Pareto Strategy Research Articles

A pareto strategy based on multi-objective optimal integration of distributed generation and compensation devices regarding weather and load fluctuations

In this study, we present a comprehensive optimization framework employing the Multi-Objective Multi-Verse Optimization (MOMVO) algorithm for the optimal integration of Distributed Generations (DGs) and Capacitor Banks (CBs) into electrical distribution networks. Designed with the dual objectives of minimizing energy losses and voltage deviations, this framework significantly enhances the operational efficiency and reliability of the network. Rigorous simulations on the standard IEEE 33-bus and IEEE 69-bus test systems underscore the effectiveness of the MOMVO algorithm, demonstrating up to a 47% reduction in energy losses and up to a 55% improvement in voltage stability. Comparative analysis highlights MOMVO's superiority in terms of convergence speed and solution quality over leading algorithms such as the Multi-Objective Jellyfish Search (MOJS), Multi-Objective Flower Pollination Algorithm (MOFPA), and Multi-Objective Lichtenberg Algorithm (MOLA). The efficacy of the study is particularly evident in the identification of the best compromise solutions using MOMVO. For the IEEE 33 network, the application of MOMVO led to a significant 47.58% reduction in daily energy loss and enhanced voltage profile stability from 0.89 to 0.94 pu. Additionally, it realized a 36.97% decrease in the annual cost of energy losses, highlighting substantial economic benefits. For the larger IEEE 69 network, MOMVO achieved a remarkable 50.15% reduction in energy loss and improved voltage profiles from 0.89 to 0.93 pu, accompanied by a 47.59% reduction in the annual cost of energy losses. These results not only confirm the robustness of the MOMVO algorithm in optimizing technical and economic efficiencies but also underline the potential of advanced optimization techniques in facilitating the sustainable integration of renewable energy resources into existing power infrastructures. This research significantly contributes to the field of electrical distribution network optimization, paving the way for future advancements in renewable energy integration and optimization techniques for enhanced system efficiency, reliability, and sustainability.

Hierarchical control problem for the heat equation with dynamic boundary conditions

Abstract This paper deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg–Pareto strategy.

Dynamic Analysis and Optimization of Vehicle-Bridge Interaction System under Road Roughness and Time Variability of Element Interpolation Function

Vehicle-induced load, as one of the main excitation factors to bridge vibration and fatigue damage, plays a vital role in the analyzing of the vehicle-bridge interaction (VBI) system, but is still limited in both spatial location and numerical value. This paper presents an improved VBI system to investigate bridge vibration and vehicle vibration considering the coherent roughness and multiple lanes excitation. The vehicle and bridge subsystems and coherent roughness road are developed and are further integrated to form the VBI system based on the displacement relationship between wheels and the bridge. Further, the solution method of the VBI system is given, and the calculation platform is constructed. Meanwhile, the natural frequencies and mode shapes, as well as the mid-span displacement of the bridge, are verified with the results calculated in commercial software. Subsequently, the responses of the VBI system are investigated under different degrees of freedom of vehicle vibration, bridge damping ratio, road roughness class, multiple lanes, and velocity. It can be concluded that road roughness and velocity have a complex nonlinear relationship with the vibration of the VBI system. Finally, the Pareto strategy is applied to find the optimized value of suspension stiffness and damping, and the depth, unit mass, and elastic modulus of the bridge to minimize the system vibration. The results show an obvious improvement in the vibration of the VBI system.

Day-Ahead and Intraday Dispatch of an Integrated Biomass-Concentrated Solar System: A Multi-Objective Risk-Controlling Approach

Solar energy and bioenergy are two leading renewable forms of energy in the move toward a near-zero-emission electric power industry. Concentrated solar power units coupled with thermal storage and biomass power plant offer dispatchable electricity, raising their ever-growing role in future renewable-dominated networks. This paper proposes a day-ahead and intraday dispatch model for maximizing the profit of an Integrated Biomass-Concentrated Solar (IBCS) system considering the synergies arising from their coupled operation. To sensibly capture uncertainty and decision sequence of real-life electricity markets, a two-stage stochastic structure is proposed, while the solar-related uncertainty is involved using Information Gap Decision Theory (IGDT). The model is complemented with a novel multi-objective architecture based on the compound of IGDT and Conditional Value-at-Risk (CVaR), which allows handling risk exposure to both stochastic and IGDT inputs. The Pareto strategies in the multi-objective model are extracted through an expanded form of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -constraint method, whereas <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> approach based upon the out-of-sample assessment is applied to derive the optimal dispatch pattern among the generated Pareto strategies. The simulation results demonstrate that: 1) the proposed integrated dispatch model achieves substantial profitability, and 2) the performance of the suggested CVaR-IGDT model is superior to conventional approaches.

