Although for many years scientists and engineers have been faced with the problem of optimizing discrete functions, no general analytical method has been proposed for multidimensional discrete optimization. All the methods that have already been reported in the literature are algorithmic. In one dimensional discrete optimization, no general analytical method has yet been proposed to find all the local minima and maxima of multimodal one dimensional discrete functions either. In this paper, for the first time, a general analytical method has been proposed for solving multidimensional and multimodal discrete optimization problems. Here, first we will introduce the method and present its mathematical proof, and then confirm its validity through some examples and computer simulations.

Here the advantages of employing a biorefinery approach in conjunction with optimization techniques were utilized to attain high overall process efficiency. Initially, an alkaline pH-shift process assisted by ultrasonic and its subsequent optimization were employed to maximize the extraction yield and whiteness index of muscle proteins isolated from lanternfish (B. pterotum). The optimal strategy was determined as follows: 6 mL g-1, pH1 (solubilization) 11.5, 310 W, and pH2 (precipitation) 5.8 with desirability of 0.84. Collagen hydrolysate was obtained from the connective tissue-containing sediment residue emerging during pH-shift process. The optimal isolated protein (OIP) was utilized to produce heat-set gels in combination with collagen hydrolysate. Breaking force and deformation of the OIP gel were measured at 123 (g) and 10.12 (mm) respectively. Collagen hydrolysate made breaking force (up to 2% w/w) and deformation (up to 10% w/w) improved and had positive effects on color characteristics (especially whiteness index) as well as water holding capacity. Hence, it can be concluded that the integration of a novel extraction technique such as ultrasonic with pH-shift process followed by optimization, as well as concurrent utilization of muscle and connective tissue proteins through a biorefinery approach; provides a significant advancement towards scaling up the extraction process.

1. Introduction: One of the main concerns in optimization methods is reduction the number of function evaluation which is mentioned in many studies like (Gholizadeh et al, 2018). The present study focuses on a method and series of actions designed to achieve the answer with the aim of minimization the total number of analysis,and so the time,needed for global and local search. Although the suggested elite particles method (EPM) can be used for any population based optimization method, but here it is applied to one of the fundamental and widely developed metaheuristic algorithms,namely particle swarm optimization (Eberhart et al, 1995) to handle the truss structures optimization with discrete design variables. As the original version of the assumed method suffers from the slow convergence rate,specially when dealing with the discrete optimization problems,the elite particles modification algorithm,which can be used in almost all population based metaheuristic optimization methods,will be implemented for that method. Here the elite particles method is attached with the particle swarm optimization method and the gained metaheuristic algorithm is named modified particle swarm optimization (MPSO). MPSO utilizes two computational strategies named ‘, Regeneration’,and ‘, Mutation’, . . .

محاسبه وزن مواد بار کوره های ذوب، با موازنه جرم عناصر آلیاژی مواد ورودی و خروجی انجام می شود. اما فرایند ذوب، پیچیدگی هایی دارد، که اغلب در محاسبات نادیده گرفته می شود، و باعث عدم اطمینان در وزن مواد بار، اصلاح چندباره ذوب، تأخیر در تخلیه، افزایش هزینه و کاهش کیفیت مذاب می شود. هدف پژوهش حاضر، توسعه مدلی است، که نه تنها وزن مواد اولیه برای ترکیب شیمیایی ذوب هدف را محاسبه و بهینه سازی کند، بلکه هدررفت ناهمگن عناصر آلیاژی، ناخالصی های غیرفلزی مواد بار، و اصلاح ذوب اولیه در کوره را نیز در نظر بگیرد. مقاله حاضر، فرمولاسیون یک مدل محاسبه بار کوره ی ذوب آلیاژ را ارایه می کند، که بر اساس موازنه جرم غیرخطی و بهینه سازی استاندارد توسعه یافته و همراه با یک الگوریتم حلقه ی تکرار برای حل عددی، ویژگی های موردنظر را برای ذوب تمام آلیاژها در برمی گیرد. برای ارزیابی مدل، یک مساله ذوب آلیاژ برنج با 7 عنصر آلیاژی و 8 نوع مواد بار در مقیاس صنعتی طرح و بررسی گردید. با حل مساله به کمک مدل توسعه یافته، کسر وزنی مواد اولیه، وزن و ترکیب شیمیایی ذوب اصلاح شده و کمترین هزینه مواد محاسبه گردید. مدل پیش بینی کرد که وزن کل مواد ورودی 9909 kg (همراه با ذوب اولیه)، هدررفت مواد معادل 262 kg، وزن نهایی مذاب اصلاح شده 9646 kg و بازدهی ذوب 97.3% باشد. تحلیل بهینه بودن جواب، تایید کرد که کمترین هزینه مواد به دست آمده است. مدل استاندارد غیرخطی، ابزاری سریع برای بهینه سازی هزینه و محاسبه بار کوره است که پتانسیل هایی برای کاهش هزینه و تسهیل اتوماسیون صنعتی فرایند ذوب ایجاد می کند.

