Modelling-to-generate-alternatives Research Articles

A Computational Comparison of Three Nature-Inspired, Population-Based Metaheuristic Algorithms for Modelling-to-Generate Alternatives

In “real life” decision-making situations, inevitably, there are numerous unmodelled components, not incorporated into the underlying mathematical programming models, that hold substantial influence on the overall acceptability of the solutions calculated. Under such circumstances, it is frequently beneficial to produce a set of dissimilar–yet “good”–alternatives that contribute very different perspectives to the original problems. The approach for creating maximally different solutions is known as modelling-to-generate alternatives (MGA). Recently, a data structure that permits MGA using any population-based solution procedure has been formulated that can efficiently construct sets of maximally different solution alternatives. This new approach permits the production of an overall best solution together with n locally optimal, maximally different alternatives in a single computational run. The efficacy of this novel computational approach is tested on four benchmark optimization problems.

Intersecting near-optimal spaces: European power systems with more resilience to weather variability

We suggest a new methodology for designing robust energy systems. For this, we investigate so-called near-optimal solutions to energy system optimisation models; solutions whose objective values deviate only marginally from the optimum. Using a refined method for obtaining explicit geometric descriptions of these near-optimal feasible spaces, we find designs that are as robust as possible to perturbations. This contributes to the ongoing debate on how to define and work with robustness in energy systems modelling.We apply our methods in an investigation using multiple decades of weather data. For the first time, we run a capacity expansion model of the European power system (one node per country) with a three-hourly temporal resolution and 41 years of weather data. While an optimisation with 41 weather years is at the limits of computational feasibility, we use the near-optimal feasible spaces of single years to gain an understanding of the design space over the full time period. Specifically, we intersect all near-optimal feasible spaces for the individual years in order to get designs that are likely to be feasible over the entire time period. We find significant potential for investment flexibility, and verify the feasibility of these designs by simulating the resulting dispatch problem with four decades of weather data. They are characterised by a shift towards more onshore wind and solar power, while emitting more than 50% less CO2 than a cost-optimal solution over that period.Our work builds on recent developments in the field, including techniques such as Modelling to Generate Alternatives (MGA) and Modelling All Alternatives (MAA), and provides new insights into the geometry of near-optimal feasible spaces and the importance of multi-decade weather variability for energy systems design. We also provide an effective way of working with a multi-decade time frame in a highly parallelised manner. Our implementation is open-sourced, adaptable and is based on PyPSA-Eur.

Alternative Generation in Complex Decision Modelling Using a Firefly Algorithm Metaheuristic Approach

Decision-making in the “real world” can become dominated by inconsistent performance requirements and incompatible specifications that can be difficult to detect when supporting mathematical programming models are formulated. There are invariably unmodelled elements, not apparent during model construction, which can greatly impact the acceptability of the model's solutions. Consequently, it can frequently prove beneficial to construct a set of options that provide dissimilar approaches to such problems. These alternatives should possess near-optimal objective measures with respect to all known objectives, but be maximally different from each other in terms of their decision variables. The approach for creating maximally different sets of solutions is referred to as modelling-to-generate-alternatives (MGA). This article provides an efficient biologically-inspired algorithm that can generate sets of maximally different alternatives by employing the Firefly Algorithm metaheuristic. The computational efficacy of this MGA approach is demonstrated on a commonly-tested benchmark problem.

Exploring the impact space of different technologies using a portfolio constraint based approach for multi-objective optimization of integrated urban energy systems

Optimization-based modelling provides valuable guidance for designing integrated urban energy systems. However, modelers have to make certain assumptions and they may lack awareness of realistic conditions such as decision-makers’ preferences on certain technology, which can easily lead the obtained optimal solution to be invalid. Therefore, instead of focusing on one “fragile” optimal solution, this paper provides a systematic overview of the contribution each technology can bring to the whole system design so as to achieve the optimum. To achieve this, a portfolio constraint based approach is proposed, which is inspired by the modelling to generate alternatives (MGA) method as well as the eps-constraint method for multi-objective optimization. By varying the threshold values of portfolio constraints, a series of solutions can be gathered as an “impact space” representing the economic and environmental contributions of each technology for the whole system design. A practical Fitting of Ellipses method is further applied to quantify the size of the impact space. Through observing the formation of the impact space, more valuable insights on system design can be obtained.The proposed approach is applied to a case study of an urban district in Shanghai, China, where a generalized urban energy system model involving commonly used energy supply technologies is established. Various technologies and design options lead to significantly different impact spaces, where CHP is found to have the largest impact on system design. Overall, instead of merely providing decision-maker a very specific solution, this paper introduces a new approach to evaluate multiple technologies when designing integrated urban energy systems.