Adaptive multi-objective service composition reconfiguration approach considering dynamic practical constraints in cloud manufacturing

Dynamic uncertainty factors such as equipment faults are common in practically implemented cloud manufacturing (CMfg) environments, often causing the manufacturing service to be invalidated. In that case, efficient reconfiguration of the original service composition under practical constraints is critical; however, existing research scarcely focuses on it. This paper proposes a dynamic service composition reconfiguration model to bridge the gap by considering practical constraints (DSCRPC) in a real-life cloud manufacturing environment. Based on the constraints considered in this study, the DSCRPC model redefines three objectives: time (T*), cost (C*), and product service quality (Q*S*). To optimize the DSCRPC model, this study developed an adaptive multi-population multi-objective whale optimization algorithm (AMPOWOA) based on the Pareto strategy. The algorithm adopts four balancing strategies and adaptively optimizes and adjusts the key parameters under various balancing strategies through well-designed reinforcement learning models. Finally, we conduct numerical experiments and actual application case tests to compare the performances of AMPOWOA and other algorithms (MOWOA, MOHHO, NSGA-II). The results show that DSCRPC can continuously tackle the cloud manufacturing service composition (CMSC) reconfiguration issue with constraints until an order is completed. Moreover, AMPOWOA is superior to the other algorithms optimizing the DSCRPC model. This significantly enhances the robustness of service composition reconfiguration in real-life CMfg.

Optimization and Mechanism of the Wicket Gate Closing Law for High-Head Pumped Storage Power Stations

The high-head pumped storage power station (PSPS) has complex working conditions and severe transient processes. Under load rejection conditions, the turbine speed and the flow channel pressure will threaten the unit. By adjusting the wicket gate closing law (WGCL), we can effectively alleviate the adverse effects of the transient process. In this study, a full flow channel refined model of a high-head PSPS was constructed, and the influence mechanism of load rejection conditions on key parameters was analyzed by tracking the operating trajectory on the S characteristic curves and simulating the transient flow field inside the pumped turbine by three-dimensional computational fluid dynamics (3D-CFD). Given the contradiction between different parameters in the wicket gate closing process, a third-generation non-dominated genetic algorithm based on reference point selection (NSGA-III) was introduced, and a high-dimensional multi-objective WGCL optimization model was constructed. We compared parameter changes in the two-phase and three-phase WGCL optimized elite solutions and explained the rationality of adopting the three-phase WGCL in high-head PSPSs. By proposing an improved three-phase WGCL, a new scheme—the most suitable WGCL under load rejection—was obtained through precise optimization. The research embodied the excellent effect of the heuristic multi-objective (MO) optimization algorithm based on the Pareto strategy in solving the operation problem of the large fluctuation transient process of hydraulic machinery. It revealed the theoretical basis of engineering adjustment for the safe production and operation of hydropower.

Fault-tolerant control for four-wheel independent actuated electric vehicle using feedback linearization and cooperative game theory

This paper presents a novel fault-tolerant control (FTC) approach based on the cooperative game to guarantee the stability of four-wheel independent drive electric vehicles, in which four different players are modeled and interacted to find a solution to the FTC problem. First, a feedback linearization approach is employed to handle the nonlinearities in the system. Then, to study the interaction among actuators in an actuator failure scenario, the FTC problem can be viewed as a cooperative game so that its four players, namely the four in-wheel motors can cooperate to provide more stability of the vehicle. The distributed model predictive control theory is adopted as a general framework, the Pareto strategies among the players are derived using an interactive model based on a convex iterative method. Furthermore, the conditions that guarantee the practical stability of the closed-loop system are provided. The intrinsic differences between the cooperative game and noncooperative game are investigated via a numerical simulation. The effectiveness and real-time of the proposed control strategy are verified in a real-time hardware-in-the-loop test, and the results prove that the control strategy can effectively guarantee the stability of the vehicle in various actuator failure scenarios.

