Two storage inventory model in a mixed environment

A global optimization method for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the global topology optimization method in flow problems, this research works on two single-objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and the multi-objective optimization problem, which combines these two problems. The shape of flow channels is represented by the level set function, and the pressure loss and the temperature of the channels are evaluated by the Building-Cube Method (BCM), which is a Cartesian-mesh CFD approach. The proposed method resulted in an agreement with previous study in the single-objective problems in its topology, and achieved global exploration of non-dominated solutions in the multi-objective problem.

This chapter presents two methodologies for solving quadratic programming problems with multiple objectives under fuzzy stochastic environments. The right side parameters of the chance constraints of both the models are chosen as fuzzy random variables (FRVs) following different probability distributions. Like the previous chapters, chance constrained programming (CCP) methodology is employed to the fuzzy chance constraints to develop fuzzy programming model. In the first model, cut of fuzzy sets and fuzzy partial order relations are incorporated to the fuzzy programming model to develop an equivalent deterministic model. For the second model, defuzzification method of fuzzy numbers (FNs), which are presented in Chapter 2, are taken into consideration to generate equivalent quadratic programming model in a crisp environment. As the objective functions are quadratic in nature, it is easy to understand that the membership functions obtained through methodological development process are also quadratic in nature. To linearize the quadratic membership functions, linearization techniques are employed in this chapter. Finally, for achieving the maximum degree of each of the membership goals of the objectives, a fuzzy goal programming (FGP) approach is developed for the linearized membership goals and solved by minimizing under-deviational variables and satisfying modified system constraints in fuzzy stochastic decision-making environments. To illustrate the acceptability of the developed methodology presented in this chapter, some numerical examples are included.

Recent research activity has shown an interest in multi-objective optimization of dynamic processes, both for design and for real-time control; see Liu et al. (2018), Valderrama & Ruiz (2018), and de Sousa Santos et al. (2018) for some recent examples. Many of the methods proposed for these problems are based on converting the multi-objective problem into a single objective through the use of weights. Some works, for instance, Liu et al. (2018), however, consider the multi-objective problem directly but even in these cases, the problem is treated as a single objective problem with other objectives incorporated as constraints. All of these methods may not necessarily generate a satisfactory trade-off or Pareto optimal curve when this trade-off curve is non-convex. In this paper, we illustrate the use of a plant propagation nature inspired algorithm for the solution of design and control problems for dynamic processes. Being population based, it is able to identify an approximation to the Pareto optimal frontier simultaneously. A simple example from the literature is used to demonstrate how this problem can be formulated. The open source, freely available, Fresa application (http://www.ucl.ac.uk/~ucecesf/fresa.html),written in Julia, is used and the discussion concentrates on the problem formulation. The result shows how a multi-objective approach may lead to better insight into the design or control issues. The illustrated problem was originally formulated as a single objective problem. In doing so, information about alternative designs and how these could affect the performance of the system may be hidden. A multi-objective formulation allows the engineer to make better informed design decisions.

This paper proposes a modified particle swarm optimization algorithm for engineering optimization problems with constraints, in which the penalty function is employed to the traditional PSO algorithm, and at the same time adjusts the personal optimum and global optimum to make PSO being able to solve the non-linear programming problems, then the multi-objective problem can be converted into single objective problem. Moreover, the constraint term played its role in the process of generating particles, those pariticles which don't meet the constraint condition are eliminated. The actual engineering design optimization problem is tested and the results show that the multi-objective particle swarm optimization algorithm can be used to solve the multi-objective constrained optimization problem. Comparison with Genetic Algorithm confirms that the proposed algorithm can find better solutions, and converge quickly.

Parameters optimization of selected casting processes using teaching–learning-based optimization algorithm

In this paper, the tradeoff between spectrum efficiency (SE) and energy efficiency (EE) is investigated in terms of interference management and power allocation for heterogeneous networks (HetNets) with non-orthogonal multiple access (NOMA). The EE and SE tradeoff is modeled as a multi-objective problem (MOP) under the maximum power and quality of service (QoS) constraints, which is non-convex. The MOP is relaxed into a convex single objective problem (SOP) by adopting a weighted sum strategy with the hypograph transformation. The SOP is solved in two steps. In the first step, we propose a power allocation technique based on non-cooperative (NC) game for EE and SE in NOMA HetNets. In the proposed NC game, the macro base station (MBS) and the small BSs (SBSs) compete with an equal priority in order to optimize their transmit powers towards maximizing the weighted sum of SE and EE. In the second step, a closed-form formula is proposed to control the power allocated to users while taking into account both QoS constraint and successive interference cancellation (SIC) condition. From simulations, the proposed technique can, in some dedicated settings, considerably improve the tradeoff between EE and SE over conventional techniques.

