Pareto Efficient Solutions Research Articles

Computational Optimisation of Urban Design Models: A Systematic Literature Review

The densification of urban spaces globally has contributed to a need for design tools supporting the planning of more sustainable, efficient, and liveable cities. Urban Design Optimisation (UDO) responds to this challenge by providing a means to explore many design solutions for a district, evaluate multiple objectives, and make informed selections from many Pareto-efficient solutions. UDO distinguishes itself from other forms of design optimisation by addressing the challenges of incorporating a wide range of planning goals, managing the complex interactions among various urban datasets, and considering the social–technical aspects of urban planning involving multiple stakeholders. Previous reviews focusing on specific topics within UDO do not sufficiently address these challenges. This PRISMA systematic literature review provides an overview of research on topics related to UDO from 2012 to 2022, with articles analysed across seven descriptive categories. This paper presents a discussion on the state-of-the-art and identified gaps present in each of the seven categories. Finally, this paper argues that additional research to improve the socio-technical understanding and usability of UDO would require: (i) methods of optimisation across multiple models, (ii) interfaces that address a multiplicity of stakeholders, (iii) exploration of frameworks for scenario building and backcasting, and (iv) advancing AI applications for UDO, including generalizable surrogates and user preference learning.

Environmentally sustainable inventory control for perishable products: A bi-objective reorder-level policy

In order to improve sustainability and transparency in the decision making for inventory control, this paper presents a reorder-level model that considers product perishability. Conversely to most inventory control policies, the classical economic perspective is paired with an environmental one for a stochastic bi-objective optimization approach to reduce inventory logistics emissions and costs. In order to contrast stockouts, lost-sale costing and a service level constraint are integrated for a more comprehensive approach. Results show how the two objectives may be in contrast, and how Pareto-efficient solutions can help to analyze and select the proper trade-offs during decision making. Experiments indicate, for a case-study application, how the most relevant aspects affecting system performance are product shelf life and the possible need of temperature control during storage. Moreover, considering multiple sustainability perspectives in inventory management can help businesses consolidate and future-proof their operations, as well as meet environmental standards and customer demand for greener products and processes.

Resource-constrained project scheduling with multiple states: Bi-objective optimization model and case study of aircraft maintenance

This paper introduces a new resource-constrained project scheduling problem in which the project has multiple possible states and whether an activity can be performed at a certain time depends on the state at that time. We are motivated by aircraft maintenance projects where activities need to be performed in particular aircraft states, such as power on/off and jack on/off. We formulate a bi-objective optimization model for this problem, which determines the schedule of activities and the selection of states over the planning horizon, subject to resource constraints, precedence relationship, and state restrictions. The model concerns both the minimization of the project duration and the minimization of the number of state changes over time. A heuristic algorithm, which utilizes genetic algorithm techniques, is developed to obtain Pareto efficient solutions of the model. Its effectiveness is demonstrated through a comparison with CPLEX and an adaptation of NSGA-II. Furthermore, we conduct a case study about aircraft maintenance C-check projects in a major airline. The case study demonstrates that our optimization-based approach is applicable and beneficial to the project scheduling practice with the consideration of states.

A Spectral Gap-Based Topology Control Algorithm for Wireless Backhaul Networks

This paper presents the spectral gap-based topology control algorithm (SGTC) for wireless backhaul networks, a novel approach that employs the Laplacian Spectral Gap (LSG) to find expander-like graphs that optimize the topology of the network in terms of robustness, diameter, energy cost, and network entropy. The latter measures the network’s ability to promote seamless traffic offloading from the Macro Base Stations to smaller cells by providing a high diversity of shortest paths connecting all the stations. Given the practical constraints imposed by cellular technologies, the proposed algorithm uses simulated annealing to search for feasible network topologies with a large LSG. Then, it computes the Pareto front of the set of feasible solutions found during the annealing process when considering robustness, diameter, and entropy as objective functions. The algorithm’s result is the Pareto efficient solution that minimizes energy cost. A set of experimental results shows that by optimizing the LSG, the proposed algorithm simultaneously optimizes the set of desirable topological properties mentioned above. The results also revealed that generating networks with good spectral expansion is possible even under the restrictions imposed by current wireless technologies. This is a desirable feature because these networks have strong connectivity properties even if they do not have a large number of links.

