application provides a fragrance reconstruction method, device, medium and product, relates to the technical field of perfume manufacturing, and the method comprises the following steps: obtaining target sample chemical analysis data and olfactory sensory data; determining a sensory contribution weight value according to a GC-O intensity value and a flavor dilution factor value; calculating a sensory contribution value by combining an olfactory threshold, a relative concentration and the sensory contribution weight value; converting an odor description text into a digital fragrance feature vector by using a natural language processing technology, and synthesizing a fragrance profile vector by weighting; based on a raw material database, iteratively calculating a raw material combination by using a multi-objective optimization genetic algorithm according to constraint conditions and optimization objectives of maximizing a predicted fragrance profile vector and the fragrance profile vector similarity and minimizing a cost, to obtain a Pareto optimal formula set. The scheme solves the technical problem of how to stably output a fragrance formula with optimal comprehensive indexes.

This invention relates to the field of low-altitude emergency response technology and discloses a method for joint scheduling optimization of heterogeneous equipment for low-altitude emergency response tasks. The method includes: obtaining a task set and a set of heterogeneous equipment for the low-altitude emergency response task; constructing a dual-objective joint scheduling model for the low-altitude emergency response task based on the task set and the heterogeneous equipment set; performing non-dominated sorting optimization on the dual-objective joint scheduling model to generate a Pareto optimal solution set for the low-altitude emergency response task; executing the scheduling scheme in the Pareto optimal solution set; and monitoring the heterogeneous equipment of the low-altitude emergency response task in real time based on a preset dynamic rescheduling mechanism to obtain triggering events for the heterogeneous equipment; dynamically rescheduling the scheduling scheme based on the triggering events to generate a scheduling update scheme for the low-altitude emergency response task. This invention can improve the overall success rate, resource utilization efficiency, and system robustness of low-altitude emergency response tasks.

This invention discloses an ecological management zoning method and system based on static and dynamic supply and demand matching, belonging to the field of ecological management technology. The invention constructs a node feature matrix by calculating a comprehensive static supply and demand matching index and a comprehensive dynamic change trend index, then generates a dynamic spatiotemporal adjacency matrix to construct a spatiotemporal physical connectivity graph. This graph is then input into a spatiotemporal graph neural network for processing, outputting predicted static supply and demand matching indices and predicted dynamic change trend indices. Based on the zero-value boundaries of these indices, the study area is divided into initial four-level basic management zones. A Markov decision process is then constructed, and a Pareto optimal solution set is obtained through reinforcement learning algorithms to fine-tune the spatial boundaries of the initial four-level basic management zones. The resulting refined ecological management zoning map and management priority sequence are output, making the zoning results more targeted for management. This solves the problem that existing ecological management zoning results lag behind actual changes and are difficult to effectively support adaptive management.

The application provides a multi-target path collaborative optimization method based on space-time feature enhancement and graph neural network guidance, comprising the following steps: step 1, constructing a basic data system supporting path optimization; step 2, generating a node embedding vector capable of guiding path search; step 3, reconstructing the relevance of the distribution task in the feature space, and generating a high-quality initial solution set through heuristic guidance; step 4, realizing fine iteration of the distribution scheme through an improved genetic operator; and step 5, establishing a fast lookup table mechanism based on time axis discretization preprocessing and state recursion. The method effectively improves the real adaptability and algorithm optimization accuracy of the path planning scheme, realizes the collaborative optimization of distribution efficiency and driving safety, greatly reduces the calculation complexity in the dynamic scene, can generate a Pareto optimal solution considering multi-target requirements, meets the real-time scheduling and decision-making requirements of complex urban distribution scenes, and has good engineering application value.

The application discloses a multi-target-oriented power distribution network safety domain operation point screening method, medium and equipment, belongs to the field of power system operation and optimal control, and comprises the following steps: firstly, constructing a static safety domain containing a power flow equation and multiple constraints based on power distribution network nodes, branch information and safety criteria; secondly, accurately obtaining a safety domain boundary through adaptive direction search and error correction; thirdly, generating a candidate operation point by Monte Carlo sampling, combining economic and reliable indexes, and obtaining a Pareto optimal solution set through fast non-dominated sorting; finally, screening an optimal operation point considering safety, economy and reliability through fuzzy multi-attribute decision and decision maker preference analysis; the application realizes three-dimensional target collaborative optimization, is high in calculation efficiency and strong in robustness, can adapt to real-time optimization requirements of high-proportion distributed power distribution networks, and can be widely applied to active power distribution network safety evaluation, energy storage configuration and economic dispatching scenes.

This invention belongs to the field of power grid investment optimization technology, and relates to a regional power grid investment optimization method based on a multi-objective programming model. It includes the following steps: Step S1: Considering the decoupling requirements between regional power grid investment and electricity generation, a multi-dimensional parameter system covering investment, electricity generation, safety, and green / low-carbon parameters is constructed; Step S2: Based on the multi-dimensional parameter system, a multi-objective programming model is constructed to maximize the net present value of investment, maximize the power grid safety margin, and maximize the investment-electricity decoupling degree; Step S3: An improved multi-objective particle swarm optimization algorithm is used to solve the model, and the Pareto optimal solution set is output to obtain the optimal investment scheme. This invention quantifies the decoupling relationship between investment and electricity generation through a multi-dimensional parameter system, and optimizes the balance between economic efficiency, power supply safety, and resource allocation efficiency using a multi-objective model, solving the problems of excessive coupling between investment and electricity generation and insufficient functional value mining in existing planning.

The application discloses a multi-objective path optimization method based on a Pareto dominance relationship, and comprises the following steps: S1, before each path exploration, candidate paths are selected according to the Pareto dominance relationship between the explored paths; S2, breadth-first traversal is performed on the candidate paths in sequence, and single-step exploration of the paths is realized; S3, after each round of path exploration, the current path is compared with the paths in the known optimal solution set, and the paths that cannot become the optimal solution are removed; and S4, steps S1-S3 are repeatedly executed until no new optimal solution appears. The application realizes the Pareto optimal solution through multiple rounds of path exploration, and solves the problems of how to improve the efficiency of the multi-objective path optimization problem and how to improve the quality of the multi-objective path optimization solution set.