Mathematical Optimization

Cooling water systems are generally designed with a set of heat exchangers arranged in parallel. This arrangement results in higher cooling water flowrate and low cooling water return temperature thus reducing cooling tower efficiency. Previous research on cooling water systems has focused mainly on heat exchanger network thus excluding the interaction between heat exchanger network and the cooling towers. This manuscript presents a technique for grassroot design of cooling water system for wastewater minimization which incorporates the performances of the cooling towers involved. The study focuses mainly on cooling systems consisting of multiple cooling towers that supply a common set of heat exchangers. The heat exchanger network is synthesized using the mathematical optimization technique. This technique is based on superstructure in which all opportunities for cooling water reuse are explored. The cooling tower model is used to predict the thermal performance of the cooling towers.

After a series of publications of T.E. O'Neil et al. (e.g. in 2010), dynamic programming seems to be the most promising way to solve knapsack problems. Some techniques are known to make dynamic programming algorithms (DPA) faster. One of them is the graphical method that deals with piecewise linear Bellman functions. For some problems, it was previously shown that the graphical algorithm has a smaller running time in comparison with the classical DPA and also some other advantages. In this paper, an exact graphical algorithm (GrA) and a fully polynomial-time approximation scheme based on it are presented for an investment optimization problem having the best known running time. The algorithms are based on new Bellman functional equations and a new way of implementing the GrA.

The problem of voltage collapse in power systems due to increased loads can be solved by adding renewable energy sources like wind and photovoltaic (PV) to some bus-bars. This option can reduce the cost of the generated energy and increase the system efficiency and reliability. In this paper, a modified smart technique using particle swarm optimization (PSO) has been introduced to select the hourly optimal load flow with renewable distributed generation (DG) integration under different operating conditions in the 30-bus IEEE system. Solar PV and wind power plants have been introduced to selected buses to evaluate theirs benefits as DG. Different solar radiation and wind speeds for the Dammam site in Saudi Arabia have been used as an example to study the feasibility of renewable energy integration and its effect on power system operation. Sensitivity analysis to the load and the other input data has been carried out to predict the sensitivity of the results to any deviation in the input data of the system. The obtained results from the proposed system prove that using of renewable energy sources as a DG reduces the generation and operation cost of the overall power system.

This article focuses broadly on the area known as optimization. The intent is to provide in broad brush strokes a perspective on the area in order to orient the reader to more detailed treatments of specific subdisciplines of optimization throughout WIREs: Computational Statistics. In this article we provide background on mathematical programming, Lagrange multipliers, Karush-Kuhn-Tucker Conditions, numerical optimization methods, linear programming, dynamic programming, the calculus of variations, and metaheuristic algorithms .

Recent developments lead to increasingly complex production systems, especially in the case of series production with a great number of variants. As a result, considerable challenges exist in planning the technical capacity with strategic time horizon efficiently, transparently and flexibly. Since numerous interdependencies must be considered, it can be observed in practice that completeness and understandability of the models are mutually exclusive. To solve this conflict of objectives, a software-based workflow is proposed, which was implemented in the newly developed software AURELIE. The workflow relies on the graphical modeling of a planned system of value streams, the automated validation and transformation of the graphical model and the automated optimization of the resulting mathematical model. The starting point is a graphical model, which is not only understandable, but also reflects the system completely with respect to its complexity. From a research perspective, the essential contribution, besides a formal system description and the identification of the research gap, lies in the development of the required models and algorithms. The degree of novelty is given by the holistic solution approach, which is proven feasible by the software AURELIE. From a practical perspective, efficiency, transparency and flexibility in the planning process are significantly increased. This is confirmed by the worldwide implementation of the software AURELIE at the locations of Bosch Rexroth AG. [Original title: "Strategische Planung technischer Kapazität in komplexen Produktionssystemen: mathematische Optimierung grafischer Modelle mit der Software AURELIE". Available online: https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa2-708436]

