Multi-objective Harmony Search Algorithm Research Articles

A Multi-Objective Mixed-Model Assembly Line Sequencing Problem With Stochastic Operation Time

In today’s competitive market, those producers who can quickly adapt themselves todiverse demands of customers are successful. Therefore, in order to satisfy these demands of market, Mixed-model assembly line (MMAL) has an increasing growth in industry. A mixed-model assembly line (MMAL) is a type of production line in which varieties of products with common base characteristics are assembled on. This paper focuses on this type of production line in a stochastic environment with three objective functions: 1) total utility work cost, 2) total idle cost, and 3) total production rate variation cost that are simultaneously considered. In real life, especially in manual assembly lines, because of some inevitable human mistakes, breakdown of machines, lack of motivation in workers and the things alike, events are notdeterministic, sowe consideroperation time as a stochastic variable independently distributed with normal distributions; for dealing with it, chance constraint optimization is used to model the problem. At first, because of NP-hard nature of the problem, multi-objective harmony search (MOHS) algorithm is proposed to solve it. Then, for evaluating the performance of the proposed algorithm, it is compared with NSGA-II that is a powerful and famous algorithm in this area. At last, numerical examples for comparing these two algorithms with some comparing metrics are presented. The results have shown that MOHS algorithm has a good performance in our proposed model.

A Bi-Objective Airport Gate Scheduling with Controllable Processing Times Using Harmony Search and NSGA-II Algorithms

Optimizing gate scheduling at airports is an old, but also a broad problem. The main purpose of this problem is to find an assignment for the flights arriving at and departing from an airport, while satisfying a set of constraints.A closer look at the literature in this research line shows thatin almost all studies airport gate processing time has been considered as a fix parameter. In this research, however, we investigate a more realistic situation in which airport gate processing time is a controllable. It is also assumed that the possible compression/expansion processing time of a flight can be continuously controlled, i.e. it can be any number in a given interval.Doing sohas some positive effectswhich lead to increasing the total performance at airports’ terminals. Depending on the situation, different objectives become important.. Therefore, a model which simultaneously (1) minimize the total cost of tardiness, earliness, delay andthe compression as well as the expansion costs of job processing time, and (2) minimize passengers overcrowding on gate is presented. In this study, we first propose a mixed-integer programming model for the formulated problem. Due to complexity of problem, two multi-objective meta-heuristic algorithms, i.e. multi-objective harmony search algorithm (MOHSA) and non-dominated sorting genetic algorithm II (NSGA-II) are applied in order to generate Pareto solutions. For calibrating the parameter of the algorithms, Taguchi method is used and three optimal levels of the algorithm’s performance are selected. The algorithms are tested with real-life data from Mehrabad International Airport for nine medium size test problems. The experimental results show that NSGA-II has better convergence near the true Pareto-optimal front as compared to MOHSA; however, MOHSA finds a better spread in the entire Pareto-optimal region.Finally, it is possible to apply some practical constraints into the model and also test them with even large real-life problems instances.

Optimizing Reliability and Cost of system for Aggregate Production Planning in Supply Chain

In this paper, the researchers presented a multi-objective model for multi-product, multi-site aggregate production planning model in a supply chain. The goals are to minimize the total cost of the supply chain, including inventory costs, manufacturing costs, work force costs, hiring, and firing costs, and to maximize the minimum of suppliers’ reliability by considering probabilistic lead times tosimultaneously improve performance of the system. Since the problem is NP-Hard, a Pareto-based multi-objective harmony search algorithm is proposed. To demonstrate the performance of the presented algorithm, a non-dominated sorting genetic algorithm (NSGA-II) and a non-dominated ranking genetic algorithm (NRGA) are applied. The results demonstrate the robustness of the proposed algorithm to probe the Pareto solutions.

