Noninferior Set Research Articles

Bi-objective goal programming for balancing costs vs. nutritional adequacy.

Linear programming (LP) is often used within diet optimization to find, from a set of available food commodities, the most affordable diet that meets the nutritional requirements of an individual or (sub)population. It is, however, not always possible to create a feasible diet, as certain nutritional requirements are difficult to meet. In that case, goal programming (GP) can be used to minimize deviations from the nutritional requirements in order to obtain a near feasible diet. With GP the cost of the diet is often overlooked or taken into account using the ε-constraint method. This method does not guarantee to find all possible trade-offs between costs and nutritional deficiency without solving many uninformative LPs. We present a method to find all trade-offs between any two linear objectives in a dietary LP context that is simple, does not solve uninformative LPs and does not need prior input from the decision maker (DM). This method is a bi-objective algorithm based on the NonInferior Set Estimation (NISE) method that finds all efficient trade-offs between two linear objectives. In order to show what type of insights can be gained from this approach, two analyses are presented that investigate the relation between cost and nutritional adequacy. In the first analysis a diet with a restriction on the exact energy intake is considered where all nutrient intakes except energy are allowed to deviate from their prescription. This analysis is especially helpful in case of a restrictive budget or when a nutritionally adequate diet is either unaffordable or unattainable. The second analysis only relaxes the exact energy intake, where the other nutrients are kept within their requirements, to investigate how the energy intake affects the cost of a diet. Here, we describe in what situations the so-called more-for-less paradox takes place, which can be induced by requiring an exact energy intake. To the best of our knowledge, we are the first to address how to obtain all efficient trade-offs of two linear objectives in a dietary LP context and how this can be used for analyses.

Exploring multiobjective training in multiclass classification

Multinomial logistic loss and L2 regularization are often conflicting objectives as more robust regularization leads to restrained multinomial parameters. For many practical problems, leveraging the best of both worlds would be invaluable for better decision-making processes. This research proposes a novel framework to obtain representative and diverse L2-regularized multinomial models, based on valuable trade-offs between prediction error and model complexity. The framework relies upon the Non-Inferior Set Estimation (NISE) method – a deterministic multiobjective solver. NISE automatically implements hyperparameter tuning in a multiobjective context. Given the diverse set of efficient learning models, model selection and aggregation of the multiple models in an ensemble framework promote high performance in multiclass classification. Additionally, NISE uses the weighted sum method as scalarization, thus being able to deal with the learning formulation directly. Its deterministic nature and the convexity of the learning problem confer scalability to the proposal. The experiments show competitive performance in various setups, taking a broad set of multiclass classification methods as contenders.

Simulation of Sports Venue Based on Ant Colony Algorithm and Artificial Intelligence

In order to improve the congestion of the evacuation plan and further improve the evacuation efficiency, this paper proposes the priority Pareto partial order relation and the vector pheromone routing method based on the priority Pareto partial order relation. Numerical experiments show that compared with the hierarchical multiobjective evacuation path optimization algorithm based on the hierarchical network, the fragmented multiobjective evacuation path optimization algorithm proposed in this paper effectively improves the evacuation efficiency of the evacuation plan and the convergence of the noninferior plan set. However, the congestion condition of the noninferior evacuation plan obtained by the fragmented multiobjective evacuation route optimization algorithm is worse than the congestion condition of the noninferior evacuation plan obtained by the hierarchical multiobjective evacuation route optimization algorithm. The multiple factors that affect the routing process considered in the probability transfer function used in the traditional ant colony algorithm routing method must be independent of each other. However, in actual route selection, multiple factors that affect route selection are not necessarily independent of each other. In order to fully consider the various factors that affect the routing, this paper adopts the vector pheromone routing method based on the traditional Pareto partial order relationship instead of the traditional ant colony algorithm. The model mainly improves the original pheromone distribution and volatilization coefficient of the ant colony, speeds up the convergence speed and accuracy of the algorithm, and obtains ideal candidate solutions. The method is applied to the location of sports facilities and has achieved good results. The experimental results show that the improved ant colony algorithm model designed in this paper is suitable for solving the problem of urban sports facilities location in large‐scale space.