Energy produced from biofuels or there conversion products represent an important part among today's energy sources. As biofuels are renewable, abundant and has domestic usage, the sources of biofuels can help the world reduce its dependence on petroleum products and natural gas. Biofuels can be converted into liquid, solid and gaseous fuels with the help of some physical, chemical and biological conversion processes. The conversion of biofuel material has a precise objective to transform a carbonaceous solid material, which is originally difficult to handle, bulky and of low energy concentration, into fuels having physico-chemical characteristics that permit economic storage and transferability through pumping systems. The use of biofuel products provides substantial benefits as far as the environment is concerned. A simulation study has been carried out to arrive at the power output under limiting conditions as well as perform changes in the fuel gas system for the augmentation. The simulation study has been carried out on the simulation software Aspen HYSYS and the findings show that, the available fuel gas obtained from the biomass can be optimally used for the power generation in the gas turbine.

In this paper we address the optimal production of second generation of biodiesel using waste cooking oil and algae oil. We consider 5 different technologies for the transesterification of the oil (homogeneous acid or alkali catalyzed, heterogeneous basic catalyzed, enzymatic and supercritical non catalyzed). We formulate the problem as an MINLP where the models for each of the reactors are based on surface response methodology to capture the effect of the variables on the yield. The aim is to simultaneously optimize and heat integrate the production of biodiesel from each of the different oil sources in terms of the technology to use and the operating conditions required. The optimal conditions in the reactors differ from the ones traditionally used because the separation stages were not taking into account in the design. When using algae oil, the optimal process employs alkali as catalyst with a production cost of 0.42$/gal, 1.94 MJ/gal of energy consumption and freshwater consumption 0.60 galwater / galethanol . For cooking oil the optimal process is the one with heterogeneous catalyst, with production cost, energy and water consumption of $0.66/gal, 1.94 MJ/gal and 0.33galwater / galethanol, respectively.

This article presents a mathematical model for the synthesis of resource conservation networks with interception placement. A comprehensive superstructure that incorporates all possible network configurations is used to facilitate the formulation. The synthesis task involves the allocation and interception of process sources to satisfy process sinks and environmental constraints. In particular, the interaction between the sinks and sources is addressed as the subject of the present study. Two literature case studies are solved to illustrate the proposed approach.

Association Rules Mining (ARM) is one of the most popular and well-known approaches for the decision-making process. All existing ARM algorithms are time consuming and generate a very large number of association rules with high overlapping. To deal with this issue, we propose a new ARM approach based on penguins search optimisation algorithm (Pe-ARM for short). Moreover, an efficient measure is incorporated into the main process to evaluate the amount of overlapping among the generated rules. The proposed approach also ensures a good diversification over the whole solutions space. To demonstrate the effectiveness of the proposed approach, several experiments have been carried out on different datasets and specifically on the biological ones. The results reveal that the proposed approach outperforms the well-known ARM algorithms in both execution time and solution quality.

This paper presents application of PSO (Particle Swarm Optimization) and GA (Genetic Algorithm) techniques to estimate oil demand in Iran, based on socioeconomic indicators. The models are developed in two forms (exponential and linear) and applied to forecast oil demand in Iran. PSOeDEM and GAeDEM (PSO and GA demand estimation models) are developed to estimate the future oil demand values based on population, GDP (gross domestic product), import and export data. Oil consumption in Iran from 1981 to 2005 is considered as the case of this study. The available data is partly used for finding the optimal, or near optimal values of the weighting parameters (1981e1999) and partly for testing the models (2000e2005). For the best results of GA, the average relative errors on testing data were 2.83% and 1.72% for GAeDEM exponential and GAeDEM linear , respectively. The corresponding values for PSO were 1.40% and 1.36% for PSOeDEM exponential and PSOeDEM linear , respectively. Oil demand in Iran is forecasted up to year 2030.

