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on Computational Economics |
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Issue of 2007‒02‒17
eleven papers chosen by |
| By: | Mishra, SK |
| Abstract: | In this paper we test a particular variant of the (Repulsive) Particle Swarm method on some rather difficult global optimization problems. A number of these problems are collected from the extant literature and a few of them are newly introduced. First, we introduce the Particle Swarm method of global optimization and its variant called the 'Repulsive Particle Swarm' (RPS) method. Then we endow the particles with some stronger local search abilities - much like tunneling - so that each particle can make a search in its neighborhood to optimize itself. Next, we introduce the test problems, the existing as well as the new ones. We also give plots of some of these functions to help appreciation of the optimization problem. Finally, we present the results of the RPS optimization exercise and compare the results with those obtained by using the Genetic algorithm (GA)and/or Simulated annealing (SA) method. We append the (Fortran) computer program that we have developed and used in this exercise. Our findings indicate that neither the RPS nor the GA/SA method can assuredly find the optimum of an arbitrary function. In case of the Needle-eye and the Corana functions both methods perform equally well while in case of Bukin's 6th function both yield the values of decision variables far away from the right ones. In case of zero-sum function, GA performs better than the RPS. In case of the Perm #2 function, both of the methods fail when the dimension grows larger. In several cases, GA falters or fails while RPS succeeds. In case of N#1 through N#5 and the ANNs XOR functions the RPS performs better than the Genetic algorithm. It is needed that we find out some criteria to classify the problems that suit (or does not suit) a particular method. This classification will highlight the comparative advantages of using a particular method for dealing with a particular class of problems. |
| Keywords: | Repulsive Particle Swarm; Global optimization; non-convex functions; Bounded rationality; local optima; Bukin; Corana; Rcos; Freudenstein Roth; Goldenstein Price; ANNs XOR; Perm; Power sum; Zero sum; Needle-eye; Genetic algorithms; variants; Fortran; computer program; benchmark; test |
| JEL: | C63 C61 C65 C69 C6 |
| Date: | 2006–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1742&r=cmp |
| By: | Mishra, SK |
| Abstract: | Our objective in this paper is to compare the performance of the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization. To this end, some relatively difficult test functions have been chosen. These functions are: Perm, Power-Sum, Bukin, Zero-Sum, Hougen, Giunta, DCS, Kowalik, Fletcher-Powell and some now functions. Our results show that DE (with the exponential crossover scheme) mostly fails to find the optimum of most of these functions. Of course, it succeeds in case of some functions (perm#2, zero-sum) for very small dimension (m), but begins to falter as soon as the dimension is increased. In case of DCS function, it works well up to m (dimension) = 5. When we use no crossover (only probabilistic replacement) we obtain better results in case of several of the functions under study. Thus, overall, table #2 presents better results than what table #1 does. In case of Perm#1, Perm#2, Zero-sum, Kowalik, Hougen and Power-sum functions the advantage is clear. Whether crossover or no crossover, DE falters when the optimand function has some element of randomness. This is indicated by the functions: Yao-Liu#7, Fletcher-Powell, and “New function#2”. DE has no problems in optimizing the “New function#1”. But the “New function #2” proves to be a hard nut. However, RPS performs much better for such stochastic functions. When the Fletcher-Powell function is optimized with non-stochastic c vector, DE works fine. But as soon as c is stochastic, it becomes unstable. Thus, it may be observed that an introduction of stochasticity into the decision variables (or simply added to the function as in Yao-Liu#7) interferes with the fundamentals of DE, which works through attainment of better and better (in the sense of Pareto improvement) population at each successive iteration. |
| Keywords: | Repulsive particle swarm; Differential evolution; Global optimization; Stochasticity; random disturbances; Crossover; Perm; zero sum; Kowalik; Hougen; Power sum; DCS; Fletcher Powell; multimodal; benchmark; test functions; Bukin; Giunta |
| JEL: | C63 C61 |
| Date: | 2006–10–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1743&r=cmp |
| By: | Petra Huck (Environmental Economics and Agricultural Policy Group, Technical University of Munich) |
| Abstract: | Differential games combine strategic interactions between agents and optimization concerning time. Decisions made in the past determine the present and even the future .in pay off as well as in the opportunities available . for oneself and for the rival players, eventually too. Unfortunately, due to high complexity it is hard to find a Nash-equilibrium within a differential game and it is even harder to get some results in comparative statics. It is the purpose of the paper at hand to present findings concerning comparative statics in a differential game discussed by Wacker and Blank (1999). Comparative statics become available due to a routine solving for the open-loop Nash equilibrium for each parameter combination under consideration. A description of the routine . a 4 step simulation run which approximates the equilibrium numerically . was presented in an earlier Working Paper. In the earlier Paper Excel was applied as it is a wild spread tool. Here again Excel, its Solver and Macros constitute the main instruments; they are used to get repeated simulation runs for varying parameter constellations. The findings presented here concern varying allocations in initial stocks. Generalization to comparative statics in further parameters is in progress. |