Solving a bi-objective unrelated parallel batch processing machines scheduling problem: A comparison study

Nowadays in competitive markets, production organizations are looking to increase their efficiency and optimize manufacturing operations. In addition, batch processor machines (BPMs) are faster and cheaper to carry out operations; thus the performance of manufacturing systems is increased. This paper studies a production scheduling problem on unrelated parallel BPMs with considering the release time and ready time for jobs as well as batch capacity constraints. In unrelated parallel BPMs, modern machines are used in a production line side by side with older machines that have different purchasing costs; so this factor is introduced as a novel objective to calculate the optimum cost for purchasing various machines due to the budget. Thus, a new bi-objective mathematical model is presented to minimize the makespan (i.e., Cmax), tardiness/earliness penalties and the purchasing cost of machines simultaneously. The presented model is first coded and solved by the ε-constraint‌ method. Because of the complexity of the NP-hard problem, exact methods are not able to optimally solve large-sized problems in a reasonable time. Therefore, we propose a multi-objective harmony search (MOHS) algorithm. the results are compared with the multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective ant colony optimization algorithm (MOACO). To tune their parameters, the Taguchi method is used. The results are compared by five metrics that show the effectiveness of the proposed MOHS algorithm compared with the MOPSO, NSGA-II and MOACO. At last, the sensitivity of the model is analyzed on new parameters and impacts of each parameter are illustrated on bi- objective functions.

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

ABSTRACTIn multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.

Application of the NSGA-II algorithm to a multi-period inventory-redundancy allocation problem in a series-parallel system

In this paper, we formulate a mixed-integer binary non-linear programming model to study a series-parallel multi-component multi-periodic inventory-redundancy allocation problem (IRAP). This IRAP is a novel redundancy allocation problem (RAP) because components (products) are purchased under an all unit discount (AUD) policy and then installed on a series-parallel system. The total budget available for purchasing the components, the storage space, the vehicle capacities, and the total weight of the system are limited. Moreover, a penalty function is used to penalize infeasible solutions, generated randomly. The overall goal is to find the optimal number of the components purchased for each subsystem so that the total costs including ordering cost, holding costs, and purchasing cost are minimized while the system reliability is maximized, simultaneously. A non-dominated sorting genetic algorithm-II (NSGA-II), a multi-objective particle swarm optimization (MOPSO), and a multi-objective harmony search (MOHS) algorithm are applied to obtain the optimal Pareto solutions. While no benchmark is available in the literature, some numerical examples are generated randomly to evaluate the results of NSGA-II on the proposed IRAP. The results are in favor of NSGA-II.

A Multi-Objective Harmony Search Algorithm for Sustainable Design of Floating Settlements

This paper is concerned with the application of computational intelligence techniques to the conceptual design and development of a large-scale floating settlement. The settlement in question is a design for the area of Urla, which is a rural touristic region located on the west coast of Turkey, near the metropolis of Izmir. The problem at hand includes both engineering and architectural aspects that need to be addressed in a comprehensive manner. We thus adapt the view as a multi-objective constrained real-parameter optimization problem. Specifically, we consider three objectives, which are conflicting. The first one aims at maximizing accessibility of urban functions such as housing and public spaces, as well as special functions, such as a marina for yachts and a yacht club. The second one aims at ensuring the wind protection of the general areas of the settlement, by adequately placing them in between neighboring land masses. The third one aims at maximizing visibility of the settlement from external observation points, so as to maximize the exposure of the settlement. To address this complex multi-objective optimization problem and identify lucrative alternative design solutions, a multi-objective harmony search algorithm (MOHS) is developed and applied in this paper. When compared to the Differential Evolution algorithm developed for the problem in the literature, we demonstrate that MOHS achieves competitive or slightly better performance in terms of hyper volume calculation, and gives promising results when the Pareto front approximation is examined.