Selective catalytic reduction (SCR) is an emissions control technique that primarily reduces harmful emissions of oxides of nitrogen (NO x). To maintain SCR performance, catalyst layers maybe added, removed, or replaced to improve NO x reduction efficiency. To make these changes, power plants must be temporarily shut down, and SCR maintenance during scheduled power plant outages can be very expensive. Consequently, developing a fleet-wide SCR management plans that are both efficient at reducing NO x and limiting operating costs would be extremely desirable. We propose an SCR management framework that finds an optimal SCR management plan that minimizes NO x emissions using integer programming. The SCR management tool consists of two main modules-the SCR schedule generation module and the SCR optimization module. Furthermore, the SCR management framework addresses decision making from the fleet-wide perspective as well as a single plant as opposed to only a single plant, which is currently commercially available. We demonstrate the effectiveness of the tool and provide a tradeoff between NO x reduction and operating cost using Pareto optimal efficient frontiers.

In the real world, one of the major factor that contributes to the complexity of supply chains is the structure of supply chain. Compared with a supply chain with two members, operations planning in a manufacturing network where members are independent entities require a special attention to the details. This paper will focus on the specific case of manufacturing network planning. Our objective is to propose a new planning methodology between independent production companies to achieve an agreed plan.

A method providing the efficient way of construction of weighted coefficients for linear weighted sum method is provided. By applying this method, all of the resulting points are Pareto optimal points of the corresponding multi-objective optimization problem. A method for the efficient construction of weighting coefficients w i > 0 in programming package MATHEMATICA is presented. Run-time symbolic transformations of the objective functions and constraints into the corresponding single-objective constrained problem are emphasized. The implementation details and the graphical representations of two and three variables case are given, in order to depict the introduced method.

Multi-objective optimization methods provide a valid support to buildings' design. They aim at identifying the most promising building variants on the basis of diverse and potentially contrasting needs. However, optimization has been mainly used to optimize the energy performance of buildings, giving secondary importance to thermal comfort and usually neglecting visual comfort and the indoor air quality. The present study addresses the design of a detached net zero-energy house located in Southern Italy to minimize thermal and visual discomfort. The optimization problem admits four objective functions (thermal discomfort during winter and summer and visual discomfort due to glare and an inappropriate quantity of daylight) and uses the non-dominated sorting genetic algorithm, implemented in the GenOpt optimization engine through the Java genetic algorithms package, to instruct the EnergyPlus simulation engine. The simulation outcome is a four-dimensional solution set. The building variants of the Pareto frontier adopt diverse and non-intuitive design alternatives. To derive good design practices, two-dimensional projections of the solution set were also analyzed. Finally, in cases of complex optimization problems with many objective functions, optimization techniques are recommended to effectively explore the large number of available building variants in a relatively short time and, hence, identify viable non-intuitive solutions.

The proposed model can cope with important features implicit in plannin9 studies such as consideration of multiple and conflictin9 objectives, time-phased representation, piecewise linearization for representation of network losses and so .forth. A variant of the basic Benders' decomposition algorithm is applied to the problem, since the formulation can be embedded under the framework of mixed integer linear programming. Special procedures are applied to solve the linear programmin9 sub-problems and pure integer pro-9rammin9 (master) problem involved in the decomposition solution procedure. The method determines non-dominated solutions and allows the decision maker (or plannin9 engineer) to express his preferences and determine the best compromise solution. A case study illustrates the proposed methodology, when numerical results are presented.

We propose a novel technique for improving the stochastic gradient descent (SGD) method to train deep networks, which we term pbSGD. The proposed pbSGD method simply raises the stochastic gradient to a certain power elementwise during iterations and introduces only one additional parameter, namely, the power exponent (when it equals to 1, pbSGD reduces to SGD). We further propose pbSGD with momentum, which we term pbSGDM. The main results of this paper present comprehensive experiments on popular deep learning models and benchmark datasets. Empirical results show that the proposed pbSGD and pbSGDM obtain faster initial training speed than adaptive gradient methods, comparable generalization ability with SGD, and improved robustness to hyper-parameter selection and vanishing gradients. pbSGD is essentially a gradient modifier via a nonlinear transformation. As such, it is orthogonal and complementary to other techniques for accelerating gradient-based optimization such as learning ra...