Modeling habitat connectivity in support of multiobjective species movement: An application to amphibian habitat systems

Reasoning about the factors underlying habitat connectivity and the inter-habitat movement of species is essential to many areas of biological inquiry. In order to better describe and understand the ways in which the landscape may support species movement, an increasing amount of research has focused on identification of paths or corridors that may be important in providing connectivity among habitat. The least-cost path problem has proven to be an instrumental analytical tool in this sense. A complicating aspect of such path identification methods is how to best reconcile and integrate the array of criteria or objectives that species may consider in traversal of a landscape. In cases where habitat connectivity is thought to be influenced or guided by multiple objectives, numerous solutions to least-cost path problems can exist, representing tradeoffs between the objectives. In practice though, identification of these solutions can be very challenging and as such, only a small proportion of them are typically examined leading to a weak characterization of habitat connectivity. To address this computational challenge, a multiobjective optimization framework is proposed. A generalizable multiobjective least-cost path model is first detailed. A non-inferior set estimation (MONISE) algorithm for identifying supported efficient solutions to the multiobjective least-cost path model is then described. However, it is well known that unsupported efficient solutions (which are equally important) can also exist, but are typically ignored given that they are more difficult to identify. Thus, to enable the identification of the full set of efficient solutions (supported and unsupported) to the multiobjective model, a multi-criteria labeling algorithm is then proposed. The developed framework is applied to assess different conceptualizations of habitat connectivity supporting amphibian movement in a wetland system. The results highlight the range of tradeoffs in characterizations of connectivity that can exist when multiple objectives are thought to contribute to movement decisions and that the number of unsupported efficient solutions (which are typically ignored) can vastly outweigh that of the supported efficient solutions.

An extension of the non-inferior set estimation algorithm for many objectives

This work proposes a novel multi-objective optimization approach that globally finds a representative non-inferior set of solutions, also known as Pareto-optimal solutions, by automatically formulating and solving a sequence of weighted sum method scalarization problems. The approach is called MONISE (Many-Objective NISE) because it represents an extension of the well-known non-inferior set estimation (NISE) algorithm, which was originally conceived to deal with two-dimensional objective spaces. The proposal is endowed with the following characteristics: (1) uses a mixed-integer linear programming formulation to operate in two or more dimensions, thus properly supporting many (i.e., three or more) objectives; (2) relies on an external algorithm to solve the weighted sum method scalarization problem to optimality; and (3) creates a faithful representation of the Pareto frontier in the case of convex problems, and a useful approximation of it in the non-convex case. Moreover, when dealing specifically with two objectives, some additional properties are portrayed for the estimated non-inferior set. Experimental results validate the proposal and indicate that MONISE is competitive, in convex and non-convex (combinatorial) problems, both in terms of computational cost and the overall quality of the non-inferior set, measured by the acquired hypervolume.

Revealing the water-energy-food nexus in the Upper Yellow River Basin through multi-objective optimization for reservoir system

Since the 21st century, the natural runoff from the headwater region of the Yellow River has generally been decreasing, resulting in a particularly prominent contradiction in utilization of water resources. In this study, key components were identified from the perspective of water-energy-food (WEF) nexus, and a WEF nexus model was established for the Upper Yellow River Basin (UYRB), taking into consideration the benefits of water supply to the middle and lower reaches of Yellow River, food growth in major food-producing areas in the UYRB and hydropower utilization of the UYR reservoir system. The Multi-start Solver of LINGO and the ε constraint method were used to carry out multi-objective optimization, revealing the trade-off between the WEF benefits. 1) The model computed the Pareto non-inferior set of solutions for the electricity generated by the UYR reservoir system and the degree to which the water demands of the main intake areas (Ningxia and Inner Mongolia irrigated areas, and Toudaoguai section) are satisfied, quantifying the improvement room for the overall benefits brought about by the jointly optimal operation of the WEF sectors. 2) The historical operation of Longyangxia Reservoir, a multi-year storage reservoir, was evaluated, the results of which show that the realization of the WEF benefits is determined by the proper operation of Longyangxia Reservoir. To guarantee the overall benefits in the long term, Longyangxia Reservoir should maintain a high water level. 3) The trade-offs between the WEF benefits under different boundary conditions were discussed, including various initial/final fore-bay water levels of Longyangxia Reservoir and inflows of various total water amounts from the headwater region of the UYRB. The research reveals the WEF nexus in the UYRB under different scenarios, and moreover, the formulated multi-objective optimization model is a good example that can be extended to other similar WEF nexus systems worldwide.