Synchronous self-learning Pareto strategy

PurposeIn recent decades, development of effective methods for optimizing a set of conflicted objective functions has been absorbing an increasing interest from researchers. This refers to the essence of real-life engineering systems and complex natural mechanisms which are generally multi-modal, non-convex and multi-criterion. Until now, several deterministic and stochastic methods have been proposed to cope with such complex systems. Advanced soft computational methods such as evolutionary games (cooperative and non-cooperative), Pareto-based techniques, fuzzy evolutionary methods, cooperative bio-inspired algorithms and neuro-evolutionary systems have effectively come to the aid of researchers to build up efficient paradigms with application to vector optimization. The paper aims to discuss this issue.Design/methodology/approachA novel hybrid algorithm called synchronous self-learning Pareto strategy (SSLPS) is presented for the sake of vector optimization. The method is the ensemble of evolutionary algorithms (EA), swarm intelligence (SI), adaptive version of self-organizing map (CSOM) and a data shuffling mechanism. EA are powerful numerical optimization algorithms capable of finding a global extreme point over a wide exploration domain. SI techniques (the swarm of bees in our case) can improve both intensification and robustness of exploration. CSOM network is an unsupervised learning methodology which learns the characteristics of non-dominated solutions and, thus, enhances the quality of the Pareto front.FindingsTo prove the effectiveness of the proposed method, the authors engage a set of well-known benchmark functions and some well-known rival optimization methods. Additionally, SSLPS is employed for optimal design of shape memory alloy actuator as a nonlinear multi-modal real-world engineering problem. The experiments show the acceptable potential of SSLPS for handling both numerical and engineering multi-objective problems.Originality/valueTo the author’s best knowledge, the proposed algorithm is among the rare multi-objective methods which fosters the use of automated unsupervised learning for increasing the intensity of Pareto front (while preserving the diversity). Also, the research evaluates the power of hybridization of SI and EA for efficient search.

Development of Pareto strategy multi-objective function method for the optimum design of ship structures

It is necessary to develop an efficient optimization technique to perform optimum designs which have given design spaces, discrete design values and several design goals. As optimization techniques, direct search method and stochastic search method are widely used in designing of ship structures. The merit of the direct search method is to search the optimum points rapidly by considering the search direction, step size and convergence limit. And the merit of the stochastic search method is to obtain the global optimum points well by spreading points randomly entire the design spaces. In this paper, Pareto Strategy (PS) multi-objective function method is developed by considering the search direction based on Pareto optimal points, the step size, the convergence limit and the random number generation. The success points between just before and current Pareto optimal points are considered. PS method can also apply to the single objective function problems, and can consider the discrete design variables such as plate thickness, longitudinal space, web height and web space. The optimum design results are compared with existing Random Search (RS) multi-objective function method and Evolutionary Strategy (ES) multi-objective function method by performing the optimum designs of double bottom structure and double hull tanker which have discrete design values. Its superiority and effectiveness are shown by comparing the optimum results with those of RS method and ES method.

Comparison of Robust Optimization and Info-Gap Methods for Water Resource Management under Deep Uncertainty

This paper evaluates two established decision-making methods and analyzes their performance and suitability within a water resources management (WRM) problem. The methods under assessment are info-gap (IG) decision theory and robust optimization (RO). The methods have been selected primarily to investigate a contrasting local versus global method of assessing water system robustness to deep uncertainty, but also to compare a robustness model approach (IG) with a robustness algorithm approach (RO), whereby the former selects and analyzes a set of prespecified strategies and the latter uses optimization algorithms to automatically generate and evaluate solutions. The study presents a novel area-based method for IG robustness modeling and assesses the applicability of utilizing the future flows climate change projections in scenario generation for water resource adaptation planning. The methods were applied to a case study resembling the Sussex North Water Resource Zone in England, assessing their applicability at improving a risk-based WRM problem and highlighting the strengths and weaknesses of each method at selecting suitable adaptation strategies under climate change and future demand uncertainties. Pareto sets of robustness to cost are produced for both methods and highlight RO as producing the lower cost strategies for the full range of varying target robustness levels. IG produced the more expensive Pareto strategies due to its more selective and stringent robustness analysis, resulting from the more complex scenario ordering process.

