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O objetivo deste trabalho é apresentar uma metodologia para fornecer uma solução para o Problema de Roteamento de Veículos Green Bi-objetivo (Bi-objective Green Vehicle Routing Problem, BGVRP). A metodologia, ilustrada por meio de um estudo de caso (problema de distribuição de jornais) e instâncias da literatura, foi dividida em três etapas: Etapa 1, tratamento dos dados; Etapa 2, abordagens meta-heurísticas (híbridas ou não híbridas), utilizadas comparativamente; Etapa 3, análise dos resultados, com comparação dos algoritmos. Uma otimização de 19,9% foi alcançada para a Função Objetivo 1 (FO1; minimização das emissões de CO2) e, consequentemente, o mesmo percentual para a minimização da distância total, e 87,5% para a Função Objetivo 2 (FO2; minimização da diferença na demanda). Abordagens meta-heurísticas híbridas alcançaram resultados superiores para o estudo de caso e as instâncias. Desta forma, o procedimento aqui apresentado poderá trazer benefícios para a sociedade já que considera questões ambientais, além do balanceamento do trabalho entre os roteiros, garantindo economia e satisfação para possíveis usuários.

Mobile edge computing and nonorthogonal multiple access (NOMA) have been considered as promising technologies that can satisfy rigorous requirements of industrial internet of things systems. However, system dynamics, including channel states and computation task requests, may continuously change NOMA decoding order and computation uploading time, making it difficult to reduce latency using conventional highly complex optimization methods. In this study, we investigate a novel scheme that effectively reduces the average task delay to improve the quality of service for all users by jointly optimizing subchannel assignment (SA), offloading decision (OD), and computation resource allocation (CRA). To deal with the high complexity, the original multi-server problem is first decomposed into multiple single-server problems. Subsequently, each single-server problem is decoupled into CRA and SA/OD subproblems. Using convex optimization, a closed-form solution is derived for the optimal CRA action. Concurrently, the optimal SA/OD action is obtained using a distributed multi-agent deep reinforcement learning algorithm. Simulation results reveal that the proposed scheme significantly outperforms the state-of-the-art schemes. In particular, it reduces the action decision duration by 30 times while achieving a near-optimal performance of up to 97% of the optimum under the exhaustive search scheme.

Magnesium (Mg) alloys are extensively used in the automotive and aircraft industries due to their prominent properties. The selection of appropriate process parameters is an important decision to be made because of the cost reduction and quality improvement. This decision entails the selection of suitable process parameters concerning various conflicting factors, so it has to be addressed with the Multiple Criteria Decision Making (MCDM) method. Therefore, this work addresses the MCDM problem through the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and COPRAS (COmplex PRoportional ASsessment) methods. The assessment carried out in the material Mg AZ91 with the Solid Carbide (SC) drill bit. The dependent parameters like drilling time, burr height, burr thickness, and roughness are considered with the independent parameters like spindle speed and feed rate. Drilling alternatives are ranked using the above said two methods and the results are evaluated. The optimum combination was found on the basis of TOPSIS and COPRAS for simultaneous minimization of all the responses which is found with a spindle speed of 4540 rpm and a feed rate of 0.076 mm/rev. The identical sequencing order was observed in TOPSIS and COPRAS method. The empirical model was developed through Box-Behnken design for each response. Superior empirical model developed for drilling time which is 3.959 times accurate than the conventional equation. The trends of various dependents based on the heterogeneity of various independents are not identical, these complex mechanisms are identified and reported. The optimized results of the Desirability Function Approach are greater accordance with the TOPSIS and COPRAS top rank. The confirmation results are observed with lesser deviation suggesting the selection of the above independent parameters.

We study decentralized non-convex finite-sum minimization problems described over a network of nodes, where each node possesses a local batch of data samples. In this context, we analyze a single-timescale randomized incremental gradient method, called GT-SAGA. GT-SAGA is computationally efficient as it evaluates one component gradient per node per iteration and achieves provably fast and robust performance by leveraging node-level variance reduction and network-level gradient tracking. For general smooth non-convex problems, we show the almost sure and mean-squared convergence of GT-SAGA to a first-order stationary point and further describe regimes of practical significance where it outperforms the existing approaches and achieves a network topology-independent iteration complexity respectively. When the global function satisfies the Polyak-Lojaciewisz condition, we show that GT-SAGA exhibits linear convergence to an optimal solution in expectation and describe regimes of practical interest where the performance is network topology-independent and improves upon the existing methods. Numerical experiments are included to highlight the main convergence aspects of GT-SAGA in non-convex settings.

This paper presents a rolling optimization algorithm for minimizing total vehicle delay for real-time traffic signal control in urban road networks, where the vehicle delay minimization problem is formulated as a quadratically-constrained quadratic programming problem, which is NP-hard. The programming problem is relaxed and resolved using the rolling optimization algorithm in a distributed manner. In particular, we introduce network partition to a large-scale urban road network and then present a regional rolling optimization algorithm to eliminate the low efficiency caused by the large number of decision variables. Numerical experiments are performed on one of Beijing's district road networks to validate the efficiency of the proposed method in benchmark against several typical techniques.

This paper considers scheduling in a two-machine flow shop to maximize the total early work subject to a common due date. The early work of a job is a parameter defined as the total amount of the job that is processed before the specified due date. We mainly focus on the unweighted model in this paper, and propose a dynamic programming approach running in O ( n 2 d 2 ) time (compared with the previous result in O ( n 2 d 4 ) time for the weighted case discussed in the literature). Then we analyse the problem from an approximation point of view, in which we first show that Johnson’s algorithm, one of the most classical ones in flow shop scheduling, can only achieve the worst performance ratio for the considered problem (although it is an optimal one for makespan minimization). With the motivation of proposing better approximation algorithms, we further design a fully polynomial time approximation scheme (FPTAS). Finally, we point out that the approximation results also work for the weighted model - if a specific constraint is satisfied.