An effective genetic algorithm approach to multiobjective resource allocation problems (MORAPs)

Classification is important task of data mining used to extract knowledge from huge volume of data. By nature, classification is multi-objective problem, as it required optimization of multiple objectives simultaneously like accuracy, sensitivity, squared error, precision etc. Traditionally, evolutionary algorithms were used to solve multi-objective classification problem by considering it as single-objective problem, but this approach gives single solution to problem. Therefore, multi-objective evolutionary algorithms are used to solve classification problem. In this paper, we have used Pareto approach to optimize neural network to solve classification problem. Non-dominated sorting genetic algorithm is used to simultaneously optimize accuracy and mean squared error objectives of neural network along with local search. As slow convergence to optimal solutions is major disadvantage of evolutionary algorithm. To speed up convergence to optimal solutions hybrid technique is adopted by augmenting evolutionary technique with local search algorithm. This proposed approach gives set of Pareto optimal solutions which represent different solutions for given classification problem.

Numerical comparisons of migration models for Multi-objective Biogeography-Based Optimization

Although various optimization methods for solving single-objective problems have been developed in the last few decades, these methods have lost their eligibility due to the fact that today’s engineering problems are toward multiple objective optimization problems, in real applications. For single-objective optimization problems, for example, in case of a minimization problem, this value is the decision vector giving the smallest objective that can be achieved within the specified constraints. Hence the minimum decision vector within all possible (feasible) solution vectors is the so-called optimal solution and/or optimal design. However, in multi-objective optimization problems, since a different objective value is generated against each decision vector, the superiority of the solutions over each other is determined by considering the trade-off among the objective values. Therefore, the solution of multi-objective optimization problems, unlike single-objective problems, is a set of vectors rather than a single decision vector. In multi-objective optimization problems, especially if there are intricate objectives, the computational cost of the problem increases. In other words, while synchronously trying to maximize one of the objectives and to minimize another one makes it difficult to find the global optimum design. One of the important techniques used in multi-objective optimization problems is Pareto optimality which enables to select the global optimum solution taking into account the trade-off among all objectives. In this context, using of derivative-based methods has decreased, but the use of metaheuristic methods has increased due to the rapid availability of global optimum solution. This is because the improvements in the field of optimization are progressing in proportion to technology and varying according to the needs. In this chapter, one of the recent metaheuristic optimization methods based on swarm intelligence that is so-called a Pareto-based bat algorithm inspired by the behavior of determining the direction and distance of an object using the echo of the sound called the echolocation of bats is used in order to obtain optimum solutions for multi-objective engineering design problems. In this regard, a four-bar planar truss, a real-sized welded steel beam as well as a multi-layer radar absorber are selected as multi-objective engineering design optimization problems. In case the obtained results (optimal designs) are examined, the potency and the reliability of the proposed multi-objective Pareto-based bat algorithm are demonstrated.

A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines

A new economic order quantity model for deteriorated items under the joint effects of stock dependent demand and inflation

Optimal production inventory policy for defective items with fuzzy time period

This paper addresses a rough multi-objective genetic algorithm (R-MOGA) to solve constrained multi-objective solid travelling salesman problems (CMOSTSPs) in rough, fuzzy rough and random rough environments. In the proposed R-MOGA, “3- and 5-level linguistic-based rough age oriented selection” and “adaptive crossover” are used along with a new generation-dependent mutation. In the present study, the age of each chromosome is termed as 3-level by young, middle and old and 5-level by very young, young, middle, old and very old. Here, we model the CMOSTSP with travelling costs and times as two objectives and a constraint for route risk/discomfort factors. The costs, times and risk/discomfort are rough, fuzzy rough and random rough in nature. To test the efficiency, combining same size single objective problems from standard TSPLIB, the results of such multi-objective problems are obtained by the proposed algorithm, simple MOGA and NSGA-II are compared. Moreover, a statistical analysis (analysis of variance) is carried out to show the supremacy of the proposed algorithm.

In this paper, a multi-objective faculty course allocation problem with result analysis and feedback analysis based on uncertain preferences mathematical model is presented. To deal with an uncertain model, three different ranking criteria are being used to develop: a) Expected value, b) Optimistic value, c) Dependent optimistic value criterion. These mathematical models are transformed into their corresponding deterministic forms using the basic concepts of uncertainty theory. The deterministic model of DOCM consists of fractional objectives which are converted into their linear form using Charnes and Cooper’s transformation. These deterministic formulations MOFCAP are converted into a single objective problem by using the fuzzy programming technique with linear and exponential membership functions. Further, the single objective problem for all the defined models is solved in the Lingo 18.0 software to derive the Pareto-optimal solution. The sensitivity of the models is also performed to examine the variation in the objective function due to the variation in parameters. Finally, a numerical example is given to exhibit the application and algorithm of the models.