Multiobjective Economic Load Dispatch Studies in 2-D and 3-D Space by Particle Swarm Optimization Technique

In this paper, three important objectives of power systems—cost of generation (FC), system transmission losses (FL) and environmental emissions (FE)—have been considered. The multiobjective economic load dispatch problem has been formulated using weighting method. The noninferior set for IEEE 5 bus, IEEE 14 bus and IEEE 30 bus systems has been generated using particle swarm optimization technique. The noninferior set obtained has been displayed in 3-D space considering all the three objectives and in 2-D space all the combinations of two objectives, viz. for FC & FL, FC & FE and FL & FE for IEEE 5 bus, IEEE 14 bus and IEEE 30 bus systems. The target point or best compromise solution has been obtained by maximizing the minimum relative attainments of all the objectives.

Multiobjective Economic Load Dispatch in 3-D Space by Genetic Algorithm

This paper presents the application of genetic algorithm to Multiobjective Economic Load Dispatch (MELD) problem considering fuel cost, transmission losses and environmental pollution as objective functions. The MELD problem has been formulated using constraint method. The non-inferior set for IEEE 5, 14 and 30-bus system has been generated by using genetic algorithm and the target point has been obtained by using maximization of minimum relative attainments.

PSO for Multiobjective Economic Load Dispatch (MELD) for Minimizing Generation Cost and Transmission Losses

In this paper, multiobjective economic load dispatch (MELD) problem considering generation cost and transmission losses has been formulated using priority goal programming (PGP) technique. In this formulation, equality constraint has been considered by inclusion of penalty parameter K. It has been observed that fixing its value to 1,000 keeps the equality constraint within limits. The non-inferior set for IEEE 5, 14 and 30-bus systems has been generated by Particle Swarm Optimization (PSO) technique. The best compromise solution has been chosen as the one which gives equal percentage saving for both the objectives.

Dimensional optimization of a minimally invasive surgical robot system based on NSGA-II algorithm

Based on the proposed end-effector structure of a laparoscopic minimally invasive surgical manipulator, a dimensional optimization method is investigated to enlarge the motion range of the mechanical arm in the specific target area and reduce the collision among the mechanical arms simultaneously. Both the length of the kinematics links and the overall size of the integrated system are considered in the optimization process. The NSGA-II algorithm oriented to the multi-objective optimization is utilized to calculate the Pareto solution set of the objective function. Finally, the dependence of the evaluation indexes is analysed to filter the non-inferior set, which guarantees the selection of the optimization solution.

A Multi-Objective Optimization Model for Coordinated Regulation of Flow and Sediment in Cascade Reservoirs

This paper presents a multi-objective optimization model for the coordinated regulation of flow and sediment in cascade reservoirs. The model was developed to address two contradicting issues: sediment trapping and flow regulation. The benefits of flood control, hydropower generation and navigation, and sedimentation in cascade reservoirs were considered as the target functions; then the corresponding submodels for reservoir operation and sediment computation were established. The model was implemented by reducing it to a single objective nonlinear model using the constraint method. Non-inferior solutions were obtained by solving the model with catfish effect particle swarm optimization algorithm. The model was applied to the cascade system of Xiluodu and Xiangjiaba reservoirs in the lower Jinsha River in the flood recession period. Under the safety of flood control and navigation, a non-inferior set for impounding time, power generation, and siltation-loss rate of capacity was obtained and optimal solutions with different weights were derived. The results demonstrate that the model is a useful tool in coordinated operations of cascade reservoirs.