In this study, we propose an efficient optimization algorithm that is a hybrid of the iterated greedy and simulated annealing algorithms (hereinafter, referred to as IGSA) to solve the flexible job shop scheduling problem with crane transportation processes (CFJSP). Two objectives are simultaneously considered, namely, the minimization of the maximum completion time and the energy consumptions during machine processing and crane transportation. Different from the methods in the literature, crane lift operations have been investigated for the first time to consider the processing time and energy consumptions involved during the crane lift process. The IGSA algorithm is then developed to solve the CFJSPs considered. In the proposed IGSA algorithm, first, each solution is represented by a 2-D vector, where one vector represents the scheduling sequence and the other vector shows the assignment of machines. Subsequently, an improved construction heuristic considering the problem features is proposed, which can decrease the number of replicated insertion positions for the destruction operations. Furthermore, to balance the exploration abilities and time complexity of the proposed algorithm, a problem-specific exploration heuristic is developed. Finally, a set of randomly generated instances based on realistic industrial processes is tested. Through comprehensive computational comparisons and statistical analyses, the highly effective performance of the proposed algorithm is favorably compared against several efficient algorithms.

Capacitor banks, when optimally placed in an electrical network improve power quality and reliability. For determining the capacitors optimal location, the prevailing index methods mainly focus on single criterion, e.g., either of voltage stability, loss reduction, system loadability, and neglect some of the equally critical quantities while proving the solution. For obtaining a pragmatically feasible techno-commercial solution, it is advantageous to consider multiple criteria. This article proposes a novel approach for optimal capacitor allocation, which allows to choose as many objective functions (criteria) as desired. In the proposed approach, initially, the load flow study is executed to obtain the networks quantities for an uncompensated network. Subsequently, optimal locations of capacitor banks are identified through the proposed indexing method based on the application of Shannons Entropy. The capacitor banks optimal sizes are determined using the particle swarm optimization algorithm. The cost function is formulated as the minimization of sum of active power loss cost and the incurred annual capacitors cost subject to different operational constraints. The proposed approach is compared with that of the previously published methods by applying on radial distribution networks of different sizes (IEEE-12 bus, 34-bus and 108-bus) and the proposed approach is found to be superior.

by Suresh Velamuri, S. Hari Charan Cherukuri, Suresh Kumar Sudabattula, Natarajan Prabaharan and Eklas Hossain

This study proposes an exact model for timetable recovery after disturbances in the context of high-frequency public transport services. The objective of our model is the minimization of the deviation between the actual headway and the respective planned value. The resulting mathematical program for the rescheduling problem is nonlinear and non-smooth; thus, it cannot be solved to optimality. To rectify this, we reformulate the model using slack variables. The reformulated model can be solved to global optimality in real-time with quadratic programming. We apply the model to real data from the red metro line in Washington D.C. in a series of experiments. In our experiments, we investigate how many upstream trips should be rescheduled to respond to a service disturbance. Our findings demonstrate an improvement potential of service regularity of up to 30% if we reschedule the five upstream trips of a disturbed train.

Due to the existence of multiple magnetization states (MSs) of the low coercive force (LCF) PMs, the losses minimization of variable flux memory machine (VFMM) under different MSs unable obtained simultaneously. This paper proposes a loss-reduction-oriented (LRO) optimization methodology for overall efficiency improvement in VFMM. Firstly, a recently developed hybrid-magnetic-circuit (HMC) VFMM is selected as a design example to investigate the proposed optimization methodology. Subsequently, the architecture and overall flowchart of the proposed LRO optimization methodology are introduced and given, which includes two rounds of optimization, namely dual-operating-mode rough optimization (DOM-RO) and multiple-operating-mode elaborate optimization (MOM-EO). Besides, a computationally efficient multi-mode field-circuit coupled (MMFC) model is established in finite element (FE) software to account for multiple operating modes within two simple case studies. On this basis, the proposed optimization methodology is applied to the HMC-VFMM, in which the LRO objective function is defined in terms of the time proportions of various MSs in an overall driving cycle. According to the optimization results, the electromagnetic characteristics of the machine are investigated, especially the machine loss and its efficiency maps under different MSs are analyzed. Finally, a prototype is manufactured and tested to verify the validity of the proposed optimization strategy.

The advent of vehicular edge computing (VEC) has generated enormous attention in recent years. It pushes the computational resources in close proximity to the data sources and thus caters for the explosive growth of vehicular applications. Owing to the high mobility of vehicles, these applications are of latency-sensitive requirements in most cases. Accordingly, such requirements still pose a great challenge to the computing capabilities of VEC, when these applications are outsourced and executed in VEC. Against this backdrop, we propose a new mathematical model which respectively generalizes the computation and communication models, and applies application oriented caching into VEC in this paper. Based on this model, a new strategy is further proposed to optimize the average response time of applications over an infinite time-slotted horizon for VEC. A long-term energy consumption constraint is imposed to guarantee the stability of VEC system, and the Lyapunov optimization technology is adopted to tackle this constraint issue. Two greedy heuristics are put forward to help find the approximate optimal solution in the drift-plus-penalty based algorithm. Extensive experiments have been conducted to evaluate the response time and energy consumption in the caching assisted VEC. The simulation results have shown that the proposed strategy can dramatically optimize the average response time while satisfying the long-term energy consumption constraint.