A Stochastic Simulation-Optimization Method for Generating Waste Management Alternatives Using Population-Based Algorithms

While solving difficult stochastic engineering problems, it is often desirable to generate several quantifiably good options that provide contrasting perspectives. These alternatives should satisfy all of the stated system conditions, but be maximally different from each other in the requisite decision space. The process of creating maximally different solution sets has been referred to as modelling-to-generate-alternatives (MGA). Simulation-optimization has frequently been used to solve computationally difficult, stochastic problems. This paper applies an MGA method that can create sets of maximally different alternatives for any simulation-optimization approach that employs a population-based algorithm. This algorithmic approach is both computationally efficient and simultaneously produces the prescribed number of maximally different solution alternatives in a single computational run of the procedure. The efficacy of this stochastic MGA method is demonstrated on a waste management facility expansion case.

An Algorithm for Generating Sets of Maximally Different Alternatives Using Population-Based Metaheuristic Procedures

“Real world” problems typically possess complex performance conditions peppered with inconsistent performance requirements. This situation occurs because multifaceted problems are often riddled with incompatible performance objectives and contradictory design requirements which can be difficult – if not impossible – to specify when the requisite decision models are formulated. Thus, it is often desirable to generate a set of disparate alternatives that provide diverse approaches to the problem. These dissimilar options should be close-to-optimal with respect to any specified objective(s), but remain maximally different from all other solutions in the decision space. The approach for creating maximally different sets of solutions is referred to as modelling-to-generate-alternatives (MGA). This paper outlines an MGA algorithmic approach that can simultaneously generate a set of maximally different alternatives using any population-based metaheuristic.

A Biologically-Inspired Metaheuristic Approach for the Simultaneous Generation of Alternatives

Decision-making in the “real world” involves complex problems that tend to be riddled with competing performance objectives and possess requirements which are very difficult to incorporate into any underlying decision support models. There are invariably unmodelled elements, not apparent during model construction, which can greatly impact the acceptability of the model's solutions. Consequently, it is preferable to generate numerous dissimilar alternatives that provide disparate perspectives to the problem. These alternatives should possess near-optimal objective measures with respect to all known objectives, but be maximally different from each other in terms of their decision variables. This maximally different solution creation approach is referred to as modelling-to-generate-alternatives (MGA). This article provides an efficient biologically-inspired algorithm that simultaneously generates multiple, maximally different alternatives by employing the Firefly Algorithm metaheuristic. The effectiveness of this algorithm is demonstrated on an engineering optimization benchmark test problem

A Computational Algorithm for Simultaneously Creating Alternatives to Optimal Solutions

In solving many practical mathematical programming applications, it is generally preferable to formulate several quantifiably good alternatives that provide distinct perspectives to the particular problem. This is because decision-making typically involves complex problems that are riddled with incompatible performance objectives and contain competing design requirements which are very difficult – if not impossible – to capture and quantify at the time that the supporting decision models are actually constructed. There are invariably unmodelled design issues, not apparent at the time of model construction, which can greatly impact the acceptability of the model’s solutions. Consequently, it is preferable to generate several, distinct alternatives that provide multiple, disparate perspectives to the problem. These alternatives should possess near-optimal objective measures with respect to all known modelled objective(s), but be fundamentally different from each other in terms of their decision variables. This solution approach is referred to as modelling to generate-alternatives (MGA). This paper provides an efficient computational procedure for simultaneously generating multiple different alternatives to optimal solutions that employs the Firefly Algorithm. The efficacy of this approach will be illustrated using a well-known engineering optimization benchmark problem..