Multi‐objective spectrum assignment in heterogeneous cognitive radio networks for internet of things

SummaryInternet of Things (IoT) applications have massively increased in the last few years. Future‐generation IoTs are going to be massive in number, heterogeneous in nature, and extremely demanding in terms of computation and communication requirements. Therefore, effective techniques are needed to optimize the use of scarce communication resources. This work proposes a novel multi‐objective framework to investigate the channel assignment problem in cognitive radio network (CRN)‐based IoT applications. The multi‐objective optimization framework comprises three objective functions. The first objective aims to maximize the overall system throughput fairness, the second objective aims to maximize the overall system residual energy, and the third objective aims to increase the user satisfaction level by maximizing the overall priority index. The problem of channel assignment is modeled and solved using Mixed Integer Linear Programming (MILP) and ‐constraint technique. This technique generates a set of Pareto efficient solutions, and an optimal solution among these solutions is selected using a fuzzy logic decision mechanism. Moreover, power level selection is incorporated by solving the problem multiple times for different power levels and obtaining a preferred solution for each power level. The simulations are conducted to unveil an interesting trade‐off between the conflicting system design objectives, that is, the overall throughput and the overall residual energy while incorporating the significance of primary user (PU) activity when preforming channel assignment in CRN.

Integrating Cloud Computing, Bayesian Optimization, and Neural-Additive Modeling for Enhanced CAM Systems in 5-Axis Milling

This publication introduces the development and application of an advanced CAD/CAM/CAE system that leverages the computational capabilities of an edge-cloud infrastructure. The developed system consists of containerized technology models for various complex process planning simulation tasks in 5-axis-milling, such as toolpath calculation, cutter-workpiece-engagement, uncut chip geometry or cutting force simulations. Moreover, a Bayesian optimization (BO) algorithm is coupled with the system enabling multi-objective optimizations of the considered machining operations by varying predefined CAM-parameters. The result of the optimization consists of a set of Pareto-efficient solutions. Each solution realizes a different tradeoff between the technological objectives of the process planner. Since mastering the complexity of the design space is a major challenge in today’s CAM programming workflow, a Neural-Additive Model (NAM) is coupled with the system improving guided search through the configuration/result space. This reduces the convergence time to an optimal CAM parameter set. The coupling of the cloud computing, multi-objective optimization and artificial intelligence method with a CAM-kernel is demonstrated based on the process design of 5-axis milling operations for a blade-integrated disk (blisk).

Knowledge Equivalence in Digital Twins of Intelligent Systems

A digital twin contains up-to-date data-driven models of the physical world being studied and can use simulation to optimise the physical world. However, the analysis made by the digital twin is valid and reliable only when the model is equivalent to the physical world. Maintaining such an equivalent model is challenging, especially when the physical systems being modelled are intelligent and autonomous. The paper focuses in particular on digital twin models of intelligent systems where the systems are knowledge-aware but with limited capability. The digital twin improves the acting of the physical system at a meta-level by accumulating more knowledge in the simulated environment. The modelling of such an intelligent physical system requires replicating the knowledge-awareness capability in the virtual space. Novel equivalence maintaining techniques are needed, especially in synchronising the knowledge between the model and the physical system. This paper proposes the notion of knowledge equivalence and an equivalence maintaining approach by knowledge comparison and updates. A quantitative analysis of the proposed approach confirms that compared to state equivalence, knowledge equivalence maintenance can tolerate deviation thus reducing unnecessary updates and achieve more Pareto efficient solutions for the trade-off between update overhead and simulation reliability.

Similarity-based bus services assignment with capacity constraint for staggered bus stops

The assignment of bus services to appropriate stops is a crucial parameter in ensuring a high level of service for commuters at staggered bus stops. In this study, an innovative similarity-based assignment method is proposed to assign a set of bus services to a set of stop areas in such a configuration, while considering the capacity constraint of the bus stop areas. First, a new concept of the time series of bus stop occupancy is introduced to dynamically track if a bus stop is occupied by a specific bus service. Then, a dynamic time warping-based algorithm is proposed to measure the similarity level of the time series of bus stop occupancy between different bus services. Considering both capacity constraint and performance of similarity level at each bus stop area, bus services assignment can be modelled as a Pareto efficiency problem. We can trade off within the Pareto efficient solutions and determine the best assignment scheme. Finally, the performance of our proposed method is evaluated using data collected from four staggered bus stops in Singapore. To evaluate the model’s stability and reliability, sensitivity analyses are conducted to test the effect of (i) pre-defined bus arrival rate, (ii) time interval used for creating the time series of bus stop occupancy, and (iii) day of week on staggered bus stop performance. The proposed method developed in this study can help transit agencies and operators determine the appropriate bus service assignment within a staggered bus stop configuration.