This paper discusses the makespan minimization of a production batch within a specific concurrent system, seru production system. A seru production system consists of multiple independent serus. A seru is a compact assembly origination in which products are assembled from-the-beginning-to-the-end without disruptions. One capability of a seru production system is its responsiveness. A performance measure used to evaluate a seru system’s responsiveness is the makespan of production batches assembled within the seru system. This study addresses the makespan minimization problem through an optimal seru loading policy. The problem is formulated as a min-max integer optimization model. An exact dimension-reduction Algorithm is developed to obtain the optimal allocation that minimizes the makespan. We show that the solution space increases very quickly. In contrast, our algorithm is efficient with a polynomial computational complexity of O ( n 2 ) , where n is the total number of serus in a seru system. To verify the usefulness of the developed exact dimension-reduction algorithm, we compare it with a widely practiced greedy algorithm through experiments. We find that our optimal algorithm is robust in most cases and the greedy algorithm is efficient when variability in production efficiencies is high. This result can guide us to adopt different algorithms under different business environments. If the variability in production efficiencies is high, e.g., new employees and/or new products assembly, the greedy algorithm is efficient. For other cases, our optimal algorithm should be adopted to obtain the minimum makespan. We also extend the method to the application of a rotating seru.

The best performing approximate methods proposed for the permutational flow shop scheduling problem with makespan minimization are the well known NEH constructive heuristic and the iterated greedy algorithm. Both methods are based on the successive insertion (or reinsertion) of jobs into a partial schedule, evaluating the makespan of the resulting schedule for all insertion positions, and selecting the insertion position that presents the shortest makespan. Frequently, there are many tied insertion positions that produce such shortest makespan. Thus, a tiebreaker must be used to discern a selection among the tied insertion positions. Many tiebreakers have been proposed in the literature for this case. These tiebreakers improve the results produced by approximate methods when embedded into them. In this paper we propose two new tiebreakers that use a weighted and an unweighted approximation of the idle time increment produced by inserting the job into each tied insertion position. They were designed considering the reversibility property of the PFSSP. Our computational experiments show that the proposed tiebreakers outperform tiebreakers from the literature when evaluated within the NEH heuristic and within the iterated greedy algorithm. The iterated greedy algorithms with the proposed tiebreakers embedded are the best approximate methods so far for the permutational flow shop scheduling problem.

This study addresses the problem of minimizing tool switching instants in automated manufacturing systems. There exist a single machine and a group of jobs to be processed on it. Each job requires a set of tools, and due to limited tool magazine capacity, and because it is not possible to load all available tools on the machine, tools must be switched. The ultimate goal, in this framework, is to minimize the total number of tool switching instants. We provide a mathematical programming model and two constraint programming models for the problem. Because the problem is proven to be NP-hard, we develop two heuristic approaches, and compare their performance with methods described in the literature. Our analysis indicates that our constraint programming models perform relatively well in solution quality and execution time in small-sized problem instances. The performance of our greedy approach shows potential, reaching the optimal solution in 82.5% of instances. We also statistically demonstrate that the search algorithm enhances the quality of the solution obtained by the greedy heuristic, particularly in large sets. Hence, the solution approach, i.e., the greedy heuristic and the search algorithm proposed in this study is able to quickly reach near-optimal solutions, showing that the method is appropriate for manufacturing settings requiring sudden adjustments.

In this paper, a joint design for cooperative spectrum sharing framework of multiple-input multiple-output (MIMO) radar and MIMO communication system in radar multi-target optimization is proposed. The interesting design Degrees of Freedom (DOFs) include radar transceiver beamforming vector and communication system codebook, whereby the designed problem is a constrained minimization of total radar effective interference power under power limited conditions and communication rate constraint guaranteeing both the two coexistence systems performance. As to the non-convex multi-variables problem, an alternating iteration approach is developed to solve the three suitably transformed subproblems, the closed form solutions are derived, and the convergence of the proposed design is guaranteed. Finally, numerical results show the spectrum sharing performance of the proposed approaches.

This paper considers a novel single-stage scheduling problem with jobs being delivered in batches on flexibly definable customer-dependent delivery dates. To be applicable to real-world make-to-order processes, this versatile proposal significantly extends related approaches that require equidistant delivery dates. Moreover, job release dates and deadlines are covered. The objective function of the proposed optimization model pursues the minimization of the sum of incurred holding and transportation costs. In order to solve the model to optimality, a Branch&Bound procedure is generated that applies several bounding and domination rules. Furthermore, a randomized adaptive search procedure is proposed that attains promising heuristic solutions under tight time restrictions. The practicability of the proposed algorithms is validated by means of a comprehensive computational study in comparison with a commercial solver. While the Branch&Bound approach considerably outperforms the standard solver, the heuristic approach provides optimal or close to optimal upper bounds under tight time restrictions.

Optimal operation of a compressor station is important since it accounts for 25 % to 50 % of a company’s total operating budget. In short-term management of a compressor station, handling demand uncertainty is important yet challenging. Previous studies either require precise information about the distribution of uncertain parameters or greatly simplify the compressor model. We build a two-stage robust optimization framework of power cost minimization in a natural gas compressor station with non-identical compressors. In the first stage, decision variables are the ON/OFF state of each compressor and discharge pressure. The worst-case cost of the second stage is incorporated in the first stage. First-stage decision variables feasibility is discussed and proper feasibility cuts are also proposed for the first stage. We employ a piece-wise approximation and propose accelerate methods. Our numerical results highlight two advantages of robust approach when managing uncertainty in practical settings: (1) the feasibility of first-stage decision can be increased by up to 45 % , and (2) the worst-case cost can be reduced by up to 25 % compared with stochastic programming models. Furthermore, our numerical experiments show that the designed accelerate algorithm has time improvements of 1518.9% on average (3785.9% at maximum).