Identical parallel robot scheduling problem for minimizing mean tardiness with precedence constraints is a very important scheduling problem. But, the solution of this problem becomes much difficult when there are a number of robots, jobs and precedence constraints. Genetic algorithm is ...

This paper presents application of PSO (Particle Swarm Optimization) and GA (Genetic Algorithm) techniques to estimate oil demand in Iran, based on socioeconomic indicators. The models are developed in two forms (exponential and linear) and applied to forecast oil demand in Iran. PSOeDEM and GAeDEM (PSO and GA demand estimation models) are developed to estimate the future oil demand values based on population, GDP (gross domestic product), import and export data. Oil consumption in Iran from 1981 to 2005 is considered as the case of this study. The available data is partly used for finding the optimal, or near optimal values of the weighting parameters (1981e1999) and partly for testing the models (2000e2005). For the best results of GA, the average relative errors on testing data were 2.83% and 1.72% for GAeDEM exponential and GAeDEM linear , respectively. The corresponding values for PSO were 1.40% and 1.36% for PSOeDEM exponential and PSOeDEM linear , respectively. Oil demand in Iran is forecasted up to year 2030.

A decision support system (DSS) developed to assist the planner in decisions concerning the overall management of solid waste at a municipal scale is described. The DSS allows to plan the optimal number of landfills and treatment plants, and to determine the optimal quantities and the characteristics of the refuse that has to be sent to treatment plants, to landfills and to recycling. The application of the DSS is based on the solution of a constrained non-linear optimization problem. Various classes of constraints have been introduced in the problem formulation, taking into account the regulations about the minimum requirements for recycling, incineration process requirements, sanitary landfill conservation, and mass balance. The cost function to be minimized includes recycling, transportation and maintenance costs. The DSS has been tested on the municipality of Genova, Italy, and the results obtained are presented.

The article presents the improvements in the preprocessing part of the deciphering method (shortly preprocessing algorithm) for historical inscriptions of unknown origin. Glyphs used in historical inscriptions changed through time; therefore, various versions of the same script may contain different glyphs for each grapheme. The purpose of the preprocessing algorithm is reducing the running time of the deciphering process by filtering out the less probable interpretations of the examined inscription. However, the first version of the preprocessing algorithm leads incorrect outcome or no result in the output in certain cases. Therefore, its improved version was developed to find the most similar words in the dictionary by relaying the search conditions more accurately, but still computationally effectively. Moreover, a sophisticated similarity metric used to determine the possible meaning of the unknown inscription is introduced. The results of the evaluations are also detailed.

EOQ fuzzy model is EOQ model that can estimate the cost from existing information. Using trapezoid fuzzy functions can estimate the costs of existing and trapezoid membership functions has some points that have a value of membership . TR C value results of trapezoid fuzzy will be higher than usual TRC value results of EOQ model . This paper aims to determine the optimal amount of inventory in the company, namely optimal Q and optimal V, using the model of partial backorder will be known optimal Q and V for the optimal number of units each time a message . EOQ model effect on inventory very closely by using EOQ fuzzy model with triangular and trapezoid membership functions with partial backorder. Optimal Q and optimal V values for the optimal fuzzy models will have an increase due to the use of trapezoid and triangular membership functions that have a different value depending on the requirements of each membership function value. Therefore, by using a fuzzy model can solve the compa...

This paper demonstrates a hybrid between two optimization methods which are the Artificial Immune System (AIS) and Genetic Algorithm (GA). The novel algorithm called the immune genetic algorithm (IGA), provides improvement to the results that enable GA and AIS to work separately which is the main objective of this hybrid. Negative selection which is one of the techniques in the AIS, was employed to determine the input variables (populations) of the system. In order to illustrate the effectiveness of the IGA, the comparison with a steady-state GA, AIS, and PSO were also investigated. The testing of the performance was conducted by mathematical testing, problems were divided into single and multiple objectives. The five single objectives were then used to test the modified algorithm, the results showed that IGA performed better than all of the other methods. The DTLZ multi-objective testing functions were then used. The result also illustrated that the modified approach still had the best performance.

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on th...