A multi-objective multi-state series-parallel redundancy allocation model using tuned meta-heuristic algorithms

ABSTRACTIn this paper, we study a series-parallel multi-objective multi-state redundancy allocation problem (MSRAP) with known performance levels and corresponding state probabilities. The problem is comprised of multiple subsystems in series and each subsystem is comprised of multiple components in parallel. The system components have a range of performance level from complete working to complete failure. The subsystems contain homogenous redundant components and the component prices come under an all-unit discount policy if a unique brand (type) is chosen for purchasing all subsystem components. Each component is characterised by its cost, weight and availability. The goals are to find the optimal combination of the components in each subsystem that maximises system availability and minimises the total cost under a weight constraint. We propose a multi-objective harmony search (MOHS) algorithm, a non-dominated sorting genetic algorithm (NSGA-II), and a multi-objective genetic algorithm (MOGA) to solve this problem. In addition, the Taguchi method is utilised to tune the parameters in each algorithm. We use a number of numerical examples to demonstrate the applicability and exhibit the efficacy of the three algorithms. The results show that the MOHS outperforms the NSGA-II and MOGA with respect to all of the considered metrics.

Optimum islanded microgrid reconfiguration based on maximization of system loadability and minimization of power losses

Abstract Distribution grids are being transformed from passive to active networks. The active distribution systems are constructed through the implementation of microgrids (MGs) which are characterized as the “building blocks of smart grids”. This type of network eases the integration of distributed generation into power networks and makes it possible to define a new index for voltage stability, power flow development and a development reconfiguration method. In this paper, an improved indicator is proposed to estimate the voltage stability margin of a two-bus system based on both saddle node and limited induced bifurcations. A new concept named reduced islanded MG network (RIN), is used for generalization of the proposed index to n-bus islanded MGs and a development power flow algorithm by splitting these networks. The increasing loadability index of microgrids in the islanding mode is more important than the index of the grid-connected mode due to its operational limitations such as reactive power generation. In this process, islanded microgrid reconfiguration (IMGR) is proposed as an operational tool for improving loadability as well as decreasing power losses using an Adaptive Multi Objective Harmony Search Algorithm. The performance and effectiveness of the proposed method are demonstrated on 33- and 69-bus test systems.

Multi-objective multi-layer congested facility location-allocation problem optimization with Pareto-based meta-heuristics

Facility location-allocation problems arise in many practical settings from emergency services to telecommunication networks. We propose a multi-objective multi-layer facility location-allocation (MLFLA) model with congested facilities using classical queuing systems. The goal is to determine the optimal number of facilities and the service allocation at each layer. We consider three objective functions aiming at: (1) minimizing the sum of aggregate travel and waiting times; (2) minimizing the cost of establishing the facilities; and (3) minimizing the maximum idle probability of the facilities. The problem is formulated as a multi-objective non-linear integer mathematical programming model. To find and analyze the Pareto optimal solutions, we propose a Pareto-based multi-objective meta-heuristic approach based on the multi-objective vibration damping optimization (MOVDO) and the multi-objective harmony search algorithm (MOHSA). We demonstrate the effectiveness of the proposed model and exhibit the efficacy of the procedures and algorithms by comparing MOVDO and MOHSA with two well-known evolutionary algorithms, namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective simulated annealing (MOSA).

A self-adaptive multi-objective harmony search algorithm based on harmony memory variance

Although harmony search (HS) algorithm has shown many advantages in solving global optimization problems, its parameters need to be set by users according to experience and problem characteristics. This causes great difficulties for novice users. In order to overcome this difficulty, a self-adaptive multi-objective harmony search (SAMOHS) algorithm based on harmony memory variance is proposed in this paper. In the SAMOHS algorithm, a modified self-adaptive bandwidth is employed, moreover, the self-adaptive parameter setting based on variation of harmony memory variance is proposed for harmony memory considering rate (HMCR) and pitch adjusting rate (PAR). To solve multi-objective optimization problems (MOPs), the proposed SAMOHS uses non-dominated sorting and truncating procedure to update harmony memory (HM). To demonstrate the effectiveness of the SAMOHS, it is tested with many benchmark problems and applied to solve a practical engineering optimization problem. The experimental results show that the SAMOHS is competitive in convergence performance and diversity performance, compared with other multi-objective evolutionary algorithms (MOEAs). In the experiment, the impact of harmony memory size (HMS) on the performance of SAMOHS is also analyzed.