Electric vehicles (EVs) endow great potentials for future transportation systems, while efficient charge scheduling strategies are crucial for improving profits and mass adoption of EVs. Two critical and open issues concerning EV charging are how to minimize the total charging cost (Objective 1) and how to minimize the peak load (Objective 2). Although extensive efforts have been made to model EV charging problems, little information is available about model properties and efficient algorithms for dynamic charging problems. This paper aims to fill these gaps. For Objective 1, we demonstrate that the greedy-choice property applies, which means that a globally optimal solution can be achieved by making locally optimal greedy choices, whereas it does not apply to Objective 2. We propose a non-myopic charging strategy accounting for future demands to achieve global optimality for Objective 2. The problem is addressed by a heuristic algorithm combining a multi-commodity network flow model with customized bisection search algorithm in a rolling horizon framework. To expedite the solution efficiency, we derive the upper bound and lower bound in the bisection search based on the relationship between charging volume and parking time. We also explore the impact of demand levels and peak arrival ratios on the system performance. Results show that with prediction, the peak load can converge to a globally optimal solution, and that an optimal look-ahead time exists beyond which any prediction is ineffective. The proposed algorithm outperforms the state-of-the-art algorithms, and is robust to the variations of demand and peak arrival ratios.

We consider a scheduling problem on identical machines, where the cost for each machine is the total size of jobs assigned to it, excluding its largest job. The objective is to minimize the cost of the schedule, which is the maximum cost over all machines. We study online algorithms with and without migration. We design an algorithm with competitive ratio 3 for the purely online variant and provide a lower bound of 2.26953 on the competitive ratio of any online algorithm. For two machines, we find tight bounds of 2 on the competitive ratio. Additionally, we design a polynomial time approximation scheme for the variant with migration. We also briefly discuss the same online problem on uniformly related machines.

More and more cloud data centers are turning to leverage on-site renewable energy to reduce power cost for sustainable development. But how to effectively coordinate the intermittent renewable energy with workload remains to be a great challenge. This paper investigates the problem of workload scheduling for power cost minimization under the constraints of different Service Level Agreements (SLAs) of delay tolerant workload and delay sensitive workload for green data centers in a smart grid. Different from the existing studies, we take into consideration of the impact of zero price in the smart grid and the cost of on-site renewable energy. To handle the randomness of workload, electricity price and renewable energy availability, we first formulate the problem as a constrained stochastic problem. Then we propose an efficient online control algorithm named ODGWS (Online Delay-Guaranteed Workload Scheduling) which makes online scheduling decisions achieve a bounded guarantee from the worst scheduling delay for delay tolerant workload. Compared with the existing solutions, our ODGWS decomposes the problem into that of solving a simple optimization problem within each time slot in O ( 1 ) time without needing any future information. The rigorous theoretical analysis demonstrates that our algorithm achieves a [ O ( 1 V ) , O ( V ) ] cost-delay tradeoff, where V is a balance parameter between the cost optimality and service quality. Extensive simulations based on real-world traces are done to evaluate the performance of our algorithm. The results show that ODGWS saves about 5% average power cost compared with the baseline algorithms.

This study proposes a non-threshold consensus model that combines the minimum cost and maximum consensus-increasing for multi-attribute large group decision-making (MALGDM). First, the large-scale experts is classified into several clusters via the combination of the similarities of evaluation information, unit consensus cost, and adjustment willingness. Then, a more sensitive consensus measure method that combines the mean value and variance of the similarities among clusters is presented. Next, a comprehensive identification rule is put forward to determine the cluster with a low consensus level, low unit consensus cost, and high adjustment willingness for information adjustment. An optimization model that combines the minimization of the cost of the cluster and the maximization of the increase of the global consensus level is then constructed to obtain the adjusted information. Also, the adjustment willingness is considered in the constraints to limit the adjustment range. Moreover, instead of the use of a predefined threshold and a maximum number of iterations, a termination index is developed to terminate the consensus reaching process (CRP) to make the CRP more objective and rational. Finally, an application example is presented, and comparison and simulation analyses are performed to validate the feasibility and effectiveness of the proposed model.

Optimizing all the objectives of the printed circuit board assembly (PCBA) optimization in a multifunctional placer remains a formidable challenge till now. This article converts the original PCBA optimization problem to a newly defined component allocation problem, which decides the component-type handled by each head per pickup-and-place (PAP) cycle. The component allocation problem is a quadratic 3-D assignment problem (Q3AP) and effectively combines the optimization of all the main objectives. It is possible that one head stays idle, so the assigning 2-D locations are uncertain. We propose the cell division genetic algorithm (CDGA) to solve such a complex Q3AP. The CDGA allocates a component cell as the basic unit. Each of the first-generation component cells contains the mounting points of the same type. A cell chromosome decoding heuristic is designed to determine the next assigning head. By doing so, the problem dimension is reduced, so the conventional GA can be used for searching the optimal component allocation formed by the current-generation cells. When a better allocation can no longer be found by allocating the current cells, the cell division operation is performed to divide each cell into two new cells. The new cells are used in the next round of GA searching, which further optimizes the allocation from two perspectives: better balancing the minimization of nozzle changes and PAP cycles, more flexibly maximizing the simultaneous pickups with the uncertain locations. The CDGA works continuously until the current cells cannot bring any improvement. In simulations and experiments using the industrial samples, the proposed algorithm significantly reduces the PCBA time compared to two recent studies and the built-in optimizer of the widely used multifunctional placer, Hanwha SM482 PLUS, which demonstrates its effectiveness and superiority.

