Multi-objective Harmony Search Algorithm Research Articles

Optimal Sizing and Deployment of Renewable Energy Generators in Practical Transmission Network Using Grid-Oriented Multiobjective Harmony Search Algorithm for Loss Reduction and Voltage Profile Improvements

This paper presents grid-oriented multiobjective harmony search algorithm (GOMOHSA) to incorporate the multiple grid parameters for minimization of the active power loss, reactive power loss, and total voltage deviations (TVD) in a part of practical transmission network of Rajasthan Rajya Vidyut Prasaran Nigam Limited (RVPN) in southern parts of Rajasthan state of India. This is achieved by optimal deployment of optimally sized renewable energy (RE) generators using GOMOHSA. Performance indexes such as active power loss minimization index (APMLI), the reactive power loss minimization index (RPMLI), and the total voltage deviation improvement index (TVDII) are introduced to evaluate the health of the test network with different load scenarios. Performance of proposed GOMOHSA has been tested for five different operating scenarios of loads and RE generation. It is established that the proposed GOMOHSA finds the optimal deployment of optimally sized RE generators, and the investment cost of deployment of these RE generators can be recovered within a time period that is less than 5 years. Performance of GOMOHSA is superior compared to a conventional genetic algorithm (GA) in terms of performance indexes, RE generator capacity, payback period, and parameter sensitivity. Study is performed using MATLAB software for loading scenario of base year 2021 and projected year 2031.

Collaborative multidepot electric vehicle routing problem with time windows and shared charging stations

Logistics distribution using electric vehicles (EVs) is gradually becoming popular in urban logistics networks with the promise of carbon peak and carbon neutrality. A collaborative mechanism among multiple depots can effectively increase the efficiency and sustainability of a logistics network. Sharing charging stations (CSs) is presented as a critical strategy to improve the efficiency of logistics networks and facilitate collaboration further. Solving a collaborative multidepot EV routing problem with time windows and shared charging stations (CMEVRPTW-SCS) involves centralized transportation services among multiple depots, coordinated delivery services among multiple depots and the charging needs of EVs. A bi-objective nonlinear programming model for CMEVRPTW-SCS is formulated to minimize the total operating cost and number of EVs, wherein the operating cost contains transportation costs among depots and vehicle routing costs in each depot. Gaussian mixture clustering algorithm is developed to cluster customers and assign them to depots probabilistically to reduce the computational complexity, and an improved multi-objective genetic algorithm with tabu search (IMOGA-TS) is designed to optimize the EV routes and charging locations in CMEVRPTW-SCS. With the combination of local and global searches and the improvement of solutions at each iteration by TS, the proposed hybrid algorithm can significantly accelerate the efficient exploration of optimal solutions. The comparative results of the IMOGA-TS with multi-objective genetic algorithm, non-dominated sorting genetic algorithm-II and multi-objective harmony search algorithm show the superiority of the proposed algorithm in solving CMEVRPTW-SCS. Then, a Shapley value model based on game theoretical methods is proposed to find the best profit allocation scheme. A real-world case study of CMEVRPTW-SCS in Chongqing City, China is conducted, and three scenarios of various collaborative alliances and 11 schemes with and without shared CSs are further discussed. The experimental results show that the proposed methods are of practical significance in reducing operating costs, improving transportation efficiency, and achieving sustainable operation in EV-based logistics distribution networks.

A clustering-based extended genetic algorithm for the multidepot vehicle routing problem with time windows and three-dimensional loading constraints

