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Economic load dispatch (ELD) is one of the crucial optimization problems in power system planning and operation. The ELD problem with valve point loading (VPL) and multi-fuel options (MFO) is defined as a non-smooth and non-convex optimization problem with equality and inequality constraints, which obliges an efficient heuristic strategy to be addressed. The purpose of this study is to present a new and powerful heuristic optimization technique (HOT) named as squirrel search algorithm (SSA) to solve non-convex ELD problems of large-scale power plants.

The suggested SSA approach is aimed to minimize the total fuel cost consumption of power plant considering their generation values as decision variables while satisfying the problem constraints. It confers a solution to the ELD issue by anchoring with foraging behavior of squirrels based on the dynamic jumping and gliding strategies. Furthermore, a heuristic approach and selection rules are used in SSA to handle the constraints appropriately.

Empirical results authenticate the superior performance of SSA technique by validating on four different large-scale systems. Comparing SSA with other HOTs, numerical results depict its proficiencies with high-qualitative solution and by its excellent computational efficiency to solve the ELD problems with non-smooth fuel cost function addressing the VPL and MFO. Moreover, the non-parametric tests prove the robustness and efficacy of the suggested SSA and demonstrate that it can be used as a competent optimizer for solving the real-world large-scale non-convex ELD problems.

This study has compared various HOTs to determine optimal generation scheduling for large-scale ELD problems. Consequently, its comparative analysis will be beneficial to power engineers for accurate generation planning.

To the best of the authors’ knowledge, this manuscript is the first research work of using SSA approach for solving ELD problems. Consequently, the solution to this problem configures the key contribution of this paper.

The purpose of this paper is to solve the optimal power dispatch problem of thermal generating units with cubic fuel cost and emission functions.

The proposed Simplified Direct Search Method (SDSM) is developed from the Direct Search Method (DSM) that is a prevailing method for solving economic dispatch (ED) problems. The SDSM performs a direct search on solution space that starts with the minimum generation limits and provides the most economical schedule in a single execution for all load demands that the system can meet.

A simple methodology is developed to obtain the optimal dispatches of the generators in a thermal power plant. The results of the proposed methodology illustrate improvements in the savings of total cost and marginal reduction in transmission loss. It is also suitable for solving environmental constrained power dispatch problems. The proposed approach is computationally efficient for large‐scale systems.

A simple methodology has been developed to obtain the real power dispatches of thermal generating units with higher order fuel cost and emission functions.

The purpose of the paper is to solve hydrothermal scheduling (HTS) problem for energy-efficient management by allocating the optimal real power outputs for thermal and hydroelectric generators.

HTS can be formulated as a complex and non-linear optimization problem which minimizes the total fuel cost and emissions of thermal generators subject to various physical and operational constraints. As the artificial bee colony algorithm has proven its ability to solve various engineering optimization problems, it has been used as a main optimization tool to solve the fixed-head HTS problem.

A meta-heuristic search technique-based algorithm has been implemented for hydrothermal energy management, and the simulation results show that this approach can provide trade-off between conflict objectives and keep a rapid convergence speed.

The proposed methodology is implemented on the standard test system, and the numerical results comparison indicates a considerable saving in total fuel cost and reduction in emission.

The purpose of this paper is to measure the financial risk and optimal capital structure of a corporation.

Irregular disjunctive programming problems arising in firm models and risk management can be solved by the techniques presented in the paper.

Parallel processing and mathematical modeling provide a fruitful basis for solving ultra-scale non-convex general disjunctive programming (GDP) problems, where the computational challenge in direct mixed-integer non-linear programming (MINLP) formulations or single processor algorithms would be insurmountable.

The test is limited to a single firm in an experimental setting. Repeating the test on large sample of firms in future research will indicate the general validity of Monte-Carlo-based VAR estimation.

The authors show that the risk surface of the firm can be approximated by integrated use of accounting logic, corporate finance, mathematical programming, stochastic simulation and parallel processing.