Modelling to generate alternatives: A technique to explore uncertainty in energy-environment-economy models

In this study we describe a novel formulation of the so-called modelling to generate alternatives (MGA) methodology and use it to explore the near cost optimal solution space of the global energy-environment-economy model TIAM-UCL. Our implementation specifically aims to find maximally different global energy system transition pathways and assess the extent of their diversity in the near optimal region. From this we can determine the stability of the results implied by the least cost pathway which in turn allows us to both identify whether there are any consistent insights that emerge across MGA iterations while at the same time highlighting that energy systems that are very similar in cost can look very different. It is critical that the results of such an uncertainty analysis are communicated to policy makers to aid in robust decision making. To demonstrate the technique we apply it to two scenarios, a business as usual (BAU) case and a climate policy run. For the former we find significant variability in primary energy carrier consumption across the MGA iterations which then projects further into the energy system leading to, for example, large differences in the portfolio of fuels used in and emissions from the electricity sector. When imposing a global emissions constraint we find, in general, less variability than the BAU case. Consistent insights do emerge with oil use in transport being a robust finding across all MGA iterations for both scenarios and, in the mitigation case, the electricity sector is seen to reliably decarbonise before transport and industry as total system cost is permitted to increase. Finally, we compare our implementation of MGA to the so-called Hop-Skip-Jump formulation, which also seeks to obtain maximally different solutions, and find that, when applied in the same way, the former identifies more diverse transition pathways than the latter.

Creating Alternatives for Stochastic Water Resources Management Decision-Making Using a Firefly Algorithm-Driven Simulation-Optimization Approach

Abstract: In solving complex water resources management (WRM) problems, it can prove preferable to create numerous quantifiably good alternatives that provide multiple, disparate perspectives. This is because WRM normally involves multifaceted problems that are riddled with incompatible performance objectives and contain inconsistent design requirements, which are very difficult to quantify and capture when supporting decisions must be constructed. By producing a set of options that are maximally different from each other in terms of their unmodelled variable structures, it is hoped that some of these dissimilar solutions may convey very different perspectives that may serve to address these unmodelled objectives. In environmental planning, this maximally different option production procedure is referred to as modelling-to-generate-alternatives (MGA). In addition, many components of WRM problems possess extensive stochastic uncertainty. This study provides a firefly algorithm-driven simulation-optimization approach for MGA that can be used to efficiently create multiple solution alternatives to problems containing significant stochastic uncertainties that satisfy required system performance criteria and yet are maximally different in their decision spaces. This algorithmic approach is both computationally efficient and simultaneously produces a prescribed number of maximally different solution alternatives in a single computational run of the procedure. The effectiveness of this stochastic MGA approach for creating alternatives in “real world”, environmental policy formulation is demonstrated using a WRM case study.

Investment appraisal of cost-optimal and near-optimal pathways for the UK electricity sector transition to 2050

Deep decarbonisation of the electricity sector is central to achieving the United Kingdom’s (UK) climate policy targets for 2050 and meeting its international commitments under the Paris Agreement. While the overall strategy for decarbonising the energy system has been well established in previous studies, there remain deep uncertainties around the total investment cost requirements for the power system. The future of the power system is of critical importance because low carbon electricity may create significant opportunities for emissions reduction in buildings and transport. A key policy application of quantitative analysis using models is to explore how much investment needs to be mobilised for the energy transition. However, past estimates of energy transition costs for the UK power sector have focused only on 2030 rather than 2050 and consider a relatively narrow range of uncertainties. This paper addresses this important research gap. The UK government's main whole system energy economy model is linked to a power system model that employs an advanced approach to uncertainty analysis, combining Monte Carlo simulation with Modelling-to-Generate Alternatives (MGA), producing 800 different scenario pathways. These pathways simultaneously consider uncertainties in policy, technology and costs. The results show that with No Climate Policy, installed generation capacities in 2050 are found in the range 60–75GW, while under an 80% Reduction in GHG Emissions, between 100GW and 130GW of plant are required. Meeting climate targets for 2050 is also found to increase the investment requirements for new electricity generation. The interquartile range for cumulative investments in new generation under the No Climate Policy scenario ranges from £60bn to £75bn, while under an 80% Reduction in GHG Emissions, investment requirements approximately double to £110bn - £140bn. The exercise demonstrates the importance of uncertainty analysis to policy evaluation, yielding insights for future research practice both in the UK and internationally.