Is Multiobjective Optimization Ready for Water Resources Practitioners? Utility’s Drought Policy Investigation

Is Multiobjective Optimization Ready for Water Resources Practitioners? Utility’s Drought Policy Investigation

Corridor Location for Infrastructure Development

Corridor location for developing new infrastructure such as transmission lines, roadways, and pipelines over terrain must consider numerous factors when determining the set of optimal route candidates. Previous researchers have cast this problem as a multiobjective least cost path problem, where competing objectives represent cost, environmental impact, and other major noncommensurate objectives. To fully characterize the optimal trade-off solution set, one must be able to generate both supported and unsupported nondominated solutions. Fortunately, the supported, nondominated solutions are relatively easy to identify by using a single-objective shortest path algorithm in conjunction with the noninferior set estimation method of Cohon, Church, and Sheer. But, finding the unsupported nondominated solutions can be nondeterministic polynomial time hard. This article proposes a heuristic approach that is capable of determining a Pareto frontier that is very near exact in polynomial time. This heuristic approach uses gateway node and gateway arc paths to generate a large set of spatially diverse locally optimal candidate solutions with few shortest path solver iterations, which are shown to represent a solution set that approximates to a high degree, the exact Pareto set. The method is described within the context of a bi-objective corridor location problem and applied to several data sets that have been used in past work. A comparison between this new approach and existing exact algorithms is provided. Overall, the new method is shown to be effective at finding a sizable number of the unsupported nondominated solutions in a very small amount of computational time.

Improved multi-objective ant colony optimization algorithm and its application in complex reasoning

The problem of fault reasoning has aroused great concern in scientific and engineering fields. However, fault investigation and reasoning of complex system is not a simple reasoning decision-making problem. It has become a typical multi-constraint and multi-objective reticulate optimization decision-making problem under many influencing factors and constraints. So far, little research has been carried out in this field. This paper transforms the fault reasoning problem of complex system into a paths-searching problem starting from known symptoms to fault causes. Three optimization objectives are considered simultaneously: maximum probability of average fault, maximum average importance, and minimum average complexity of test. Under the constraints of both known symptoms and the causal relationship among different components, a multi-objective optimization mathematical model is set up, taking minimizing cost of fault reasoning as the target function. Since the problem is non-deterministic polynomial-hard(NP-hard), a modified multi-objective ant colony algorithm is proposed, in which a reachability matrix is set up to constrain the feasible search nodes of the ants and a new pseudo-random-proportional rule and a pheromone adjustment mechinism are constructed to balance conflicts between the optimization objectives. At last, a Pareto optimal set is acquired. Evaluation functions based on validity and tendency of reasoning paths are defined to optimize noninferior set, through which the final fault causes can be identified according to decision-making demands, thus realize fault reasoning of the multi-constraint and multi-objective complex system. Reasoning results demonstrate that the improved multi-objective ant colony optimization(IMACO) can realize reasoning and locating fault positions precisely by solving the multi-objective fault diagnosis model, which provides a new method to solve the problem of multi-constraint and multi-objective fault diagnosis and reasoning of complex system.

Efficiency evaluation for allocating community-based health services

When allocating community-based health services for a geographically defined region, health planners are often faced with the serious conflict for improved health service and a limited budget. This paper extends the cost-based P-median location–allocation model (Daskin & Dean, 2005) to include a public service element and uses the non-inferior set estimation (NISE) method for evaluation of cost/service trade-offs. Service is measured by the percentage of demand volume that can be served within exogenously specified coverage distances. Importantly, we evaluate the efficiency (i.e. the relative cost and service) of the non-inferior solutions of our model using the commonly used “population-based” allocation policy as standard. Computational results illustrate the value of our model under several practical problem settings.

Multi-objective evolutionary algorithm for grid job scheduling based on adaptive neighborhood

A new adaptive neighborhood Multi-Objective Grid Task Scheduling Algorithm(ANMO-GTSA) was proposed in this paper for the multi-objective job scheduling collaborative optimization problem in grid computing.In the ANMO-GTSA,an adaptive neighborhood method was applied to find the non-inferior set of solutions and maintain the diversity of the multi-objective job scheduling population.The experimental results indicate that the algorithm proposed in this paper can not only balance the multi-objective job scheduling,but also improve the resource utilization and efficiency of task execution.Moreover,the proposed algorithm can achieve better performance on time-dimension and cost-dimension than the traditional Min-min and Max-min algorithms.