Resource allocation and leveling are among the top challenges in project management. Due to the complexity of projects, resource allocation and leveling have been dealt with as two distinct subproblems solved mainly using heuristic procedures that cannot guarantee optimum ...

Industrial production processes involving both lot-sizing and cutting stock problems are common in many industrial settings. However, they are usually treated in a separate way, which could lead to costly production plans. In this paper, a coupled mathematical model is formulated and a heuristic method based on Lagrangian relaxation is proposed. Computational results prove its effectiveness.

This report deals with the control of the positions and velocities of high-speed vehicles in a single guideway. It is assumed that each and every train measures its position and velocity every T seconds. The appropriate accelerations or decelerations to be applied to each vehicle are constrained to be constant during the sampling interval. Through the use of a control cost functional, which penalizes the system for any deviations from the desired headway and velocity, the required control accelerations and decelerations are obtained by deriving the system equations in discrete-time and, through the use of available results in the theory of discrete optimal control, the optimal linear time-invariant sampled-data feedback control system is determined. The general results, as well as the general purpose digital computer programs, are presented and are used to study the effect of changing the sampling time T upon the control-system performance. Since, in general, the cost of the communication system (in terms of required channel capacity, bandwidth, etc.) decreases with increasing values of the sampling time, the system designer has the capability of conducting trade-off studies involving the deterioration of the control system performance vs. the decrease in the cost of communication as the sampling time is increased.

In this paper we will briefly review the simulated annealing algorithm, an algorithm with applications in optimization and pattern recognition used extensively in artificial intelligence. In earlier papers the authors analyzed a simulation of the annealing of a solid, a dodecahedron in particular. Our use of this algorithm, which is based in the field of combinatorial optimization, reflects properties of Boltzman machines-a neural network characterized by massive parallelism. We will demonstrate two implementations of this algorithm in simulated annealing. Each of the implementations depends upon a neighborhood structure and a transition mechanism. In the first implementation our neighborhood structure is a linear transformation of the vector space of all configurations and the transition probability is deterministic. In this case, we will use techniques from character theory of finite groups to analyze simulated annealing. In the second implementation, a special case of which includes the first implementation, our neighborhood structure is a set-valued function and the transition mechanism is stochastic in nature. In this case, we use techniques from matrix analysis, in particular properties of doubly stochastic matrices, to analyze simulated annealing modeled and based on a class of Boltzman machines. For pattern recognition, we use the simulated annealing algorithm to solve the classic seven-segment display problem. This is a classification problem which we will solve by choosing an appropriate Boltzmann machine.

In this paper, a differential evolution (DE) algorithm is developed to solve emission constrained economic power dispatch (ECEPD) problem. Traditionally electric power systems are operated in such a way that the total fuel cost is minimized regardless of emissions produced. With increased requirements for environmental protection, alternative strategies are required. The proposed algorithm attempts to reduce the production of atmospheric

This article provides an insight for optimization the output considering combinations of scheduling constraints by using simple heuristic for multi-product inventory system. Method so proposed is easy to implement in real manufacturing situation by using heuristic procedure machines are arranged in optimal sequence for multiple product to manufacture. This reduces manufacturing lead-time thus enhance profit.

On recent trends, the reactive power planning problem has received a considerable amount of attention for the allocation of reactive power resources, both static and dynamic such as switchable capacitors and/or reactors, as well as Var compensators, respectively. The reactive power has a significant impact on voltage profile, stability and transmission loss in power systems. In recent years, voltage instability is recognized as a major threat to system operation due to a shortage of reactive power in an interconnected transmission line. These voltage conditions could be analyzed and improved by proper coordination of reactive sources/sink. In this article, the minimization of transmission loss and operating cost is performed by using the sine cosine algorithm (SCA) and quasi-oppositional based sine cosine algorithm (QOSCA) technique for standard IEEE 14 and IEEE 30 and IEEE 57 bus test system of the connected power network. The proposed QOSCA reduces the transmission losses by 6.38% in IEEE 14, 4.56% in IEEE 30 and 12.77% in IEEE 57 bus system. The results obtained by QOSCA and SCA are compared with other popular techniques recently reported in recent state-of-literature. It is observed that QOSCA yields better results in terms of reducing transmission loss, operating costs, and improving the voltage profile of each bus.