Environmental decision-making under uncertainty using a biologically-inspired simulation-optimisation algorithm for generating alternative perspectives

In solving many environmental policy formulation applications, it is generally preferable to formulate several quantifiably good alternatives that provide multiple, disparate approaches to the problem. This is because environmental decision-making typically involves complex problems that are riddled with incompatible performance objectives and possess competing design requirements which are very difficult - if not impossible - to quantify and capture at the time when supporting decision models must be constructed. By generating a set of maximally different solutions, it is hoped that some of the dissimilar alternatives can provide very different perspectives that may serve to satisfy the unmodelled objectives. This maximally different solution creation approach is referred to as modelling to generate-alternatives (MGA). This paper provides a biologically-inspired metaheuristic simulation-optimisation MGA method that can efficiently create multiple solution alternatives to environmental problems containing significant stochastic uncertainties that satisfy required system performance criteria and yet are maximally different in their decision spaces. The efficacy of this stochastic MGA approach for environmental policy formulation is demonstrated using a municipal solid waste case study. It is shown that this new computationally efficient algorithmic approach can simultaneously produce the desired number of maximally different solution alternatives in a single computational run of the procedure.

OPTIMIZATION OF IRRIGATION WATER DISTRIBUTION USING THE MGA METHOD AND COMPARISON WITH A LINEAR PROGRAMMING METHOD

Optimization of irrigation water distribution is an important item for water management in irrigation networks. A linear programming model can have problems, for example when the objective function is based on only one goal. So some methods, for example modelling to generate alternatives (MGA), can improve results. This study presented a schedule for distributing irrigation water as well as an optimal cultivation pattern aiming at maximizing net profit on one side and water productivity (WP) on the other. Since the production function is the most important part of water distribution models, the best available production functions were checked and calibrated. The obtained results revealed that WP could be enhanced by 20–40% using the MGA technique. However, investigation of water shortage conditions showed that a 30–35% water deficit could result in an increase of WP by 54%. Thus, it could be argued that the most important matter in water management in irrigation networks is the simultaneous study of WP and water economic productivity (WEP). Considering both factors, a deficit of 30%, which results in a decrease of profit by 10%, was selected as the best alternative for the economic enhancement of WP in the Qazvin Plain. Copyright © 2014 John Wiley & Sons, Ltd.

A Concurrent Modelling to Generate Alternatives Approach Using the Firefly Algorithm

Real world” decision-making applications generally contain multifaceted performance requirements riddled with incongruent performance specifications. There are invariably unmodelled elements, not apparent during model construction, which can greatly impact the acceptability of the model’s solutions. Consequently, it is preferable to generate numerous alternatives that provide dissimilar approaches to the problem. These alternatives should possess near-optimal objective measures with respect to all known objective(s), but be maximally different from each other in terms of their decision variables. This maximally different solution creation approach is referred to as modelling-to-generate-alternatives (MGA). This study demonstrates how the Firefly Algorithm can concurrently create multiple solution alternatives that both satisfy required system performance criteria and yet are maximally different in their decision spaces. This new approach is computationally efficient, since it permits the concurrent generation of multiple, good solution alternatives in a single computational run rather than the multiple implementations required in previous MGA procedures.

Generating Alternatives Using Simulation-Optimization Combined with Niching Operators to Address Unmodelled Objectives in a Waste Management Facility Expansion Planning Case

