Scheduling in parallel machines with two objectives: analysis of factors that influence the Pareto frontier

This paper explores the characteristics of solutions when scheduling jobs in a shop with parallel machines. Three classical objective functions were considered: makespan, total completion time, and total tardiness. These three criteria were combined in pairs, resulting in three bi-objective formulations. These formulations were solved using the ε-constraint method to obtain a Pareto frontier for each pair. The objective of the research is to evaluate the Pareto set of efficient schedules to characterize the solution sets. The characterization of the solutions sets is based on two performance metrics: the span of the objective functions' values for the points in the frontier and their closeness to the ideal point. Results that consider four experimental factors indicate that when the makespan is one of the objective functions, the range of the processing times among jobs has a significant influence on the characteristics of the Pareto frontier. Simultaneously, the slack of due dates is the most relevant factor when total tardiness is considered.

Optimal Allocation of a Hybrid Photovoltaic Biogas Energy System Using Multi-Objective Feasibility Enhanced Particle Swarm Algorithm

This paper aims to investigate a hybrid photovoltaic (PV) biogas on-grid energy system in Al-Ghabawi territory, Amman, Jordan. The system is accomplished by assessing the system’s reliability and economic viability. Realistic hourly measurements of solar irradiance, ambient temperature, municipal solid waste, and load demand in 2020 were obtained from Jordanian governmental entities. This helps in investigating the proposed system on a real megawatt-scale retrofitting power system. Three case scenarios were performed: loss of power supply probability (LPSP) with total net present cost (TNPC), LPSP with an annualized cost of the system (ACS), and TNPC with the index of reliability (IR). Pareto frontiers were obtained using multi-objective feasibility enhanced particle swarm optimization (MOFEPSO) algorithm. The system’s decision variables were the number of PV panels (Npv) and the number of biogas plant working hours per day (tbiogas). Moreover, three non-dominant Pareto frontier solutions are discussed, including reliable, affordable, and best solutions obtained by fuzzy logic. Double-diode (DD) solar PV model was implemented to obtain an accurate sizing of the proposed system. For instance, the best solution of the third case is held at TNPC of 64.504 million USD/yr and IR of 96.048%. These findings were revealed at 33,459 panels and 12.498 h/day. Further, system emissions for each scenario have been tested. Finally, decision makers are invited to adopt to the findings and energy management strategy of this paper to find reliable and cost-effective best solutions.

New multiobjective optimization algorithm using NBI-SASP approaches for mechanical structural problems

Various engineering design problems are formulated as constrained multi-objective optimization problems. One of the relevant and popular methods that deals with these problems is the weighted method. However, the major inconvenience with its application is that it does not yield a well distributed set. In this study, the use of the Normal Boundary Intersection approach (NBI) is proposed, which is effective in obtaining an evenly distributed set of points in the Pareto set. Given an evenly distributed set of weights, it can be strictly shown that this approach is absolutely independent of the relative scales of the functions. Moreover, in order to ensure the convergence to the Global Pareto frontier, NBI approach has to be aligned with a global optimization method. Thus, the following paper suggests NBI-Simulated Annealing Simultaneous Perturbation method (NBI-SASP) as a new method for multiobjective optimization problems. The study shall test also the applicability of the NBI-SASP approach using different engineering multi-objective optimization problems and the findings shall be compared to a method of reference (NSGA). Results clearly demonstrate that the suggested method is more efficient when it comes to search ability and it provides a well distributed global Pareto Front.

Hybrid Salp Swarm Algorithm for Solving the Green Scheduling Problem in a Double-Flexible Job Shop

Green scheduling is not only an effective way to achieve green manufacturing but also an effective way for modern manufacturing enterprises to achieve energy conservation and emission reduction. The double-flexible job shop scheduling problem (DFJSP) considers both machine flexibility and worker flexibility, so it is more suitable for practical production. First, a multi-objective mixed-integer programming model for the DFJSP with the objectives of optimizing the makespan, total worker costs, and total influence of the green production indicators is formulated. Considering the characteristics of the problem, three-layer salp individual encoding and decoding methods are designed for the multi-objective hybrid salp swarm algorithm (MHSSA), which is hybridized with the Lévy flight, the random probability crossover operator, and the mutation operator. In addition, the influence of the parameter setting on the MHSSA in solving the DFJSP is investigated by means of the Taguchi method of design of experiments. The simulation results for benchmark instances show that the MHSSA can effectively solve the proposed problem and is significantly better than the MSSA and the MOPSO algorithm in the diversity, convergence, and dominance of the Pareto frontier.