A social cost minimization problem is addressed in this article. In the considered problem, a network of agents work collaboratively to minimize the social cost function, which is defined as the sum of the agents’ local objective functions. The engaged agents are supposed to be equipped with an undirected and connected communication graph. Different from most of the existing works, the social cost function in the considered problem is allowed to be nonconvex and possibly admits local extrema. To avoid local extrema and achieve the global minimization of the social cost function, an extremum-seeking-based approach is proposed by introducing a dynamic average consensus protocol to the sinusoidal-dither-signal-based extremum seeking scheme. The dynamic average consensus protocol is leveraged in the proposed extremum-seeker for information sharing and the sinusoidal probing signal is utilized for information extraction. For the avoidance of local extrema, the amplitude of the dither signal is designed to be adaptive. Through Lyapunov stability analysis, it is shown that the proposed method enables the decision variable to converge to a neighborhood of the global minimum point if the conditions on the network connectivity, the existence of unique global minimum and achievability of the global minimum are satisfied. The theoretical result is verified via simulating a numerical example.

This letter addresses the problem of coordinating a team of pursuers to capture a fast evader in reach-avoid games. Coordination is achieved through the minimization of a locational cost objective, which results in a coverage control strategy. Coverage control dynamics are equivalently expressed as consensus dynamics. This formulation is used to guarantee optimal coverage of an implicit defense manifold without needing to rely on projection mappings as in previous works. Control barrier functions (CBFs) are used to guarantee the existence of a pursuer-defendable defense manifold for as long as feasible throughout the engagement and guarantee capture. A greedy evader strategy is proposed in terms of the solution to a quadratically constrained quadratic program, and simulation results are presented comparing the performance of an uncoordinated strategy and a pure coverage strategy to the proposed coordinated CBF strategy.

This paper proposes a single machine scheduling problem with learning-effect and release times by considering two objectives requiring minimization of makespan and total tardiness, simultaneously. Due to the NP-hardness of this problem, two memetic algorithms with meme variants are presented for solving the bi-objective problem and applied by combining three different scalarization methods, including weighted sum, conic, and tchebycheff. The performance of all memetic algorithms with the meme is investigated across randomly generated twenty-seven test problems ranging from ‘small’ to ‘large’ size. The experimental results indicate that the Multimeme Memetic Algorithm using the tchebycheff outperforms the other algorithms producing the best-known results for almost all bi-objective single machine scheduling instances with learning-effects. All algorithms perform effectively in solving large-sized problems with up to 200 jobs.

We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of approximation that is specifically tailored to the multiobjective case and its inherent trade-offs between different objectives. For minimization problems, we provide an efficient algorithm that computes an approximation of a multiobjective problem by using an exact or approximate algorithm for its weighted sum scalarization. In case that an exact algorithm for the weighted sum scalarization is used, this algorithm comes arbitrarily close to the best approximation quality that is obtainable by supported solutions – both with respect to the common notion of approximation and with respect to the new multi-factor notion. Moreover, the algorithm yields the currently best approximation results for several well-known multiobjective minimization problems. For maximization problems, however, we show that a polynomial approximation guarantee can, in general, not be obtained in more than one of the objective functions simultaneously by supported solutions.

Software testing is a valuable and time-consuming activity that aims to improve the software quality. Due to its significance, combinatorial testing focuses on fault identification by the interaction of small amount of input factors. But, deep testing is not sufficient due to time or resources availability. To select the optimal test cases with least computation time, Hybrid Multi Criteria Particle Swarm and Ranked Firefly Metaheuristic Optimization(HMCPW-RFMO) technique are introduced. Initially, the population of the test cases is randomly initialized. Then the fitness is calculated by the pairwise coverage, execution cost, fault detection capability and average execution frequency. RFM approach starts with ‘n’ fireflies. The light intensity of each firefly gets initialized.If the light intensity of one firefly is minor than the other one, it moves near the brighter one. Next, the rank is given to the firefly based on their light intensity. Lastly, the high ranked firefly is chosen as a global best solution.The result reveals that HMCPW-RFMO technique improves the software quality.

Recent improvements in vehicle-to-everything (V2X) communication and onboard computing power have enabled the development of control algorithms that jointly optimize the vehicle velocity and powertrain control in Connected and Automated Vehicles (CAVs), commonly referred to as the Eco-Driving problem. This paper presents a novel and computationally efficient algorithm to optimize the velocity planning and energy management in a CAV with a hybrid electric powertrain. The Eco-Driving problem is formulated as a dynamic, constrained optimization problem in the spatial domain, where information about the upcoming speed limits and road topography is assumed known. This problem is solved by embedding an Equivalent Consumption Minimization Strategy (ECMS) into a Dynamic Programming (DP) optimization to obtain a sub-optimal solution that provides results close to the global optimum at a fraction of the computational cost. Further, a multi-layer hierarchical control architecture is proposed as a path to a causal, real-time implementation. The DP-ECMS algorithm is converted into a Model Predictive Control (MPC) framework by using principles of Approximate Dynamic Programming (ADP). This causal implementation is finally benchmarked to a global optimal solution obtained with DP for different scenarios.

For the optimization of envelope characteristics also the shape of the building, an optimization–simulation technique is applied in this paper. To obtain the best values of all related variables for the minimization of energy consumption in residential buildings, an improved Manta-Ray Foraging Optimizer is considered as the optimization algorithm. Also, for whole-building energy simulation, RIUSKA is used. The optimization parameters are the area and type of the windows, foundation, wall and roof insulations, level of infiltration, orientation, and thermal mass. Various forms of the building including rectangle, trapezoid, T-shape, H-shape, cross, L-shape, and U-shape are studied. The model optimization process takes fewer computation time and expense. Moreover, the utilized technique implements fully proper in comparison to the particle swarm, approximating very close to the optimum in less than 50% of the simulations The lowest life cycle cost is achieved by the buildings with trapezoid and rectangle form for five various climatic conditions. Also, the minimum variation from the optimum to the worst is observed by trapezoid and rectangle. The change in the values of the life cycle cost is lower than 4.5%.