Matrix-augmentation approach for machine repair problem with generally distributed repair times during working breakdown periods

In the manufacturing industry, production facilities for product manufacturing often contain unreliable operating machines and standbys. The machines can break down and result in productivity loss, and have to be repaired by the repairmen. To evaluate the system performance in operations and production management accurately, a general mathematical model is proposed to investigate the machine repair problem with an unreliable repairman, working breakdowns, and multiple vacations. A novel matrix-augmentation approach is introduced to simplify the analysis process and to derive the stationary distribution of the number of failed machines in the system when the classical supplementary variable technique cannot evolve the steady-state probability recursively. Furthermore, explicit formulas of various performance metrics are developed and numerically computed corresponding to various repair time distributions during working breakdown periods. Finally, an optimization problem with multiple objective functions is formulated with two different objective functions: the expected cost and machine availability. The NSGA-II algorithm is applied to perform numerical experiments and to provide Pareto-efficient solutions for managers and decision-makers.

The use of phase diagrams when choosing optimal routes in the waters of the Northern Sea Route

A method for choosing optimal shipping routes using phase diagrams is developed in the paper. The topic and purpose of the study is directly related to the tasks, the implementation of which is provided for by the Plan of the Northern Sea Route Development, approved by the decree of the Government of the Russian Federation on August 1, 2022, confirmed by the financing program for the development and implementation of the digital platform of the Northern Sea Route, approved by the Government in mid-January 2023. The assessment of the current state of the shipping routes network, navigation, hydrographic and hydro meteorological support is given. The use of the method of multi-criteria evaluation of alternative routes based on a variety of safety criteria depending on the depths, ice conditions, tightness of the water area and hydrographic study of the bottom relief is justified. The dependence of the safety criteria on the draft of the vessel, its icebreaking ability and maneuverable elements is established. A method of comparative assessment of shipping routes for settlement vessels according to four main criteria has been developed. A scheme for calculating quantitative safety indicators is proposed. A procedure for normalizing indicators has been developed. A three-level scale for assessing the safety of shipping routes has been introduced. A methodology for ranking shipping routes and culling the routes assessed as dangerous and forming a set of routes assessed as safe is proposed. The method was tested using a model of the passage of an Arc4 ice category vessel with a draft of 9 m along eight alternative routes of the East Siberian Sea. A set of phase diagrams of alternative routes constructed according to pairs of basic safety criteria is presented. The states of routes are analyzed with the application of the Pareto efficient solution rule to the selection of optimal routes. It is noted that the use of phase diagrams can be extended to a larger number of indicators affecting the efficiency and safety of vessels navigation. Recommendations on the use of the developed method are given. The main directions of further research are determined.

Proximal algorithm with quasidistances for multiobjective quasiconvex inimization in Riemannian manifolds

We introduce a proximal algorithm using quasidistances for multiobjective minimization problems with quasiconvex functions defined in arbitrary Riemannian manifolds. The reason of using quasidistances instead of the classical Riemannian distance comes from the applications in economy, computer science and behavioral sciences, where the quasidistances represent a non symmetric measure. Under some appropriate assumptions on the problem and using tools of Riemannian geometry we prove that accumulation points of the sequence generated by the algorithm satisfy the critical condition of Pareto-Clarke. If the functions are convex then these points are Pareto efficient solutions.

Pareto efficiency as alternative to Nash equilibrium in competitive discrete location under delivered pricing

We address the facility location problem for firms that sell an homogeneous product and compete on delivered prices. If the firms set equilibrium prices at each market, the problem can be seen as a location game for which there exists a Nash equilibrium if demand is inelastic. However, this equilibrium may be Pareto-inefficient and the firms could decide to collude if they can guarantee themselves higher payoffs than those prescribed by the equilibrium. The aim of this paper is to study the joint profit maximization problem to obtain a collusive solution of the location game (Pareto-efficient) and determine if such a solution is also a Nash equilibrium. We develop Integer Linear Programming models to find Pareto-efficient solutions for multiple and single facility location. Nash equilibria are obtained by the best response procedure. An empirical investigation is performed to compare the joint profit of the firms and the profit of each one of the firms, got through the Pareto-efficient locations, with those got through the Nash equilibrium.