Since the multidepot vehicle routing problem with time windows and three-dimensional loading constraints (MDVRPTW-TDLC) is a multiconstraint and combinatorial optimization problem, this study proposes a resource sharing scheme on the basis of customer clustering to achieve a balance of spatial resource spatial distributions, thereby reducing the operating costs in a collaborative multidepot logistics network. Moreover, this study proposes a vehicle compartment partition strategy based on cargo characteristics such as type and sizes to increase vehicle loading rates, after which the proposed MDVRPTW-TDLC is formulated as a bi-objective mixed-integer programming model to minimize the total operating costs while maximizing the average loading rate of vehicles. Subsequently, a two-stage hybrid algorithm combining a three-dimensional (3D) k-harmonic means clustering algorithm and extended nondominated sorting genetic algorithm-II (ENSGA-II) is developed to find the Pareto optimal solutions and solve the MDVRPTW-TDLC optimization model, followed by an introduction of the 3D k-harmonic means clustering algorithm to cluster customers, thereby reducing computational complexity. The proposed ENSGA-II, integrating the improved Clarke–Wright savings algorithm and NSGA-II is then used to obtain the final optimal solutions, followed by the application of a selective exchange mechanism between the clustering algorithm and ENSGA-II to enhance the global and local optimization capability, enabling fast and efficient computation of optimal solutions. Based on our investigations revealed through an algorithm comparison using the multiobjective harmony search algorithm, multiobjective evolution algorithm, multiobjective particle swarm optimization, monarch butterfly optimization, Runge Kutta optimizer, and Harris hawks optimization, ENSGA-II demonstrates better performance in reaching high-quality objective function values. Finally, a real-world case study of Chongqing City, China is employed to verify the efficiency of the proposed model and optimization algorithm, after which a comparison of the optimization results among different vehicle compartment partition strategies demonstrates the efficiency of the proposed method. We also discuss 16 scenarios with and without the vehicle compartment partition strategy with computational results showing an improved vehicle loading rate and reduced logistics operating costs with the adopted vehicle compartment partition strategy. Therefore, our results confirm that the proposed MDVRPTW-TDLC can facilitate the sustainable development of logistics operations, and providing decision support for constructing intelligent logistics systems smart cities.

Design of low-carbon and cost-efficient concrete frame buildings: a hybrid optimization approach based on harmony search

ABSTRACT The development of sustainable building structures has been a crucial measure for carbon reduction. With consideration of both carbon emissions and costs, the sustainable design of building structures is complicated and time consuming for designers. To simplify the process of sustainable design optimization, the present study proposes a multi-objective harmony search algorithm for the design of concrete frame buildings considering low-carbon and cost-efficient requirements. This hybrid method combines structural analysis with local component optimization. Process-based life cycle assessment was used to identify carbon-intensive and high-cost structural members, and these members were optimized using discrete design variables and complicated constraints. Furthermore, a case study was conducted on a four-story frame building, in which the embodied emissions and costs were estimated as 1270.91 tCO2e and 0.67 million USD in the initial design scheme. Beams were identified as the optimization target for this building, and a set of Pareto-optimal solutions was obtained, indicating potential emission and cost reductions of 17.9% and 12.3%, respectively, compared with the initial designs. This study provides an easy and practical approach for the sustainable design of concrete frame buildings and enables designers to better understand building structural optimization from an economic and low-carbon perspective.

Adaptive binary multi-objective harmony search algorithm for channel selection and cross-subject generalization in motor imagery-based BCI

Objective. Multi-channel electroencephalogram data containing redundant information and noise may result in low classification accuracy and high computational complexity, which limits the practicality of motor imagery (MI)-based brain-computer interface (BCI) systems. Therefore, channel selection can improve BCI performance and contribute to user convenience. Additionally, cross-subject generalization is a key topic in the channel selection of MI-based BCI. Approach. In this study, an adaptive binary multi-objective harmony search (ABMOHS) algorithm is proposed to select the optimal set of channels. Furthermore, a new adaptive cross-subject generalization model (ACGM) is proposed. Three public MI datasets were used to validate the effectiveness of the proposed method. Main results. The Wilcoxon signed-rank test was performed on the test accuracies, and the results indicated that the ABMOHS method significantly outperformed all channels (p< 0.001), the C3–Cz–C4 channels (p< 0.001), and 20 channels (p< 0.001) in the sensorimotor cortex. The ABMOHS algorithm based on Fisher’s linear discriminant analysis (FLDA) and support vector machine (SVM) classifiers greatly reduces the number of selected channels, especially for larger channel sizes (Dataset 2), and obtains a comparative classification performance. Although there was no significant difference in test classification performance between ABMOHS and non-dominated sorting genetic algorithm II (NSGA-II) when FLDA and SVM were used, ABMOHS required less computational time than NSGA-II. Furthermore, the number of channels obtained by ABMOHS algorithm were significantly smaller than those obtained by common spatial pattern-Rank and correlation-based channel selection algorithm. Additionally, the generalization of ACGM to untrained subjects shows that the mean test classification accuracy of ACGM created by a small sample of trained subjects is significantly better than that of Special-16 and Special-32. Significance. The proposed method can reduce the calibration time in the training phase and improve the practicability of MI-BCI.