Multi-objective component sizing of a power-split plug-in hybrid electric vehicle powertrain using Pareto-based natural optimization machines

The urgent need to meet increasingly tight environmental regulations and new fuel economy requirements has motivated system science researchers and automotive engineers to take advantage of emerging computational techniques to further advance hybrid electric vehicle and plug-in hybrid electric vehicle (PHEV) designs. In particular, research has focused on vehicle powertrain system design optimization, to reduce the fuel consumption and total energy cost while improving the vehicle's driving performance. In this work, two different natural optimization machines, namely the synchronous self-learning Pareto strategy and the elitism non-dominated sorting genetic algorithm, are implemented for component sizing of a specific power-split PHEV platform with a Toyota plug-in Prius as the baseline vehicle. To do this, a high-fidelity model of the Toyota plug-in Prius is employed for the numerical experiments using the Autonomie simulation software. Based on the simulation results, it is demonstrated that Pareto-based algorithms can successfully optimize the design parameters of the vehicle powertrain.

A Modified SSLPS Algorithm with Logistic Pseudo-Random Sequence Generator for Improving the Performance of Neka Power Plant

Metaheuristic techniques have successfully contributed to the development and optimization of large-scale distributed power systems. The archived literature demonstrate that the modification or tuning of the parameters of specific metaheuristics can provide powerful tools suited for optimization of power plants with different types of constraints. In spite of the high potential of metaheuristics in dealing with such systems, most of the conducted researches only address the optimization of the electrical aspects of power systems. In this research, the authors intend to attest the applicability of metaheuristics for optimizing the mechanical aspects of a real-world large-scale power plant, i.e. Neka power plant sited in Mazandaran, Iran. To do so, firstly, based on the laws of thermodynamics and the physics of the problem at hand, the authors implement a mathematical model to calculate the values of exergetic efficiency, energetic efficiency, and total cost of the Neka power plant as three main objective functions. Besides, a memetic supervised neural network and Bahadori's mathematical model are used to calculate the dynamic values of specific heat over the operating procedure of the power plant. At the second stage, a modified version of a recent spotlighted Pareto based multiobjective metaheuristic called synchronous self-learning Pareto strategy (SSLPS) is proposed. The proposed technique is based on embedding logistic chaotic map into the algorithmic architecture of SSLPS. In this context, the resulting optimizer, i.e. chaos-enhanced SSLPS (C-SSLPS), uses the response of time-discrete nonlinear logistic map to update the positions of heuristic agents over the optimization procedure. For the sake of comparison, strength Pareto evolutionary algorithm (SPEA 2), non-dominated sorting genetic algorithm (NSGA-II) and standard SSLPS are taken into account. The results of the numerical study confirm the superiority of the proposed technique as compared to the other rival optimizers. Besides, it is observed that metaheuristics can be successfully used for optimizing the mechanical/energetic parameters of Neka power plant.

A robust time delay auto-regressive exogenous fuzzy inference system for real-time estimation of catalyst temperature over engines coldstart operation: a multiobjective implementation scenario

In the current investigation, the authors propose an intelligent real-time system to dynamically simulate the catalyst temperature in automotive engines over the coldstart period. In general, the behavior of an engine during the first few minutes of its operation, namely the coldstart period, is highly transient and nonlinear. However, it is important to the engineers of automotive industry to develop advanced simulation techniques capable of capturing the engine system’s behavior during coldstart periods. The main motivation behind such a fact emanates in the pursuit of making successful strides towards decreasing the amount of unburned hydrocarbon emissions (HCs) of the engine. Catalytic convertors play a pivotal role in reducing the amount of this emitted pollutant. Therefore, here, the authors develop a knowledge based intelligent identification system, based on the integration of a low-level fuzzy identification machine (FIM) identifier and a hyper-level multiobjective optimizer, to monitor the catalyst temperature over the coldstart period for a given automotive engine system. In the current investigation, the authors propose the use of synchronous self-learning Pareto strategy for the multi-objective optimization of the architecture of FIM. To suit the intelligent scheme for online applications, the authors capture the required database using the concept of nonlinear auto-regressive exogenous systems. The developed intelligent approach can be used as a real-time soft sensor to observe the state of the catalytic convertor and send the required data to the coldstart controller. To ensure the efficacy of the resulting time delay FIM framework, it is used for capturing the catalyst temperature in three different experimental conditions. Through a comparative numerical study, it is demonstrated that the proposed soft sensor can be efficiently used for real-time estimations of the catalyst temperature. Besides, the results let us make sure that intelligent approaches have an aptitude to be effectively used as real-time observers instead of expensive commercial sensors. Generally, the results of the current investigation substantiates the authenticity of advanced computational approaches for coping with the considered identification problem, to help resolving one of the challenging issues in the field of automotive engineering, that is, the coldstart HC emission reduction.