This paper describes a procedure that uses particle swarm optimization (PSO) combined with the Lagrangian Relaxation (LR) framework to solve a power-generator scheduling problem known as the unit commitment problem (UCP). The UCP consists of determining the schedule and production amount of generating units within a power system subject to operating constraints. The LR framework is applied to relax coupling constraints of the optimization problem. Thus, the UCP is separated into independent optimization functions for each generating unit. Each of these sub-problems is solved using Dynamic Programming (DP). PSO is used to evolve the Lagrangian multipliers. PSO is a population based search technique, which belongs to the swarm intelligence paradigm that is motivated by the simulation of social behavior to manipulate individuals towards better solution areas. The performance of the PSO-LR procedure is compared with results of other algorithms in the literature used to solve the UCP. The comparison shows that the PSO-LR approach is efficient in terms of computational time while providing good solutions.

The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of ob...

... This Petri net is therefore a stochastic, timed, and colored Petri net. ... in Proceedings of the 10th International IEEE Conference on Fuzzy Systems, December ... D., Varadarajan, Chinnaswamy, MR, Ramaraj, S., “Evolution of Real - Time Traffic adaptive signal control algorithms - A ...

One of the assumptions of the Capacitated Facility Location Problem (CFLP) is that demand is known and fixed. Most often, this is not the case when managers take some strategic decisions such as locating facilities and assigning demand points to those facilities. In this paper we consider demand as stochastic and we model each of the facilities as an independent queue. Stochastic models of manufacturing systems and deterministic location models are put together in order to obtain a formula for the backlogging probability at a potential facility location. Several solution techniques have been proposed to solve the CFLP. One of the most recently proposed heuristics, a Reactive Greedy Adaptive Search Procedure, is implemented in order to solve the model formulated. We present some computational experiments in order to evaluate the heuristics ’ performance and to illustrate the use of this new formulation for the CFLP. The paper finishes with a simple simulation exercise.

This paper presents a Cuckoo Search (CS) based algorithm to solve constrained economic load dispatch (ELD) problems. The proposed methodology easily deals with non-smoothness of cost function arising due to the use of valve point effects. The performance of the algorithm has been tested on systems possessing 13 and 40 generating units involving varying degrees of complexity. The findings affirm that the method outperforms the existing techniques, and can be a promising alternative approach for solving the ELD problems in practical power system.

The flow of fluids in a network is of practical importance in gas, oil and water transport for industrial and domestic use. When the flow dynamics are understood, one may be interested in the control of the flow formulated as follows: given some fluid properties at a final time, can one determine the initial flow properties that lead to the desired flow properties? In this thesis, we first consider the flow of a multiphase gas, described by the driftflux model, in a network of pipes and that of water, modeled by the shallow water equations, in a network of rivers. These two models are systems of partial differential equations of first order generally referred to as systems of conservation laws. In particular, our contribution in this regard can be summed up as follows: For the drift-flux model, we consider the flow in a network of pipes seen mathematically as an oriented graph. We solve the standard Riemann problem and prove a well posedness result for the Riemann problem at a junct...

<p>(a) Pareto optimization unconstrained to the available resources. Red points represent the suboptimal restoration plans for the frontier in 2013. Grey dashed lines represent the variability of the frontiers related to thirty Monte Carlo simulations generated considering a random white noise applied to the MCDA value. (b) Pareto frontiers constrained to the resources available for selected years of analysis; we assume that the total resources available are equal to 250 at the installation scale (Eglin AFB in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065056#pone-0065056-g001" target="_blank">Figure 1</a>). The frontiers show V<sub>H</sub> and V<sub>N</sub> (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065056#pone.0065056.e002" target="_blank">Eq. 2</a>) normalized to their maximum value. The blue and red dots represent unaffordable and affordable restoration plans (or portfolios) for 2100. All the possible values of V<sub>H</sub>(<u>R</u>) and V<sub>N</sub>(<u>R</u>) for selected years are shown along the Pareto frontiers. The choice of the Pareto set depends on relative stakeholder preferences for human and natural assets.</p