A Novel Multi-Objective Harmony Search Algorithm with Pitch Adjustment by Genotype

In this work, a new version of the Harmony Search algorithm for solving multi-objective optimization problems is proposed, MOHSg, with pitch adjustment using genotype. The main contribution consists of adjusting the pitch using the crowding distance by genotype; that is, the distancing in the search space. This adjustment automatically regulates the exploration–exploitation balance of the algorithm, based on the distribution of the harmonies in the search space during the formation of Pareto fronts. Therefore, MOHSg only requires the presetting of the harmony memory accepting rate and pitch adjustment rate for its operation, avoiding the use of a static bandwidth or dynamic parameters. MOHSg was tested through the execution of diverse test functions, and it was able to produce results similar or better than those generated by algorithms that constitute search variants of harmonies, representative of the state-of-the-art in multi-objective optimization with HS.

A multi-objective formulation of maximal covering location problem with customers’ preferences: Exploring Pareto optimality-based solutions

The maximal covering location problem (MCLP) is a well-known combinatorial optimization problem with several applications in emergency and military services as well as in public services. Traditionally, MCLP is a single objective problem where the objective is to maximize the sum of the demands of customers which are served by a fixed number of open facilities. In this article, a multi-objective MCLP is proposed where each customer has a preference for each facility. The multi-objective MCLP with customers’ preferences (MOMCLPCP) deals with the opening of a fixed number of facilities from a given set of potential facility locations and then customers are assigned to these opened facilities such that both (i) the sum of the demands of customers and (ii) the sum of the preferences of the customers covered by these opened facilities are maximized. A Pareto-based multi-objective harmony search algorithm (MOHSA), which utilizes a harmony refinement strategy for faster convergence, is proposed to solve MOMCLPCP. The proposed MOHSA is terminated based on the stabilization of the density of non-dominated solutions. For experimental purposes, 82 new test instances of MOMCLPCP are generated from the existing single objective MCLP benchmark data sets. The performance of the proposed MOHSA is compared with the well-known non-dominated sorting genetic algorithm II (NSGA-II), and it has been observed that the proposed MOHSA always outperforms NSGA-II in terms of computation time. Moreover, statistical tests show that the objective values obtained from both algorithms are comparable.

A Multi-Objective Reconfiguration Scheme for Reliability and Energy Usage Enhancement of Distribution Systems in the Presence of Wind Turbines Using the MOHSA Optimization Algorithm

The stochastic nature of the active power generated by wind turbines (WTs) has posed new challenges to the reliability assessment, load flow analysis, and reconfiguration process of distribution systems penetrated with WTs. In this paper, a new optimization approach has been presented to find the best configuration of the distribution system along with optimal locations of WTs. This is aimed at maximizing the reliability of the system, while energy losses are minimized. To this end, based on the graph theory and the system topology, a simple technique is proposed for finding minimal cut sets that could be used for calculating reliability indices. Furthermore, the multiple flow directions created in the presence of WTs cause difficulties in calculating reliability indices and in performing load flow analysis. Accordingly, a new concept called the independent reliability zone is introduced to overcome these problems. In this paper, the multi-objective harmony search algorithm, due to its suitability for multi-objective problems, is employed as a solution for solving the proposed optimization problem. The effect of the proposed approach has been evaluated on both test and real systems. The results show that using the proposed approach, a more practical solution is achieved for low-cost and reliable 24-hour planning of the system in the presence of uncertainties in DGs.