Public sector decision-making typically involves complex problems that are riddled with incompatible performance objectives and possess competing design requirements which are very difficult – if not impossible – to quantify and capture when supporting decision models need to be constructed. There are invariably unmodelled design issues, not apparent at the time of model creation, which can greatly impact the acceptability of the solutions proposed by the model. Consequently, it is generally preferable to create several quantifiably good alternatives that provide multiple, disparate perspectives and very different approaches to the particular problem. These alternatives should possess near-optimal objective measures with respect to the known modelled objective(s), but be fundamentally different from each other in terms of the system structures characterized by their decision variables. By generating a set of very different solutions, it is hoped that some of the dissimilar alternatives can provide very different perspectives that may serve to satisfy the unmodelled objectives. This study shows how simulation-optimization (SO) modelling can be combined with niching operators to efficiently generate multiple policy alternatives that satisfy required system performance criteria in stochastically uncertain environments and yet are maximally different in the decision space. This new stochastic approach is very computationally efficient, since it permits the simultaneous generation of good solution alternatives in a single computational run of the SO algorithm. The efficacy and efficiency of this modelling-to-generate-alternatives (MGA) method is specifically demonstrated on a municipal solid waste management facility expansion case.

Applications of Simulation-Optimization Methods in Environmental Policy Planning under Uncertainty

Environmental policy formulation can prove especially complicated, since in general, system components contain considerable degrees of uncertainty. However, simulation-optimization (SO) techniques can be adapted to model a wide variety of problem types in which system components are stochastic. In this paper, it is shown how multiple environmental policy alternatives meeting required system criteria, or modelling-to-generate-alternatives (MGA), can be quickly and efficiently created using SO. The efficacy of this MGA approach is illustrated using two case studies. Furthermore, since SO techniques can be adapted to problems in which many system components are stochastic, the practicality of this approach can be extended into many other operational and strategic planning applications containing significant sources of uncertainty.

Policy planning under uncertainty: efficient starting populations for simulation-optimization methods applied to municipal solid waste management

Evolutionary simulation-optimization (ESO) techniques can be adapted to model a wide variety of problem types in which system components are stochastic. Grey programming (GP) methods have been previously applied to numerous environmental planning problems containing uncertain information. In this paper, ESO is combined with GP for policy planning to create a hybrid solution approach named GESO. It can be shown that multiple policy alternatives meeting required system criteria, or modelling-to-generate-alternatives (MGA), can be quickly and efficiently created by applying GESO to this case data. The efficacy of GESO is illustrated using a municipal solid waste management case taken from the regional municipality of Hamilton-Wentworth in the Province of Ontario, Canada. The MGA capability of GESO is especially meaningful for large-scale real-world planning problems and the practicality of this procedure can easily be extended from MSW systems to many other planning applications containing significant sources of uncertainty.

Developing alternative farm plans for cropping system decision making

Declining trend of domestic food production has led to the establishment of a national agricultural programme under the National Directorate of Employment (NDE) in Nigeria. The programme is envisaged to result in increased food production by engaging educated persons in food crop farming. The programme participants, due to their level of education, are also expected to be more efficient in their use of farm resources. In this study, we have generated optimal farm plans for NDE farmers in three different locations in Ondo state, Nigeria, assessed the resource-use efficiency of the sampled farmers, and provided alternative farm plans that are nearly-optimal, and more likely to be acceptable to the farmers when considerations for risk and uncertainty are introduced, using an approach known as Modelling to Generate Alternatives (MGA). Results of our analyses suggested sole cropping as the optimal cropping system for the three locations and non-attainment of optimal gross margins ranged from 24 to 37% among the locations. Although the optimal plans suggested sole cropping, the alternative farm plans provided for mixed cropping when the resulting gross margins were allowed to decrease by as little as 1% from the optimal values. These alternative plans represent various levels of enterprise diversification depending on a particular farmer's risk attitude.

Nearly optimal linear programming as a guide to agricultural planning

Linear programming has long been used as a tool in agricultural planning. This paper presents and discusses a technique that can be used in conjunction with linear programming to evaluate ‘nearly optimal’ solutions. This technique is referred to as Nearly Optimal Linear Programming or Modelling to Generate Alternatives (MGA). MGA allows planners to incorporate important objectives that are difficult to include in a mathematical model by identifying and evaluating alternative ‘nearly optimal’ solutions. Some of these alternative solutions may be consistent with the goals or objectives of decision makers. To date, MGA has received little use in addressing agricultural planning problems. A micro-level application of MGA, concerning a dairy ration formulation problem, is presented to demonstrate the relevance of MGA to agricultural planning by decision makers. Within this application, the use of MGA to complement and enhance normal linear programming analysis is also discussed.