A bi-criteria moving-target travelling salesman problem under uncertainty

This article concerns a variant of moving target travelling salesman problem where the number and locations of targets vary with time and realizations of random trajectories. Managerial objectives are to maximize the number of visits to different targets and to minimize the total travel distance. Employing a linear value function for finding supported Pareto-efficient solutions, we develop a two-stage stochastic programming model. We propose an iterative randomized dynamic programming (RDP) algorithm which converges to a global optimum with probability one. Each iteration in RDP involves a randomized backward and forward recursion stage as well as options for improving any given schedule: swaps of targets and optimization of timing for visits. An integer linear programming (ILP) model is developed and solved by a standard ILP solver to evaluate the performance of RDP on instances of real data for scheduling an environmental surveillance boat to visit ships navigating in the Baltic Sea. Due to a huge number of binary variables, the ILP model in practice becomes intractable. For small to medium size data sets, the Pareto-efficiency of solutions found by RDP and ILP solver are equal within a reasonable tolerance; however, RDP is significantly faster and able to deal with large-scale problems in practice.

Necessary optimality conditions for approximate Pareto efficient solutions of nonsmooth fractional interval-valued multiobjective optimization problems

This paper deals with approximate Pareto efficient solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce some types of approximate Pareto efficient solutions of the considered problem by considering the lower-upper interval order relation. Then we apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions of Karush–Kuhn–Tucker (KKT)-type for these solutions.

Determining the Pareto front of distributed generator and static VAR compensator units placement in distribution networks

<span>The integration of distributed generators (DGs), which are based on renewable energy sources, energy storage systems, and static VAR compensators (SVCs), requires considering more challenging operational cases due to the variability of DG production contributed by different characteristics for different time sequences. The size, quantity, technology, and location of DG units have major effects on the system to benefit from the integration. All these aspects create a multi-objective scope; therefore, it is considered a multi-objective mixed-integer optimization problem. This paper presents an improved multi-objective salp swarm optimization algorithm (MOSSA) to obtain multiple Pareto efficient solutions for the optimal number, location, and capacity of DGs and the controlling strategy of SVC a radial distribution system. MOSSA is a bio-inspired optimizer based on swarm intelligence techniques and it is used in finding the optimal solution for a global optimization problem. Two sets of objective functions have been formulated minimizing DGs and SVC cost, voltage violation, energy losses, and system emission cost. The usefulness of the proposed MOSSA has been tested with the 33-bus and 141-bus radial distribution systems and the qualitative comparisons against two well-known algorithms, multiple objective evolutionary algorithms based on decomposition (MOEA/D), and multiple objective particle swarm optimization (MOPSO) algorithm.</span>

Lexicographic Multi-Objective Optimization Approach for Welding Flux System Design

Multiple response optimization of welding flux performance has been found to be cost effective and useful for the achievement of the best balance among conflicting welding flux quality attributes. Many multi-criteria optimization methods (MCOM) have been applied in flux formulation situations where flux quality attributes are of comparable importance. However, information on applications of MCOM to flux design situations where quality attributes are in hierarchical order of importance is scarce in the open literature. In this study, a Lexicographic Multi-objective Optimization (LMO) model was proposed for handling flux design situations in which the attributes are in hierarchical order of importance. The model was applied using data from literature. Two priority levels were used: acicular ferrite (AF) maximization was assigned first priority while the maximization of polygonal ferrite (PF) content and weld-metal impact toughness (WIT) were assigned second priority subject to oxygen content constraint of 250 – 350ppm. The respective solutions for AF, PF, WIT and oxygen content were 51.19%, 21.80%, 23.70J at -20oC and 315ppm. The corresponding flux formulation was CaO (25.90) MgO (15.00) CaF2 (31.10) and Al2O3 (8.00%). Various priority structures were used to explore trade-off options and to generate three more pareto efficient solutions from which the flux formulator can select the most preferred one. The proposed model has filled the existing gap in the literature being a pioneering work in the application of lexicographic multi-objective optimization method in welding flux design.