Harmony Search-Based Approach for Multi-Objective Software Architecture Reconstruction

The success of any software system highly depends on the quality of architectural design. It has been observed that over time, the quality of software architectural design gets degraded. The software system with poor architecture design is difficult to understand and maintain. To improve the architecture of a software system, multiple design goals or objectives (often conflicting) need to be optimized simultaneously. To address such types of multi-objective optimization problems a variety of metaheuristic-oriented computational intelligence algorithms have been proposed. In existing approaches, harmony search (HS) algorithm has been demonstrated as an effective approach for numerous types of complex optimization problems. Despite the successful application of the HS algorithm on different non-software engineering optimization problems, it gained little attention in the direction of architecture reconstruction problem. In this study, we customize the original HS algorithm and propose a multi-objective harmony search algorithm for software architecture reconstruction (MoHS-SAR). To demonstrate the effectiveness of the MoHS-SAR, it has been tested on seven object-oriented software projects and compared with the existing related multi-objective evolutionary algorithms in terms of different software architecture quality metrics and metaheuristic performance criteria. The experimental results show that the MoHS-SAR performs better compared to the other related multi-objective evolutionary algorithms.

A simulation–optimization model for solving flexible flow shop scheduling problems with rework and transportation

We propose an enhanced multi-objective harmony search (EMOHS) algorithm and a Gaussian mutation to solve the flexible flow shop scheduling problems with sequence-based setup time, transportation time, and probable rework. A constructive heuristic is used to generate the initial solution, and clustering is applied to improve the solution. The proposed algorithm uses response surface methodology to minimize both maximum completion time and mean tardiness, concurrently. We evaluate the efficacy of the proposed algorithm using computational experiments based on five measures of diversity metric, simultaneous rate of achievement for two objectives, mean ideal distance, quality metric, and coverage. The experimental results demonstrate the effectiveness of the proposed EMOHS compared with the existing algorithms for solving multi-objective problems.

Optimal expansion planning of distribution system using grid-based multi-objective harmony search algorithm

To meet the future power demand, distribution systems (DSs) need to be optimally planned. In this paper, an optimal expansion planning approach of DS is suggested. The capability of the existing DS is evaluated and load forecasting for next ten years is performed. Further, the load flow analysis by using backward-forward sweep algorithm is performed. Results show that existing networks would not be able to meet the future demand and due to this, voltage drop (VD) and power losses might be increased. Therefore, DS expansion planning is carried out considering future demand growth and distributed generation (DG) placement using grid dependent multi-objective harmony search algorithm (GrMHSA). The implementation of GrMHSA optimization technique reduces the total losses as well as VD for the targeted year. A practical Debre Markos (D/M) distribution network of Ethiopia is used for illustrating the superiority of the proposed technique and verifies its effectiveness.

A New Bi-objective Mathematical Model to Optimize Reliability and Cost of Aggregate Production Planning System in a Paper and Wood Company

In this research, a bi-objective model is developed to deal with a supply chain including multiple suppliers, multiple manufacturers, and multiple customers, addressing a multi-site, multi-period, multi-product aggregate production planning (APP) problem. This bi-objective model aims to minimize the total cost of supply chain including inventory costs, manufacturing costs, work force costs, hiring, and firing costs, and maximize the minimum of suppliers' and producers' reliability by the considering probabilistic lead times, to improve the performance of the system and achieve a more reliable production plan. To solve the model in small sizes, a e-constraint method is used. A numerical example utilizing the real data from a paper and wood industry is designed and the model performance is assessed. With regard to the fact that the proposed bi-objective model is NP-Hard, for large-scale problems one multi-objective harmony search algorithm is used and its results are compared with the NSGA-II algorithm. The results demonstrate the capability and efficiency of the proposed algorithm in finding Pareto solutions.

HS-MMGKG: A Fast Multi-objective Harmony Search Algorithm for Two-locus Model Detection in GWAS

Background:: Genome-Wide Association Study (GWAS) plays a very important role in identifying the causes of a disease. Because most of the existing methods for genetic-interaction detection in GWAS are designed for a single-correlation model, their performances vary considerably for different disease models. These methods usually have high computation cost and low accuracy. Method:: We present a new multi-objective heuristic optimization methodology named HSMMGKG for detecting genetic interactions. In HS-MMGKG, we use harmony search with five objective functions to improve the efficiency and accuracy. A new strategy based on p-value and MDR is adopted to generate more reasonable results. The Boolean representation in BOOST is modified to calculate the five functions rapidly. These strategies take less time complexity and have higher accuracy while detecting the potential models. Results:: We compared HS-MMGKG with CSE, MACOED and FHSA-SED using 26 simulated datasets. The experimental results demonstrate that our method outperforms others in accuracy and computation time. Our method has identified many two-locus SNP combinations that are associated with seven diseases in WTCCC dataset. Some of the SNPs have direct evidence in CTD database. The results may be helpful to further explain the pathogenesis. Conclusion:: It is anticipated that our proposed algorithm could be used in GWAS which is helpful in understanding disease mechanism, diagnosis and prognosis.