Parallel processing has potential to simplify large-scale MINLP and GDP problems with non-convex, multi-modal and discontinuous parameter generating functions and to solve them faster and more reliably than conventional approaches on single processors.

This study proposes targeted modernization of the Department of Defense (DoD's) Joint Forces Ammunition Logistics information system by implementing the optimized innovative information technology open architecture design and integrating Radio Frequency Identification Device data technologies and real-time optimization and control mechanisms as the critical technology components of the solution. The innovative information technology, which pursues the focused logistics, will be deployed in 36 months at the estimated cost of $568 million in constant dollars. We estimate that the Systems, Applications, Products (SAP)-based enterprise integration solution that the Army currently pursues will cost another $1.5 billion through the year 2014; however, it is unlikely to deliver the intended technical capabilities.

The purpose of this paper is to deal with the economic requirements of power system loading dispatch and reduce the fuel cost of generation units. In order to optimize the scheduling of power load, an improved chicken swarm optimization (ICSO) is proposed to be adopted, for solving economic load dispatch (ELD) problem.

The ICSO increased the self-foraging factor to the chicks whose activities were the highest. And the evolutionary operations of chicks capturing the rooster food were increased. Therefore, these helped the ICSO to jump out of the local extreme traps and obtain the global optimal solution. In this study, the generation capacity of the generation unit is regarded as a variable, and the fuel cost is regarded as the objective function. The particle swarm optimization (PSO), chicken swarm optimization (CSO), and ICSO were used to optimize the fuel cost of three different test systems.

The result showed that the convergence speed, global search ability, and total fuel cost of the ICSO were better than those of PSO and CSO under different test systems. The non-linearity of the input and output of the generating unit satisfied the equality constraints; the average ratio of the optimal solution obtained by PSO, CSO, and ICSO was 1:0.999994:0.999988. The result also presented the equality and inequality constraints; the average ratio of the optimal solution was 1:0.997200:0.996033. The third test system took the non-linearity of the input and output of the generating unit that satisfied both equality and inequality constraints; the average ratio was 1:0.995968:0.993564.

This study realizes the whole fuel cost minimization in which various types of intelligent algorithms have been applied to the field of load economic scheduling. With the continuous evolution of intelligent algorithms, they save a lot of fuel cost for the ELD problem.

The ICSO is applied to solve the ELD problem. The quality of the optimal solution and the convergence speed of ICSO are better than that of CSO and PSO. Compared with PSO and CSO, ICSO can dispatch the generator more reasonably, thus saving the fuel cost. This will help the power sector to achieve greater economic benefits. Hence, the ICSO has good performance and significant effectiveness in solving the ELD problem.

The purpose of this paper is to solve economic emission dispatch problem in connection of wind with hydro-thermal units.

The proposed hybrid methodology is the joined execution of both the modified salp swarm optimization algorithm (MSSA) with artificial intelligence technique aided with particle swarm optimization (PSO) technique.

The proposed approach is introduced to figure out the optimal power generated power from the thermal, wind farms and hydro units by minimizing the emission level and cost of generation simultaneously. The best compromise solution of the generation power outputs and related gas emission are subject to the equality and inequality constraints of the system. Here, MSSA is used to generate the optimal combination of thermal generator with the objective of minimum fuel and emission objective function. The proposed method also considers wind speed probability factor via PSO-artificial neural network (ANN) technique and hydro power generation at peak load demand condition to ensure economic utilization.

To validate the advantage of the proposed approach, six- and ten-units thermal systems are studied with fuel and emission cost. For minimizing the fuel and emission cost of the thermal system with the predicted wind speed factor, the proposed approach is used. The proposed approach is actualized in MATLAB/Simulink, and the results are examined with considering generation units and compared with various solution techniques. The comparison reveals the closeness of the proposed approach and proclaims its capability for handling multi-objective optimization problems of power systems.