The ever-growing trend of electricity demand and environmental concerns have mandated the operation of electrical energy grids in a more economical and environmentally friendly manner. In the past few years, the integration of combined heat and power units has offered a promising solution to these concerns, however, at the same time a new challenging problem has revealed itself that is finding a simultaneous optimal solution between two competing criteria of power and heat. Furthermore, this problem will be more complex when the reduction of emission gasses is taken into consideration. Thus, to solve optimal scheduling of combined heat and power units, this study proposes an intelligent sequential algorithm based on the hybridization of teaching and learning-based optimization algorithm and an improved version of particle swarm optimization. The proposed algorithm is uniquely capable of the concurrent minimization of total generation costs and multi-pollutant gasses while several physical, operational, and environmental constraints are considered. Also, to ensure the safe maintenance of systems’ constraints, this study employs an adaptive violation constraint handling technique in conjunction with the proposed hybridized optimization algorithm. Finally, the performance of the proposed algorithm is compared to the recently developed methods, in which the proposed algorithm of the study outperforms all the other algorithms and achieves up to 2.2% lower overall costs of operation in most of the studied cases.

This study suggests a new optimized model for optimum identification of the unknown variables in a Solid Oxide (SO) fuel cell. The method is conditioned by designing an improved version of metaheuristics to improve the effectiveness of the original method and using it by the Sum of Squared Error (SSE) minimization between the model and the experimental data including output voltage. The metaheuristic is based on a new improved model of a new metaheuristic, called the Red Fox Optimization Algorithm (IRFO). To assess the method’s accuracy and its consistency, it is validated by various pressure and temperature functional conditions. The results showed that the error value of the produced power by different temperatures is lower than 0.0073 kW and the error value of the output voltage by different temperatures is lower than 0.16 V which is a promising result for stack identification. Also, the achievements of the algorithm are compared with several approaches from the literature. The final results show a satisfying verification between the empirical and the optimized technique

This letter studies one-to-many capacity allocation pairings in multi-beam high throughput satellite networks employing smart gateway diversity. The minimization of total network’s capacity losses and rate matching metrics are examined. To approach the aforementioned binary optimization problems, a two-step heuristic scheme is proposed. Firstly a continuous pairing solution is given based on difference of convex programming theory and then a continuous to binary feasible allocation solution is provided. Extended simulation results highlight the lower complexity of the proposed approach, compared with the exponential complexity of the optimal exhaustive mechanism and a small relative error in its performance.

This paper presents a novel Marine Predators Algorithm for both training an Artificial Neural Network model used for predicting the energy demand and for solving a dynamic combined economic and emission dispatch of a data centre. The MPA is proposed for first finding the optimal weights and biases of the neural network based on a Mean Squared Error and Mean Absolute Error minimization objective function. Real life dataset obtained from an anonymous data centre operator in Cape Town, South Africa was used for the model implementation. The dataset was made up of a total of 564 samples and was split into training and testing set using an 80:20 ratio. The input variables contained in the dataset are the data centre’s ambient temperature, ambient relative humidity, chiller output temperature and Computer Room Air Conditioning supply temperature while the energy demand is the target variable. The optimal weights of the neural network model were analysed using a weights-based approach to determine the level of influence each input parameter of the model has on the data centre’s energy demand. Then based on the predicted energy demand of the data centre, a dynamic economic and emission dispatch problem is solved for the building while considering thermal and solar photovoltaic generations. A spinning reserve is also incorporated in the energy dispatch model to cater for any shortfall that may exist between the predicted and actual energy demand of the data centre due to possible inaccuracies in the energy demand prediction model. Results for the energy demand prediction task showed that the proposed method outperformed the state-of-the-art by producing the least Mean Squared Error, Root Mean Squared Error, Mean Absolute Error, Mean Absolute Percentage Error and highest prediction accuracy for the training and testing sets. Further analyses also highlighted that the data centre’s ambient temperature has the highest influence of about 37.63% on its energy demand pattern. For the energy dispatch task, the proposed method also identified solar photovoltaic as the preferred energy source over conventional thermal generators in fulfilling the objective function, depending on its availability. Overall, the findings presented in this study emphasize the robustness of the proposed method in solving the problems considered and its potential application towards solving even more complex problems.

Peer-to-peer interconnection of households having on-site batteries, multi-port converters and solar panels to form a multi-port converter-enabled solar DC nano-grid is an emerging approach for providing affordable energy access in rural areas. Battery charge and discharge losses, distribution losses and converter losses are significant problem when operating such nano-grids. This paper presents a centralized control algorithm that can help address the power loss problem. The proposed algorithm uses a new problem formulation where the power loss problem is formulated as a two-stage convex optimization problem. The first stage of the optimization problem is an optimal battery dispatch problem for determining optimal battery charge and discharge currents. The second stage is an optimal current flow problem for determining optimal distribution voltages which corresponds to the optimal battery currents. Simulation results of the nano-grid show that the proposed algorithm can minimize the nano-grid power losses while facilitating the power exchange between the households. The proposed algorithm is suitable for small nano-grids where privacy of households is not a concern. In Part II of this paper we propose a distributed control algorithm that preserves the privacy of the households especially where the size of the nano-grid is large.

A new efficient technique for the best selection of the unknown variables in the Solid Oxide Fuel Cell (SOFC) stack models is proposed in this paper. The main concept in this paper is the minimization of the sum of squared error values between the empirical voltage and current profile and the obtained voltage and current profiles from the method. The minimization process is defined by a new improved metaheuristic, which is the Modified African Vulture Optimizer (MAVO). The MAVO algorithm is designed to modify the algorithm and achieve results with better effectiveness as concerns convergence and accuracy. For determining the system consistency, two scenarios based on pressure and temperature variations are investigated. The technique has been finally compared with several other techniques to verify its prominence. The results show the minimum value of the SSE under different temperatures, equal to 1.87 e−4, and the minimum value of the MSE under different temperatures, equal to 1.24 e−3. This indicates promising results for the proposed method as a proper identification system. Final achievements indicate that the suggested approach provides outstanding effectiveness toward the compared methods.