Multiobjective optimization for recognition of isolated handwritten Indic scripts

Identifying the most informative regions of character images is important for a robust handwritten character recognition system. If it is to be done in an efficient and cost-effective way, this task becomes more challenging. In this work, we have proposed a new multi-objective optimization framework to identify those local regions cost-effective way. We define three objective functions to be taken into account for this purpose: 1) recognition accuracy. 2) average recognition time per character image, and 3) redundancy of the local regions. More specifically, in this work, a modified opposition-based multiobjective Harmony Search algorithm has been proposed to select the local regions from handwritten character images based on their rankings in a three-dimensional pareto-front. Our work has been evaluated on four datasets - 1) isolated handwritten Bangla Basic characters, 2) isolated handwritten Bangla numerals, 3) English numerals, and 4) isolated handwritten Devanagari characters. The results show a significant decrease in the recognition costs and redundancy and an increase in the recognition accuracy obtained on all the datasets. Thus, our system provides a cost-effective approach towards isolated handwritten character recognition.

Multi-objective Harmony Search Algorithm for Dynamic Optimal Power Flow with Demand Side Management

In modern power systems, efficient methods like demand side management (DSM) are needed for handling the peak load management problem. An intelligent DSM approach not only gives advantages to utilities but also provides indirect benefits to generating companies. This article introduces a combined model of multi-objective dynamic optimal power flow (MODOPF) and a game theory-based DSM technique. In this article, a single utility company and multiple residential energy consumers are considered for the game theory-based DSM technique. Here, the day ahead load shifting DSM technique is implemented with the help of a day-ahead pricing strategy and an energy consumption game. The total generation cost and transmission losses are considered as the main objectives in the proposed MODOPF problem. These two objectives were optimized individually and simultaneously using harmony search (HS) algorithm with different DSM participation levels for the investigation of generation side benefits. The proposed combined model was tested on two different test systems such as IEEE 30 bus and 118 bus. From the simulation results, it is clear that the combined model consisting of MODOPF and DSM is able to achieve a better economic and secure operation when compared to MODOPF alone.

Development of Multi-Objective Optimal Redundant Design Approach for Multiple Pipe Failure in Water Distribution System

This study proposes a multi-objective optimal design approach for water distribution systems, considering mechanical system redundancy under multiple pipe failure. Mechanical redundancy is applied to the system’s hydraulic ability, based on the pressure deficit between the pressure requirements under abnormal conditions. The developed design approach shows the relationships between multiple pipe failure states and system redundancy, for different numbers of pipe-failure conditions (e.g., first, second, third, …, tenth). Furthermore, to consider extreme demand modeling, the threshold of the demand quantity is investigated simultaneously with multiple pipe failure modeling. The design performance is evaluated using the mechanical redundancy deficit under extreme demand conditions. To verify the proposed design approach, an expanded version of the well-known benchmark network is used, configured as an ideal grid-shape, and the multi-objective harmony search algorithm is used as the optimal design approach, considering construction cost and system mechanical redundancy. This optimal design technique could be used to propose a standard for pipe failure, based on factors such as the number of broken pipes, during failure condition analysis for redundancy-based designs of water distribution systems.