Optimal Design of Water Supply System using Multi-objective Harmony Search Algorithm

Optimal design of the water supply pipe network aims to minimize construction cost while satisfying the required hydraulic constraints such as the minimum and maximum pressures, and velocity. Since considering one single design factor (i.e., cost) is very vulnerable for including future conditions and cannot satisfy operator`s needs, various design factors should be considered. Hence, this study presents three kinds of design factors (i.e., minimizing construction cost, maximizing reliability, and surplus head) to perform multi-objective optimization design. Harmony Search (HS) Algorithm is used as an optimization technique. As well-known benchmark networks, Hanoi network and Gyeonggi-do P city real world network are used to verify the applicability of the proposed model. In addition, the proposed multi-objective model is also applied to a real water distribution networks and the optimization results were statistically analyzed. The results of the optimal design for the benchmark and real networks indicated much better performance compared to those of existing designs and the other approach (i.e., Genetic Algorithm) in terms of cost and reliability, cost, and surplus head. As a result, this study is expected to contribute for the efficient design of water distribution networks.

Novel Pareto-based meta-heuristics for solving multi-objective multi-item capacitated lot-sizing problems

Capacitated production lot-sizing problems (LSPs) are challenging problems to solve due to their combinatorial nature. We consider a multi-item capacitated LSP with setup times, safety stocks, and demand shortages plus lost sales and backorder considerations for various production methods (i.e., job shop, batch flow, or continuous flow among others). We use multi-objective mathematical programming to solve this problem with three conflicting objectives including: (i) minimizing the total production costs; (ii) leveling the production volume in different production periods; and (iii) producing a solution which is as close as possible to the just-in-time level. We also consider lost sales, backorders, safety stocks, storage space limitation, and capacity constraints. We propose two novel Pareto-based multi-objective meta-heuristic algorithms: multi-objective vibration damping optimization (MOVDO) and a multi-objective harmony search algorithm (MOHSA). We compare MOVDO and MOHSA with two well-known evolutionary algorithms called the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective simulated annealing (MOSA) to demonstrate the efficiency and effectiveness of the proposed methods.

Harmony Search Approach Based on Ricker Map for Multi-Objective Transformer Design Optimization

Harmony search (HS) algorithm is an evolutionary optimization algorithm developed in an analogy with an improvisation process where musicians try to polish their pitches to obtain a better harmony. In this paper, a modified HS (MHS) algorithm is adapted to multi-objective optimization using external archiving, ranking with crowding distance, and control parameters tuning based on Ricker map to solve a transformer design optimization (TDO) problem with two competing objectives. Simulations applied to a TDO problem demonstrate the effectiveness of the proposed multi-objective MHS algorithm. Results indicate that, compared with other multi-objective HS algorithm, in terms of output quality, the proposed MHS is able to find competitive solutions with a good tradeoff between the design objectives.

A multi-objective harmony search algorithm to optimize multi-server location–allocation problem in congested systems

A novel bi-objective multi-server location–allocation (LA) model is developed in this paper, in which the facilities are modeled as an M/M/m queuing system. Further, capacity and budget limitations are provided to make the LA problem more realistic. The two objective functions include (1) minimizing aggregate waiting times and (2) minimizing the maximum idle time of all facilities. Since the proposed model is NP-hard, a meta-heuristic algorithm called multi-objective harmony search algorithm (MOHA) is developed to solve it. In this algorithm, a new presentation scheme that satisfies most of the model constraints is proposed. Since there is no benchmark available in the literature to validate the results obtained, the performance of MOHA is statistically compared with the ones of two other common meta-heuristics called multi-objective genetic algorithm (MOGA) and multi-objective simulated annealing (MOSA). The parameters of all algorithms are first calibrated by means of the Taguchi method using a novel metric. The comparison results based on different problem sizes are in favor of MOHA.