The ever-stringent environmental regulations force power producers to produce electricity at the cheapest price and with minimum pollutant emission levels. The electrical power generation from fossil fuel releases several contaminants into the air, and this becomes excrescent if the generating unit is fed by multiple fuel sources (MFSs). Inclusion of this issue in operational tasks is a welcome perspective. This paper aims to develop a multi-objective model comprising total fuel cost and pollutant emission.

The cost-effective and environmentally responsive power system operations in the presence of MFSs can be recognised as a multi-objective constrained optimisation problem with conflicting operational objectives. The complexity of the problem requires a suitable optimisation tool. Ant lion algorithm (ALA), the most recent nature-inspired algorithm, was used as the main optimisation tool because of its salient characteristics. The fuzzy decision-making mechanism has been integrated to determine the best compromised solution in the multi-objective framework.

This paper is the first to propose a more precise and practical operational model for studying a multi-fuel power dispatch scenario considering valve-point effects and CO₂ emission. The modern meta-heuristic algorithm ALA is applied for the first time to address the economic operation of thermal power systems with multiple fuel options.

Power companies aim to make profit by abiding by the norms of the regulatory board. To achieve economic benefits, the power system must be analysed using an accurate operational model. The proposed model integrates total fuel cost, valve-point loadings and CO₂ emission, which are prevailing power system operational objectives. The economic advantages of the operational model can be observed through economic deviation indices, and the performed analysis validates that the developed model corresponds to the actual power operation.

The realistic operational model is proposed by considering total fuel and pollutant emission, and the ALA is applied for the first time to address the proposed multi-objective problem. To validate the effectiveness of ALA, it is implemented in standard test systems with varying generating units (10-100) and the IEEE 30 bus system, and various kinds of power system operations are performed. Moreover, the comparison and performance analysis confirm that the current proposal is found enhanced in terms of solution quality.

The purpose of this paper is to focus on the cost-effective and environmentally sustainable operation of thermal power systems to allocate optimum active power generation resultant for a feasible solution in diverse load patterns using the grey wolf optimization (GWO) algorithm.

The economic dispatch problem is formulated as a bi-objective optimization subjected to several operational and practical constraints. A normalized price penalty factor approach is used to convert these objectives into a single one. The GWO algorithm is adopted as an optimization tool in which the exploration and exploitation process in search space is carried through encircling, hunting and attacking.

A linear interpolated price penalty model is developed based on simple analytical geometry equations that perfectly blend two non-commensurable objectives. The desired GWO algorithm reports a new optimum thermal generation schedule for a feasible solution for different operational strategies. These are better than the earlier reports regarding solution quality.

The proposed method seems to be a promising optimization tool for the utilities, thereby modifying their operating strategies to generate electricity at minimum energy cost and pollution levels. Thus, a strategic balance is derived among economic development, energy cost and environmental sustainability.

A single optimization tool is used in both quadratic and non-convex cost characteristics thermal modal. The GWO algorithm has discovered the best, cost-effective and environmentally sustainable generation dispatch.

This paper aims to address a pollution-routing problem with one general period of congestion (PRP-1GPC), where the start and finish times of this period can be set freely.

In this paper, three sets of decision variables are optimized, namely, travel speeds before and after congestion and departure times on given routes, aiming to minimize total cost including green-house gas emissions, fuel consumption and driver wages. A two-phase algorithm is introduced to solve this problem. First, an adaptive large neighborhood search heuristic is used where new removal and insertion operators are developed. Second, an analysis of optimal speed before congestion is presented, and a tailored speed-and-departure-time optimization algorithm considering congestion is proposed by obtaining the best node to be served first over the congested period.

The results show that the newly developed operator of congested service-time insertion with noise is generally used more than other insertion operators. Besides, compared to the baseline methods, the proposed algorithm equipped with the new operators provides better solutions in a short time both in PRP-1GPC instances and time-dependent pollution-routing problem instances.

This paper considers a more general situation of the pollution-routing problem that allows drivers to depart before the congestion. The PRP-1GPC is better solved by the proposed algorithm, which adds operators specifically designed from the new perspective of the traveling distance, traveling time and service time during the congestion period.