Bidding based generator maintenance scheduling with triple-objective optimization

A new bidding based generating unit maintenance scheduling method under the electricity market environment is presented in this paper. The method can balance overall reliability and economy, and ensure the fairness to all generation companies (GENCOs). The unit maintenance scheduling is modeled as a triple-objective non-convex optimization problem with discrete variables and is solved using an improved version of the Non-dominated Sorting Genetic Algorithm (NSGA-II). A non-inferior solution set is directly produced from huge combinations. A few candidate solutions are selected from the non-inferior set by independent system operator (ISO) based on the overall reliability and economy, whereas the final maintenance schedule is determined by voting of GENCOs. The shares of vote are calculated from the bidding information of GENCOs and the right of each GENCO is fairly guaranteed. A case study of 50 units demonstrates the effectiveness of the proposed method.

Buffer and throughput trade-offs in M/ G/1/ K queueing networks: A bi-criteria approach

The optimal design of real-life systems modeled as finite queueing networks is a difficult stochastic optimization problem. Besides being non-linear and including integer variables, different objectives often conflict with each other. For example, one conflicting pair of objectives includes first minimizing the overall number of buffers and then maximizing throughput. In this paper, we present an original methodology to solve a buffer allocation and throughput trade-off problem in single server general queueing networks. An approximation of the complete set of all best solutions, known as the Pareto optimal or non-inferior set, is derived by a special version of a multi-objective genetic algorithm (MOGA). The applied MOGA proves to be suitable for the stochastic trade-off problem. A comprehensive set of computational results attest to the efficiency and efficacy of the proposed methodology. We were able to show from a medium-sized mixed network that the squared coefficient of service time variation plays an important role in buffer allocation, which indicates the importance of using a general service model. Moreover, after the analysis of the solutions in the decision variable space, we confirm that the buffer allocation is highly dependent on the target throughput, which sometimes can be sacrificed in favor of using fewer of the usually expensive buffer spaces.

Multiobjective flux balancing using the NISE method for metabolic network analysis

Flux balance analysis (FBA) is well acknowledged as an analysis tool of metabolic networks in the framework of metabolic engineering. However, FBA has a limitation for solving a multiobjective optimization problem which considers multiple conflicting objectives. In this study, we propose a novel multiobjective flux balance analysis method, which adapts the noninferior set estimation (NISE) method (Solanki et al., 1993) for multiobjective linear programming (MOLP) problems. NISE method can generate an approximation of the Pareto curve for conflicting objectives without redundant iterations of single objective optimization. Furthermore, the flux distributions at each Pareto optimal solution can be obtained for understanding the internal flux changes in the metabolic network. The functionality of this approach is shown by applying it to a genome-scale in silico model of E. coli. Multiple objectives for the poly(3-hydroxybutyrate) [P(3HB)] production are considered simultaneously, and relationships among them are identified. The Pareto curve for maximizing succinic acid production vs. maximizing biomass production is used for the in silico analysis of various combinatorial knockout strains. This proposed method accelerates the strain improvement in the metabolic engineering by reducing computation time of obtaining the Pareto curve and analysis time of flux distribution at each Pareto optimal solution.

Environmentally conscious design of chemical processes and products: Multi-optimization method

This paper presents an environmentally conscious integrated methodology for design and optimization of chemical process especially for separation process, whose energy consumption occupies more than 70% of the whole process. The methodology incorporates environmental factors into the chemical process synthesis at the initial design stage, which is totally different with the traditional end-of-pipe treatment method. Firstly, one rigorous model for simulation of multi-stages and multi-components separation process was developed, and based on our proposed environmental impact assessment method, the calculation methods of the reasonable economic and environment objective are constructed. Then one multi-objective mixed integer non-linear mathematical model was established by considering environmental and economic factors. Finally, the high non-linear model was solved by multi-objective evolutionary algorithm (non-dominated sorting genetic algorithm). It is often difficult to find an optimum for a process that satisfies both economic and environmental objectives simultaneously. Normally, an arrangement of optimal solutions is obtained, which forms a non-inferior set. Identifying the optimum from this non-inferior set is subjective, depending on the preference of decision makers. In this paper, technique for order preference by similarity to ideal solution (TOPSIS) for identifying the set of optimal parameters is developed and used at the decision-making step, in which the preference relation for the decision-maker over the objectives is adopted by trade-off information between objectives. The proposed methodology was highlighted through two industrialized processes, dimethyl carbonate production processes by pressure-swing distillation and extraction distillation process, respectively.