Improved Multiobjective Harmony Search Algorithm with Application to Placement and Sizing of Distributed Generation

To solve the comprehensive multiobjective optimization problem, this study proposes an improved metaheuristic searching algorithm with combination of harmony search and the fast nondominated sorting approach. This is a kind of the novel intelligent optimization algorithm for multiobjective harmony search (MOHS). The detailed description and the algorithm formulating are discussed. Taking the optimal placement and sizing issue of distributed generation (DG) in distributed power system as one example, the solving procedure of the proposed method is given. Simulation result on modified IEEE 33-bus test system and comparison with NSGA-II algorithm has proved that the proposed MOHS can get promising results for engineering application.

Multiobjective Pump Scheduling Optimization Using Harmony Search Algorithm (HSA) and Polyphonic HSA

Harmony Search Algorithm (HSA) is a metaheuristic method that has attracted the scientific interest since its first presentation in 2001. It is a music inspired method, imitating the music creation process in order to find optimal solutions in complicated problems. HSA’s successful application on single – objective optimization problems has resulted to an increasing interest in the implementation of HSA towards multiobjective optimization. The authors have adjusted HSA in order to deal successfully with multi-criteria water management problems. This adjustment has resulted to the creation of Multiobjective – HSA (MO-HSA). In addition, they have designed the multiobjective variant Polyphonic-HSA (Poly-HSA), which is inspired by the independent development of different voices in music and borrows elements from Swarm Intelligence and the single-objective variant Global-Best HSA. In the first part of this paper, both methods are presented in detail. Moreover, the performance of the proposed Algorithms is evaluated using standard multiobjective test – functions. ZDT and DTLZ multiobjective tests have been chosen and indicators such as Hypervolume, C – metric and diversity metric – Δ have been used to measure the convergence to the optimal front and the diversity of the solutions obtained by the proposed methods. In the second part, MO-HSA and Poly-HSA have been introduced towards the optimization of a pump scheduling problem. The objectives considered are water supply, pumping cost, electric power peak demand and pump maintenance cost. Both methods converged to non-dominated fronts and provided excellent results which are presented in 3d figures, indicating that these methods can be effectively used in multiobjective water management problems.

Environmental/economic dispatch using multi-objective harmony search algorithm

Abstract This paper presents a new multi-objective harmony search (MOHS) algorithm for environmental/economic dispatch (EED) problem. The EED problem is formulated as a non linear and constrained optimization problem with competing and non-commensurable objectives. The two competing objectives, fuel cost and emission, were optimized simultaneously using the proposed MOHS algorithm. The MOHS algorithm uses a non dominated sorting and ranking procedure with dynamic crowding distance to develop and maintain a well distributed Pareto-optimal set. The proposed algorithm has been tested on the standard IEEE 30 bus and 118 bus systems. Simulation results are compared with the fast non dominated sorting genetic algorithm (NSGA-II) method. The results clearly show that the proposed method is able to produce a well distributed Pareto-optimal solutions than the NSGA-II method.

Multi-objective harmony search algorithm for optimal power flow problem

This paper proposes a multi-objective harmony search (MOHS) algorithm for optimal power flow (OPF) problem. OPF problem is formulated as a non-linear constrained multi-objective optimization problem where different objectives and various constraints have been considered into the formulation. Fast elitist non-dominated sorting and crowding distance have been used to find and manage the Pareto optimal front. Finally, a fuzzy based mechanism has been used to select a compromise solution from the Pareto set. The proposed MOHS algorithm has been tested on IEEE 30 bus system with different objectives. Simulation results are also compared with fast non-dominated sorting genetic algorithm (NSGA-II) method. It is clear from the comparison that the proposed method is able to generate true and well distributed Pareto optimal solutions for OPF problem.