Identifying the tool-tissue force in robotic laparoscopic surgery using neuro-evolutionary fuzzy systems and a synchronous self-learning hyper level supervisor

In this paper, two different hybrid intelligent systems are applied to develop practical soft identifiers for modeling the tool-tissue force as well as the resulted maximum local stress in laparoscopic surgery. To conduct the system identification process, a 2D model of an in vivo porcine liver was built for different probing tasks. Based on the simulation, three different geometric features, i.e. maximum deformation angle, maximum deformation depth and width of displacement constraint of the reconstructed shape of the deformed body are extracted. Thereafter, two different fuzzy inference paradigms are proposed for the identification task. The first identifier is an adaptive co-evolutionary fuzzy inference system (ACFIS) which takes advantage of bio-inspired supervisors to be reconciled to the characteristics of the problem at hand. To learn the fuzzy machine, the authors propose a co-evolutionary technique which uses a modified optimizer called scale factor local search differential evolution (SFLSDE) as the core metaheuristic. The concept of co-evolving is implemented through a consequential optimization procedure in which the degree of optimality of the ACFIS architecture is evaluated by sharing the characteristics of both antecedent and consequent parts between two different SFLSDEs. The second identifier is an adaptive neuro-fuzzy inference system (ANFIS) which is based on the use of some well-known neuro computing concepts, i.e. back-propagation learning and synaptic nodal computing, for tuning the construction of the fuzzy identifier. The two proposed techniques are used to identify the force and maximum local stress of tool-tissue. Based on the experiments, the authors have observed that each of the identifiers have their own advantages and disadvantages. However, both ACFIS and ANFIS succeed to identify the model outputs precisely. Moreover, to ascertain the veracity of the derived systems, the authors adopt a Pareto-based hyper-level heuristic approach called synchronous self-learning Pareto strategy (SSLPS). This technique provides the authors with good information regarding the optimum controlling parameters of both ACFIS and ANFIS identifiers.

Analyzing, controlling, and optimizing Damavand power plant operating parameters using a synchronous parallel shuffling self-organized Pareto strategy and neural network: a survey

In recent decades, analyzing and optimizing thermal systems have become of great interest to researchers. Recently, the engineers concentrated on variant concepts of artificial intelligence such as machine learning, simulation, fuzzy logic, game theory, and evolutionary computing to deal with complicated barriers and obstacles. Artificial intelligence and expert system techniques play an important role for surveying and controlling mechanical systems such as power plants and reservoirs. This is because of their interdisciplinary applications and versatile servicing potential in mathematical modeling of industrial systems. In this article, a new method called synchronous parallel shuffling self-organized Pareto strategy algorithm is presented which synthesizes different artificial techniques, nominally evolutionary computing, swarm intelligence techniques, and time adaptive self-organizing map that apply simultaneously incorporating with a stochastic data sharing behavior. Thereafter, it is applied to verify the optimum operating parameter of Damavand power plant as the biggest constructed power plant in Middle East with the potential of producing about 2300 MW electricity sited in Tehran, capital of Iran, as a multi-objective, multi-modal complex problem. It is also proved that implementing the governing equations of power plant leads to a multi-objective problem where some of these objectives are non-linear, non-convex, and multi-modal with different type of real-life engineering constraints. The results confirm the acceptable performance of proposed technique in optimizing the operating parameters of Damavand power plant.