Design Optimization of Plate-Fin Heat Exchanger in a Gas Turbine and Supercritical Carbon Dioxide Combined Cycle with Thermal Oil Loop

This paper presents an investigation on the optimum design for a plate-fin heat exchanger (PFHE) of a gas and supercritical carbon dioxide combined cycle which uses thermal oil as intermediate heat-transfer fluid. This may promote the heat transfer from low heat-flux exhaust to a high heat-flux supercritical carbon dioxide stream. The number of fin layers, plate width and geometrical parameters of fins on both sides of PFHE are selected as variables to be optimized by a non-dominated sorting genetic algorithm-II (NSGA-II), which is a multi-objective genetic algorithm. For the confliction of heat transfer area and pressure drop on the exhaust side, which are the objective indexes, the result of NSGA-II is a Pareto frontier. The technique for order of preference by similarity to ideal solution (TOPSIS) approach is applied to choose the optimum solution from the Pareto frontier. Finally, further simulation is performed to analyze the effect of each parameter to objective indexes and confirm the rationality of optimization results.

Bi-objective facility location under uncertainty with an application in last-mile disaster relief

Multiple and usually conflicting objectives subject to data uncertainty are main features in many real-world problems. Consequently, in practice, decision-makers need to understand the trade-off between the objectives, considering different levels of uncertainty in order to choose a suitable solution. In this paper, we consider a two-stage bi-objective single source capacitated model as a base formulation for designing a last-mile network in disaster relief where one of the objectives is subject to demand uncertainty. We analyze scenario-based two-stage risk-neutral stochastic programming, adaptive (two-stage) robust optimization, and a two-stage risk-averse stochastic approach using conditional value-at-risk (CVaR). To cope with the bi-objective nature of the problem, we embed these concepts into two criterion space search frameworks, the $$\epsilon $$ ϵ -constraint method and the balanced box method, to determine the Pareto frontier. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. In an extensive computational experiment, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal.

Optimization of the Spectrum Splitting and Auction for 5th Generation Mobile Networks to Enhance Quality of Services for IoT from the Perspective of Inclusive Sharing Economy

Fifth generation (5G) mobile networks can accomplish enhanced communication capabilities and desired to connect things in addition to people. By means of optimally splitting the spectrum to integrate more efficient segments, mobile operators can deliver better Quality of Services (QoS) for Internet of Things (IoT), even the nowadays so-called metaverse need broadband mobile communication. Drawing on the Theory of Quality Value Transformation, we developed a 5G ecosystem as a sustainable organic coalition constituted of planners, providers, and users. Most importantly, we put forward the altruism as the ethics drive for the organic cooperative evolution to sustain the inclusive sharing economy to solve the problem of the Theory of Games and Economic Behavior. On the top of the collaboration framework for the coalition game for 5G, we adopted Pareto Optimality as the target situation for the optimization via cooperative evolution and further apply ISO 25000 to define the metrics for the value of 5G corresponding to Pareto Frontier. Based on the collaboration framework as above, we conducted a survey to gather the features and costs for the 5G spectrum in relation to IoT and the financial status of the mobile operators as the constraint for the optimization. Taking Simultaneous Multi-Round Auction (SMRA) as the standard rule for spectrum auction, we developed a novel optimization program of two hybrid metaheuristics with the combination of Simulated Annealing (SA), Genetic Algorithm (GA), and Random Optimization (RO) for the multiple objectives of quality, usability, and costs. The results of the simulation show that the coalition game for 5G spectrum auction is a dynamic group decision in which the government authority and mobile operators can achieve a synergy to maximize the profits, quality score, and usability, and minimize the costs. Last but not least, the hybrid metaheuristic with SA and RO is more efficient and effective than that with GA and BO, from the perspective of inclusive sharing economy. It is the first study of its kind as we know.

Network Models for Multiobjective Discrete Optimization

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

Numerical and Experimental Investigation of Wire Cloth Heat Exchanger for Latent Heat Storages

Latent thermal energy storages (LTES) offer a high storage density within a narrow temperature range. Due to the typically low thermal conductivity of the applied phase change materials (PCM), the power of the storages is limited. To increase the power, an efficient heat exchanger with a large heat transfer surface and a higher thermal conductivity is needed. In this article, planar wire cloth heat exchangers are investigated to obtain these properties. They investigated the first time for LTES. Therefore, we developed a finite element method (FEM) model of the heat exchanger and validated it against the experimental characterization of a prototype LTES. As PCM, the commercially available paraffin RT35HC is used. The performance of the wire cloth is compared to tube bundle heat exchanger by a parametric study. The tube diameter, tube distance, wire diameter and heat exchanger distance were varied. In addition, aluminum and stainless steel were investigated as materials for the heat exchanger. In total, 654 variants were simulated. Compared to tube bundle heat exchanger with equal tube arrangement, the wire cloth can increase the mean thermal power by a factor of 4.20 but can also reduce the storage capacity by a minimum factor of 0.85. A Pareto frontier analysis shows that for a free arrangement of parallel tubes, the tube bundle and wire cloth heat exchanger reach similar performance and storage capacities.