Optimal Microgrid Topology Design and Siting of Distributed Generation Sources Using a Multi-Objective Substrate Layer Coral Reefs Optimization Algorithm

In this work, a problem of optimal placement of renewable generation and topology design for a Microgrid (MG) is tackled. The problem consists of determining the MG nodes where renewable energy generators must be optimally located and also the optimization of the MG topology design, i.e., deciding which nodes should be connected and deciding the lines’ optimal cross-sectional areas (CSA). For this purpose, a multi-objective optimization with two conflicting objectives has been used, utilizing the cost of the lines, C, higher as the lines’ CSA increases, and the MG energy losses, E, lower as the lines’ CSA increases. To characterize generators and loads connected to the nodes, on-site monitored annual energy generation and consumption profiles have been considered. Optimization has been carried out by using a novel multi-objective algorithm, the Multi-objective Substrate Layers Coral Reefs Optimization algorithm (Mo-SL-CRO). The performance of the proposed approach has been tested in a realistic simulation of a MG with 12 nodes, considering photovoltaic generators and micro-wind turbines as renewable energy generators, as well as the consumption loads from different commercial and industrial sites. We show that the proposed Mo-SL-CRO is able to solve the problem providing good solutions, better than other well-known multi-objective optimization techniques, such as NSGA-II or multi-objective Harmony Search algorithm.

A Multi-Objective Integer Melody Search Algorithm

ABSTRACTThere are a number of algorithms for the solution of continuous optimization problems. However, many practical design optimization problems use integer design variables instead of continuous. These types of problems cannot be handled by using continuous design variables-based algorithms. In this paper, we present a multi-objective integer melody search optimization algorithm (MO-IMS) for solving multi-objective integer optimization problems, which take design variables as integers. The proposed algorithm is a modified version of single-objective melody search (MS) algorithm, which is an innovative optimization algorithm, inspired by basic concepts applied in harmony search (HS) algorithm. Results show that MO-IMS has better performance in solving multi-objective integer problems than the existing multi-objective integer harmony search algorithm (MO-IHS). Performance of proposed algorithm is evaluated by using various performance metrics on test functions. The simulation results show that the proposed MO-IMS can be a better technique for solving multi-objective problems having integer decision variables.

Modeling and solving a bi-objective joint replenishment-location problem under incremental discount: MOHSA and NSGA-II

In this paper, the joint replenishment-location problem of some distribution centers (DCs) with a centralized decision maker who is responsible for ordering and dispatching shipments of a single product is modeled. The warehouse spaces of the DCs are limited and the product is sold under an incremental discount policy. The model seeks to minimize the total cost of the supply chain under the joint replenishment policy along with minimizing the cost of locating the DCs in potential sites as the first objective. The second objective is to minimize the warehouse space of all DCs using the revisable approach. As the proposed model is a bi-objective integer non-linear optimization problem (NP-Hard) and cannot be solved by an exact method in a reasonable computational time, a multi-objective harmony search algorithm is developed to solve it. Since there is no benchmark available in the literature, the non-dominated sorting genetic algorithm II is utilized as well to validate the results obtained. As the performance of a meta-heuristic algorithm is largely influenced by the choice of its parameters, the response surface methodology is employed to tune the parameters. Several numerical illustrations are provided at the end to not only demonstrate the application of the proposed methodology, but also to analyze and compare the performances of the two solution algorithms in terms of several multi-objective measures.

Optimal planning of active distribution networks with hybrid distributed energy resources using grid-based multi-objective harmony search algorithm

This paper presents a new Grid-based Multi-objective Harmony Search Algorithm (GrMHS) for optimal planning and operation of Distributed Generation (DG) in an active distribution network. Both dispatchable and non-dispatchable (renewable) distributed generations are considered in this paper. The DGs location, size and power factor of diesel generator are optimized using the proposed algorithm in three objective case to minimize three conflicting objectives such as: energy loss, voltage deviation and cost of DG integration in the distribution network. The locations of the renewable sources are also optimized. As the objectives are conflicting with each other, pareto based GrMHS algorithm is proposed where it employs non dominated sorting for ranking of solutions and environmental selection for the secondary selection of population to the next iteration. The environmental selection establishes grid setting in the objective plane and three selection criterions are proposed. All uncertainties associated with load, wind speed and solar irradiance are included in the planning model. The choice of optimisation algorithm (Harmony Search) is ascertained with comparison of results for loss reduction and the effectiveness of the proposed algorithm is demonstrated with IEEE 33-bus, IEEE 69-bus and Indian 85-bus distribution networks with two objectives. The three objective case is presented with relevant analysis for IEEE 33-bus and Indian 85-bus distribution systems.