Deriving to an Optimum Policy for Designing the Operating Parameters of Mahshahr Gas Turbine Power Plant Using a Self Learning Pareto Strategy

In the last decades, analyzing and optimizing the power plants based on thermodynamic laws and intelligent control techniques absorb an incremental interest of researchers. This is because deriving the efficient operating parameters for designing and optimizing the performance of power plants will lead to an acceptable investment and avoiding from discarding the energy. However, there are a few areas of application of mathematical optimization method. Optimizing the governing equations and designing parameters of power plants simultaneously leads to a multi-objective problem in industry. Some of these objectives are nonlinear, non-convex and multi-modal with different type of real life engineering constraints. In this paper a new method called Synchronous Parallel Shuffling Self Organized Pareto Strategy Algorithm (SPSSOPSA) is presented which synthesized evolutionary computing, swarm intelligence techniques and Time Adaptive Self Organizing Map(TASOM) simultaneously incorporating with a data shuffling behavior. Thereafter it will be applied to verifying the optimum decision making for parameter designing of Mahshahr power plant that produced about 117MW electricity, sited in Iran, as a multi-objective and multi-modal problem. The results show the deep relation of the unit cost on the change of the operating parameters. Key words : Economic optimizing; Exergetic optimizing; Work output maximization; Evolutionary algorithm; Self organized map; Power plant

Local feedback Pareto strategy for weakly coupled large-scale discrete-time stochastic systems

In this study, the author discusses a Pareto strategy implemented via state and static output feedback for a class of weakly coupled large-scale discrete-time stochastic systems with state- and control-dependent noise. The asymptotic structure along with the uniqueness and positive semi-definiteness of the solutions of cross-coupled non-linear matrix equations (CNMEs) is newly established via the implicit function theorem. The main contribution of this study is the proposal of a parameter-independent local state and static output feedback Pareto strategy. Moreover, a computational approach for solving the CNMEs is also considered if the information about the small parameter is available. Particularly, a new iterative algorithm based on the linear matrix inequality is established to design a Pareto strategy. Finally, in order to demonstrate the effectiveness of the proposed design method, a numerical example is provided for practical aircraft control problems.

Study on Scheduling Optimization for Flexible Job Shop

A hybrid genetic algorithm based on Pareto was proposed and applied to flexible job shop scheduling problem (FJSP) with multi-objective, and the multi-objective FJSP optimization model was built, where the make-span and the machine utilization rate were concerned. The algorithm embeds Pareto ranking strategy into Pareto competition method. The operation-based encoding and an active scheduling decoding method are employed. In order to promote solution diversity, the niche technology and many kinds of crossover operations are used. Pareto filter saves the optimum individual occurring in the course of evolution, which avoids losing the optimum solutions. Three simulation experiments are carried out to illustrate that the proposed method could solve multi-objective job shop scheduling problem effectively.

Application of Intelligent Strategies for Cooperative Manufacturing Planning

Manufacturing planning is crucial for the quality and efficiency of product development. Process planning and scheduling are the most important and challenging tasks in manufacturing planning. These two processes are usually arranged in a sequential way. Recently, a significant trend is to make the processes to work more concurrently and cooperatively to achieve a globally optimal result. In this paper, several intelligent strategies have been developed to build up Cooperative Process Planning and Scheduling (CPPS). Three Game Theory-based strategies, i.e., Pareto strategy, Nash strategy and Stackelberg strategy, have been introduced to analyze the cooperative integration of the two processes in a systematic way. To address the multiple constraints in CPPS, a fuzzy logic-based Analytical Hierarchical Process (AHP) technique has been applied. Modern heuristic algorithms, including Particle Swarm Optimization (PSO), Simulated Annealing (SA) and Genetic Algorithms (GAs), have been developed and applied to CPPS to identify optimal or near-optimal solutions from the vast search space efficiently. Experiments have been conducted and results show the objectives of the research have been achieved.

Pareto Optima of Multicriteria Integer Linear Programs

We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: (1) polynomial-time algorithms to determine exactly the number of Pareto optima and Pareto strategies; (2) a polynomial-space polynomial-delay prescribed-order enumeration algorithm for arbitrary projections of the Pareto set; (3) a polynomial-time algorithm to minimize the distance of a Pareto optimum from a prescribed comparison point with respect to arbitrary polyhedral norms; and (4) a fully polynomial-time approximation scheme for the problem of minimizing the distance of a Pareto optimum from a prescribed comparison point with respect to the Euclidean norm.