An efficient two-phase method for discrete optimization of pipe networks is presented in this paper. The method consists of two stages. In the first, the problem of pipe network optimization is formulated as an unconstrained optimization problem using an iterative penalty method, which is then solved by an all purpose optimization tool, DOT, to get the continuous solution for the pipe diameters. In the second stage, a second optimization tool, DOC, incorporating a branch and bound method is used to get the discrete solution starting from the already available continuous solution as a good initial guess. Two different strategies are used at the discrete solution stage. In the first, named as local here, the search space is restricted to the upper and lower diameter limits of the optimal continuous solution, while in the second strategy, so called as global, this restriction is relaxed. The method is shown to be capable of producing results comparable to the existing sophisticated algorithms with much less computational effort. The method is used to find the optimal solution to some of the benchmark pipe networks and the results are presented. The results obtained for the networks consisting of pipes are encouraging.

Nowadays, optimization is becoming one of the most important techniques in engineering and industry to provide competing products in design and manufacturing. Therefore, it is a necessity to search for optimum designs with productibility. In aerospace industry reducing weight and improving reliability of the products are major concerns. As regards the gearbox is one of the most important parts in the helicopter propulsion system, these objects should be more considered. However, most of the existing designs consider only one object, hence, it is vital to implement optimization techniques to include different objectives to improve the existing designs and provide optimum products. In this paper, optimum design parameters including module and face width of gears for the main gearbox of Sikorsky ASH-3D helicopter have been determined (modified) using single and multi-objective mixed discrete- continuous optimization method to minimize weight of the gearbox, increase the safety factor and reduce the difference between safety factors of different gears. The results show that the weight of the gears can be reduced by 27.24% comparing with the existing gearbox. The results of the multiobjective optimization have also been presented as Pareto front diagram wich can be used by the manufacturers to satisfy the prefered requiments.

In this paper application of binary coded Genetic Algorithm (GA) to continuous optimization problems is described and then it is used for plate optimization. Since binary coded GA is a discrete optimization algorithm, its application to continuous problems requires a process of search space discretization. In this paper a new method of discretization is developed in which discretization parameters are automatically refined using a stochastic process. The proposed method is capable of several well known function optimization problems are considered and results are presented. A sensitivity analysis was also carried out to assess the effect of parameters on the final results. The proposed method is then used for optimum design of a two dimensional plain stress problem and the results are presented and compared with the results of previous methods.

Facility Layout Problem (FLP) is an important issue in plant design, which directly affects production costs as well as safety concerns. Hierarchical and integrated approaches are two main methods used for the formulation of FLP. In the hierarchical approach, FLP is solved after the completion of the process design and scheduling, while the integrated approach treats FLP simultaneously with other phases. This paper presents a new approach based on the candidate groups for interactive functions; incorporating the advantages of the previous approaches.In the new approach, the design phases prior to FLP results in a set of models introducing by the engineering team in advance. Next, the models are solved such that instead of individual designs, a set of suggested structures are generated. These structures are then fed into the FLP as input data and solved by mixed integer programming technique. Some characteristics of the models are: presence of the hub stations, different and variable dimensions for each station, possibility of rotation for the stations and incorporating safety distances. Finally, test problems are solved and results are discussed. It should be noted that if a candidate group entails a different production flow then a different optimum solution might be obtained.

هدف از این تحقیق، تولید کامپوزیت زمینه آلیاژهای مس تقویت شده با ذرات الماس میکرونی و بررسی خواص مکانیکی این کامپوزیت است. از مهم ترین مسائل ساخت این نوع کامپوزیت ، بهینه سازی استحکام ذرات الماس در زمینه فلزی و خواص سایشی مد نظر این نوع کامپوزیت است. پودرهای کامپوزیتی با استفاده از آسیابکاری پرانرژی (سایشی) و به روش سینتر پرس داغ تولید شدند. به منظور بررسی استحکام خمشی، سختی و خواص سایشی، نمونه ها با اضافه کردن فلزات مختلف به زمینه، شرایط مختلف آسیابکاری و پارامترهای مختلف فشار داغ، ساخته شدند. هدف از این تحقیق، تولید کامپوزیت زمینه آلیاژهای مس تقویت شده با ذرات الماس میکرونی و بررسی خواص مکانیکی این کامپوزیت است. از مهم ترین مسائل ساخت این نوع کامپوزیت ، بهینه سازی استحکام ذرات الماس در زمینه فلزی و خواص سایشی مد نظر این نوع کامپوزیت است. پودرهای کامپوزیتی با استفاده از آسیابکاری پرانرژی (سایشی) و به روش سینتر پرس داغ تولید شدند. به منظور بررسی استحکام خمشی، سختی و خواص سایشی، نمونه ها با اضافه کردن فلزات مختلف به زمینه، شرایط مختلف آسیابکاری و پارامترهای مختلف فشار داغ، ساخته شدند.