Social Media and Misleading Information in a Democracy: A Mechanism Design Approach

In this paper, we present a resource allocation mechanism for the problem of incentivizing filtering among a finite number of strategic social media platforms. We consider the presence of a strategic government and private knowledge of how misinformation affects the users of the social media platforms. Our proposed mechanism incentivizes social media platforms to filter misleading information efficiently, and thus indirectly prevents the spread of fake news. In particular, we design an economically inspired mechanism that strongly implements all generalized Nash equilibria for efficient filtering of misleading information in the induced game. We show that our mechanism is individually rational, budget balanced, while it has at least one equilibrium. Finally, we show that for quasi-concave utilities and constraints, our mechanism admits a generalized Nash equilibrium and implements a Pareto efficient solution.

An evolutionary multi-objective path planning of a fleet of ASVs for patrolling water resources

The rapid increase of human activities with direct influence on the environment has motivated the global awareness of the need to efficiently monitor the natural resources. Among the wide range of problems addressed, such as overuse of agrochemicals, uncontrolled waste, etc., the contamination of water resources plays a protagonist role, given its close links with biodiversity and the food chain. Water monitoring is considered one of the most efficient ways to deal with these problems, especially through the use of autonomous vehicles, which can boost the capabilities and efficiency of the monitoring routines with appropriate strategies. In this work, the monitoring problem is addressed by means of the Non-Homogeneous Patrolling Problem with closed circuits. This problem has a great computational complexity, especially when multiple targets are included in a monitoring mission. A formulation based on closed metric graphs and the application of a multi-objective genetic algorithm is proposed to provide Pareto-efficient monitoring solutions for a variable number of Autonomous Surface Vehicles. To address the multi-agent, multi-objective and constrained paradigm, efficient genetic operators have been designed for the generation of valid solutions in an affordable time. The method results in Pareto-efficient solutions for scenarios with disjoint and uncorrelated objectives, which outperform the fitness of other solutions by a factor of 2, on average. The results provide decision makers a method to find different non-dominated strategies depending on the monitoring needs, depending on fleet and vehicle size.

Formation of pareto-effective managerial decisions for the society sustainable development using mass media potential

The purpose, role and functions of modern mass media influence on all socially significant components of society by forming in the last public opinion, aimed at a joint search for Pareto-efficient solutions of sustainable development, are yet to be subjected to further thorough scientific and theoretical analysis. The new directions of scientific research in the field of management technologies based on the integration and harmonization of collective intelligence have been generated and widespread due to mass media dissemination of information, on the collective, participative, partnership management and leadership, on crowdsourcing and cognitive technologies, which form a new interaction paradigm between society and state as a way of cognitive behavior transformation of the individual, their groups and organized groups, nations and states through massive attraction and use their intellectual potential in combination with modern information systems. Spatial model of the search for a Pareto-optimal point of cost-effective market interaction of three participants in market transactions on the surface of utilitarian possibilities and the model of socially responsible Pareto-effective stakeholders’ interaction formation in the socio-economic system under the mass media influence are developed in the paper.

Bi-objective coordinated production and transportation scheduling problem with sustainability: formulation and solution approaches

ABSTRACT This paper studies a new variant of integrated production scheduling and vehicle routing problem where production of customer orders are performed under job-shop environment and order deliveries are made by a heterogeneous fleet of vehicles, each of which is allowed to take multiple trips. Two conflicting objectives are considered, namely minimisation of the total amount of CO2 emitted by the vehicles and minimisation of maximum tardiness resulting from late deliveries. To this end, we present a bi-objective mixed-integer programming formulation. Augmented ε-Constraint (Augmecon) method is implemented to find Pareto optimal solutions. Due to problem complexity, Augmecon cannot provide solutions even with small-sized problems. Thus, we adopt Pareto Local Search (PLS) and non-dominated sorting genetic algorithm-II (NSGA-II) for practical sized instances. For small-sized instances involving 5, 6, and 7 customers, experimental results indicate that CPU time of Augmecon are 11, 84, and 524 sec, respectively with an average number of Pareto efficient solution of 3.5. In terms of hypervolume index, Augmecon shows the best performance, followed by NSGA-II with 11.32% and PLS with 20.75% degradation for small-sized instances. For medium and large-sized instances, PLS shows worse performance than NSGA-II by 16.87% and 40.48%.