Hybrid renewable energy system (HRES) is a nexus of several renewable energy systems that concertedly overcomes the limitations of individual systems operating in isolation. This concept of HRES is extended in this study by considering the network of several such HRESs which further improves the flexibility in overcoming the individual limitations. However, operating such a network of HRESs involves complex decision-making and requires efficient optimization. In this study, a novel hierarchical two-tier optimization methodology for a network of HRESs is proposed when they trade power with each other and with the macro grid. In the proposed methodology, the operational optimization of each HRES is carried out by minimizing the operating cost of various sub-units in the first layer. In the second layer, three cooperative optimization strategies inspired from concepts of double-auction e-marketing are applied when HRESs are assumed to operate under the grand coalition. These three cooperative strategies try to achieve the following objectives (i) minimization of power loss during local trade, (ii) maximization of total market gain, and (iii) simultaneous power loss minimization and total market gain maximization, respectively. Simulation results depict that the cooperative optimization approach yields a reduction in power loss up to 7 % and improvement in market utility up to 29% relative to a scenario when they operate non-cooperatively.

Scheduling process arises naturally upon availability of resources through a systematic approach in which prior planning and decisions should be made. Two machine flow shop scheduling problem (FSSP) was solved by Johnson in the mid of 1954 with makespan minimization as objective. Earlier we proposed two algorithms for the makespan objective; in this paper we intend to investigate the same algorithms for the objective of Total Completion Time of all the jobs (TCT). Experimental results had shown that one of our algorithms gives better results than the other two when the machine order is reversed.

SIGNSGD is able to dramatically improve the performance of training large neural networks by transmitting the sign of each minibatch stochastic gradient, which achieves gradient communication compression and keeps standard stochastic gradient descent (SGD) level convergence rate. Meanwhile, the learning rate plays a vital role in training neural networks, but existing learning rate optimization strategies mainly face the following problems: (1) for learning rate decay method, small learning rates produced lead to converge slowly, and extra hyper-parameters are required except for the initial learning rate, causing more human participation. (2) Adaptive gradient algorithms have poor generalization performance and also utilize other hyper-parameters. (3) Generating learning rates via two-level optimization models is difficult and time-consuming in training. To this end, we propose a novel adaptive learning rate schedule for neural network training via SIGNSGD optimizer for the first time. In our method, based on the theoretical inspiration that the convergence rate’s upper bound has minimization with the current learning rate in each iteration, the current learning rate can be expressed by a mathematical expression that is merely related to historical learning rates. Then, given an initial value, learning rates in different training stages can be adaptively obtained. Our proposed method has following advantages: (1) it is a novel automatic method without additional hyper-parameters except for one initial value, thus reducing the manual participation. (2) It has faster convergence rate and outperforms the standard SGD. (3) It makes neural networks achieve better performance with fewer gradient communication bits. Three numerical simulations are conducted on different neural networks with three public datasets: MNIST, Cifar-10 and Cifar-100 datasets, and several numerical results are presented to demonstrate the efficiency of our proposed approach.

In this paper, we address a variant of the identical parallel machines scheduling problem subject to common restrictive due windows. The performance measure adopted is the minimization of total weighted earliness and tardiness. Since the variant under study is an NP-hard problem for two or more machines, we develop a family of constructive heuristics, which are comprised of four phases. First, jobs are sequenced according to priority rules. Second, jobs are assigned to machines using a greedy strategy. Third, a local search is performed to find a better distribution of jobs into machines. Fourth, two heuristics are applied for individually sequencing jobs in each machine, namely RN-RGH and RN-SEA. In addition, we also propose an iterated greedy algorithm to improve the solutions of the best performing heuristic. The computational experiments were carried out to prove the ability of these heuristics to find high-quality solutions in acceptable CPU time. More specifically, the RN-SEA family of algorithms stands out as the most efficient for the problem, however, with a higher computational effort. We also confirm that the IG algorithm has the potential for improving existing solutions, specially for problems with two machines and instances with up to 100 jobs in size.

This paper is devoted to the construction and analysis of a novel hybrid optimization model of the l 0 minimization and the l 1 minimization with a given support estimate. With the help of the Moreau envelop of the l 1 norm, we provide reasonable explanation for the claim that the capped- l 1 penalty is one of the continuous relaxation to the l 0 -norm penalty and thus develop the scale iteratively reweighed l 1 -minimization (SIRL1) aiming to achieve fast reconstruction and a reduced requirement on the number of measurements compared to the l 1 minimization approach. To illustrate the theoretical results, some numerical experiments are presented to demonstrate the effectiveness and flexibility of the proposed SIRL1 algorithm.

In this study, we propose a reinforcement learning (RL) approach for minimizing the number of work overload situations in the mixed model sequencing (MMS) problem with stochastic processing times. The learning environment simulates stochastic processing times and penalizes work overloads with negative rewards. To account for the stochastic component of the problem, we implement a state representation that specifies whether work overloads will occur if the processing times are equal to their respective 25%, 50%, and 75% probability quantiles. Thereby, the RL agent is guided toward minimizing the number of overload situations while being provided with statistical information about how fluctuations in processing times affect the solution quality. To the best of our knowledge, this study is the first to consider the stochastic problem variation with a minimization of overload situations.