One of the mathematical programming techniques is data envelopment analysis (DEA), which is used for evaluating the efficiency of a set of similar decision-making units (DMUs). Fixed resource allocation and target setting with the help of DEA is a subject that has gained much attention from researchers. A new model was proposed by determining a common set of weights (CSW). All DMUs were involved with the aim of achieving higher efficiency in every DMU after the procedure. The minimum resources and targets allocated to each DMU were commensurate to the efficiency of that DMU and the share of DMU in the input resources and the output productions. To examine the proposed method, other methods in the DEA literature were examined as well, and then, the efficiency of the method was demonstrated through a numerical example.

The particle swarm optimization (PSO) technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space. This paper presents a variation on the standard PSO algorithm called the rank based particle swarm optimizer, or PSO rank , employing cooperative behavior of the particles to significantly improve the performance of the original algorithm. In this method, in order to efficiently control the local search and convergence to global optimum solution, the γ best particles are taken to contribute to the updating of the position of a candidate particle. The contribution of each particle is proportional to its strength. The strength is a function of three parameters: strivness, immediacy and number of contributed particles. All particles are sorted according to their fitness values, and only the γ best particles will be selected. The value of γ decreases linearly as the iteration increases. A time-varying inertia weight decreasing non-linearly is introduced to improve the performance. PSO rank is tested on a commonly used set of optimization problems and is compared to other variants of the PSO algorithm presented in the literature. As a real application, PSO rank is used for neural network training. The PSO rank strategy outperformed all the methods considered in this investigation for most of the functions. Experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness.

In this paper we present a mixed integer-programming model that integrates production lot sizing and scheduling decisions of beverage plants with sequence-dependent set up costs and times. The model considers that the industrial process produces soft drink bottles in different flavours and sizes, and it is carried out in two production stages: liquid preparation (Stage I) and bottling (Stage II). The model also takes into account that the production bottleneck may alternate between Stages I and II, and a synchrony of the production between these stages is required. A relaxation approach and several strategies of the relax-and-fix heuristic are proposed to solve the model. Computational tests with instances generated based on real data from a Brazilian soft drink plant are also presented. The results show that the solution approaches are capable of producing better solutions than those used by the company.

During the last few years we have witnessed impressive developments in the area of stochastic local search techniques for intelligent optimization and Reactive Search Optimization. In order to handle the complexity, in the framework of stochastic local search optimization, learning and optimization has been deeply interconnected through interaction with the decision maker via the visualization approach of the online graphs. Consequently a number of complex optimization problems, in particular multiobjective optimization problems, arising in widely different contexts have been effectively treated within the general framework of RSO. In solving real-life multiobjective optimization problems often most emphasis are spent on finding the complete Pareto-optimal set and less on decision-making. However the complete task of multiobjective optimization is considered as a combined task of optimization and decision-making. In this paper, we suggest an interactive procedure which will involve the decision-maker in the optimization process helping to choose a single solution at the end. Our proposed method works on the basis of Reactive Search Optimization (RSO) algorithms and available software architecture packages. The procedure is further compared with the excising novel method of Interactive Multiobjective Optimization and Decision-Making, using Evolutionary method (I-MODE). In order to evaluate the effectiveness of both methods the well-known study case of welded beam design problem is reconsidered.

We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. It is an outer approximation algorithm and is based on solving norm minimizing scalarizations. Unlike Pascolleti-Serafini scalarization used in the literature for similar purposes, it does not involve a direction parameter. Therefore, the algorithm is free of direction-biasedness. We also propose a modification of the algorithm by introducing a suitable compact subset of the upper image, which helps in proving for the first time the finiteness of an algorithm for convex vector optimization. The computational performance of the algorithms is illustrated using some of the benchmark test problems, which shows promising results in comparison to a similar algorithm that is based on Pascoletti-Serafini scalarization.