Optimization problems with orthogonality constraints appear widely in applications from science and engineering. We address these types of problems from a numerical approach. Our new framework combines the steepest gradient descent, using implicit information, with a projection operator in order to construct a feasible sequence of points. In addition, we adopt an adaptive Barzilai–Borwein steplength mixed with a globalization technique in order to speed-up the convergence of our procedure. The global convergence, and some theoretical related to our algorithm are proved. The effectiveness of our proposed algorithm is demonstrated on a variety of problems including Rayleigh quotient maximization, heterogeneous quadratics minimization, weighted orthogonal procrustes problems and total energy minimization. Numerical results show that the new procedure can outperform some state of the art solvers on some practically problems.

Capacitated two-stage time minimization transportation problem is an important optimization problem arising in industries. In literature, there is only one approach to solving this problem, but it has a deficiency of resulting in memory overflow in implementation on computer for large scale instances. In this paper, this problem is reduced to a series of finding the feasible flow in a network with lower and upper arc capacities, and two iterative algorithms are proposed as more robust solution method for this problem as compared to the existing approach. It is proved that both iterative algorithms find the optimal solution to this problem in a polynomial time. Due to fully utilizing the network structure characteristics inherent to this problem, both iterative algorithms have the advantage of easy implementation on computer and high computational efficiency, and successfully overcome the deficiency of existing approach. Computational experiments validate that as compared to the existing approach, both iterative algorithms are efficient and more robust method to solve this problem, where one iterative algorithm significantly outperforms the other in terms of computational time, especially for large scale instances.

PurposeOne of the main advantages of the proposed model is that it is flexible to generate n-day pairings simultaneously. It means that, despite previous researches, one-day to n-day pairings can be generated in a single model. The flexibility in generating parings causes that the proposed model leads to better solutions compared to existing models. Another advantage of the model is minimizing the risk of COVID-19 by limitation of daily flights as well as elapsed time minimization. As airports are among high risk places in COVID-19 pandemic, minimization of infection risk is considered in this model for the first time. Genetic algorithm is used as the solution approach, and its efficiency is compared to GAMS in small and medium-size problems.Design/methodology/approachOne of the most complex issues in airlines is crew scheduling problem which is divided into two subproblems: crew pairing problem (CPP) and crew rostering problem (CRP). Generating crew pairings is a tremendous and exhausting task as millions of pairings may be generated for an airline. Moreover, crew cost has the largest share in total cost of airlines after fuel cost. As a result, crew scheduling with the aim of cost minimization is one of the most important issues in airlines. In this paper, a new bi-objective mixed integer programming model is proposed to generate pairings in such a way that deadhead cost, crew cost and the risk of COVID-19 are minimized.FindingsThe proposed model is applied for domestic flights of Iran Air airline. The results of the study indicate that genetic algorithm solutions have only 0.414 and 0.380 gap on average to optimum values of the first and the second objective functions, respectively. Due to the flexibility of the proposed model, it improves solutions resulted from existing models with fixed-duty pairings. Crew cost is decreased by 12.82, 24.72, 4.05 and 14.86% compared to one-duty to four-duty models. In detail, crew salary is improved by 12.85, 24.64, 4.07 and 14.91% and deadhead cost is decreased by 11.87, 26.98, 3.27, and 13.35% compared to one-duty to four-duty models, respectively.Originality/valueThe authors confirm that it is an original paper, has not been published elsewhere and is not currently under consideration of any other journal.

This paper addresses the problem of parametric estimation in solar cells considering manufacturer datasheet information regarding open-circuit, short-circuit, and maximum power points from the point of view of mathematical optimization. To represent this problem a single-objective function is formulated associated with the minimization of the mean square error of the single-diode model evaluated in the operational points reported by the manufacturer. The solution of this nonlinear non-convex optimization model is addressed with a metaheuristic optimization technique known in specialized literature as a vortex search algorithm (VSA). This metaheuristic optimization method works with Gaussian distribution functions and variable radius to explore and exploit the solution space by generating hyperspheres that move through the solution space as a function of the best current solution. The VSA is implemented in MATLAB environment by using commercial photovoltaic module information, where numerical results demonstrate the efficiency of this optimization method with objective functions lower than 1times10-25 and processing times around 6.13s.

In the real world, the demands for some specific goods may increase in some special occasions. At such conditions, in-time delivery of the desired goods and minimization of the traveling costs will be found crucial importance for the customers and the suppliers, respectively. In this paper, a new mathematical model consisting of two objectives: minimizing traveling costs and maximizing customers’ demand satisfaction was proposed through a multi-objective optimization approach. The nonlinear equations were converted to linear equations and the proposed model was then solved using CPLEX solver by GAMS23.6.3 software. Two approaches were proposed to solve the problem based on the NSGA-II algorithm with different modifications in the mutation operator. A two-row structure was also employed for the chromosomes. This research contributes to vehicle routing literature considering time windows, multiple demands, and two conflict objectives and proposes two metaheuristic algorithms. The algorithm results were also compared with two criteria: covered non-dominated solutions and spread solutions. The results show that the improvements were made with the variation in the mutation operator in both criteria. In summary, the developed vehicle routing mathematical model works effectively for some real-world logistic problems with occasional goods, and the customer satisfaction in due time is incorporated in the mathematical model.

The optimal capacitor placement issue has a strong combinatorial nature due to the high number of possible decisions. This paper proposes a three-level method to solve this problem in unbalanced distribution systems to achieve energy losses minimization. In the first step, the Multiphase Optimal Power Flow is solved by Interior Point Method, considering heavy-load and light-load, where the reactive power and the number of fixed and switched banks are determined, where the topology constraints are modeled using a Multiphase Power Flow Method. In the second step, the position of the capacitors is determined using Genetic Algorithms, using the light-load to allocate the fixed banks and heavy-load to allocate the switched ones. Finally, the third step aims to determine the states of the switched capacitors, using binary optimization and considering the whole daily load curve. For validation, it is tested on topologies based in IEEE 4, IEEE 13, and IEEE 123 Node Test-Feeders.