| JEL: | A22 C73 Q30 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:tuu:papers:052005&r=cmp |
| By: | Petra Huck (Environmental Economics and Agricultural Policy Group, Technical University of Munich) |
| Abstract: | Differential games link strategic interactions between agents and optimization concerning time. Past and current actions of each player influence all future strategy sets and pay offs through a transition law. Due to high complexity, it is hard to find a Nash-equilibrium within a differential game and it is even harder to get some results in comparative statics. It is the purpose of the paper to describe an approximation routine for an open-loop Nash equilibrium of a simple differential game in exhaustible resources. Excel is applied as it is a wild spread tool. |
| JEL: | A22 C73 Q30 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:tuu:papers:042005&r=cmp |
| By: | Bredström, David (Dept. of Mathematics, Linköpings universitet); Rönnqvist, Mikael (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration) |
| Abstract: | In this paper we present a branch and price algorithm for the combined vehicle routing and scheduling problem with synchronization constraints. The synchronization constraints are used to model situations when two or more customers need simultaneous service. The synchronization constraints impose a temporal dependency between vehicles, and it follows that a classical decomposition of the vehicle routing and scheduling problem is not directly applicable. With our algorithm, we have solved 44 problems to optimality from the 60 problems used for numerical experiments. The algorithm performs time window branching, and the number of subproblem calls is kept low by adjustment of the columns service times. |
| Keywords: | Routing; Scheduling; Synchronization; Branch and Price |
| JEL: | L91 |
| Date: | 2007–02–13 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2007_007&r=cmp |
| By: | Yusuf, Arief Anshory |
| Abstract: | The distributional impact of policies analyzed in the CGE modelling framework have been constrained in part by the absence of a Social Accounting Matrix (SAM) with disaggregated households. Since Indonesian official SAM does not distinguish households by income or expenditure size, it has prevented accurate assesment for the distributional impact, such as calculation of inequality or poverty incidence. This paper describes how the Indonesian SAM for the year 2003, with 181 industries, 181 commodities, and 200 households (100 urban and 100 rural households grouped by expenditure per capita centiles) was constructed. The SAM (with the size of 768x768 accounts) constitutes the the most disaggregated SAM for Indonesia at both the sectoral and household level. SAM Construction is an essential part of CGE modeling, and this documentation provides greater transparency as well as replicability for further improvement. |
| Keywords: | Social Accounting Matrix; Computable General Equilibrium; Indonesia |
| JEL: | D58 D30 |
| Date: | 2006–11–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1730&r=cmp |
| By: | Vanhoucke, M. |
| Abstract: | In this paper, we present a meta-heuristic algorithm for the well-known resource-constrained project scheduling problem with discounted cash flows. This optimization procedure maximizes the net present value of project subject to the precedence and renewable resource constraints. The problem is known to be NP-hard. We investigate the use of a enhanced bi-directional generation scheme and a recursive forward/backward improvement method and embed them in a meta-heuristic scatter search framework. We generate a large dataset of project instances under a controlled design and report detailed computational results. The solutions and project instances can be downloaded from a website in order to facilitate comparison with future research attempts. |
| Keywords: | Resource-constrained project scheduling; Net present value; Scatter search |
| Date: | 2006–10–04 |
| URL: | http://d.repec.org/n?u=RePEc:vlg:vlgwps:2006-40&r=cmp |
| By: | Debels, D.; Vanhoucke, M. |
| Abstract: | We present a finite capacity production scheduling algorithm for an integrated steel company located in Belgium. This multiple-objective optimization model takes various case-specific constraints into account and consists of two steps. A machine assignment step determines the routing of an individual order through the network while a scheduling step makes a detailed timetable for each operation for all orders. The procedure has been tested on randomly generated data instances that reflect the characteristics of the steel company. We report promising computational results and illustrate the flexibility of the optimization model with respect to the various input parameters. |
| Keywords: | Master production scheduling; manufacturing planning and control; scheduling/sequencing. |
| Date: | 2006–10–04 |
| URL: | http://d.repec.org/n?u=RePEc:vlg:vlgwps:2006-41&r=cmp |
| By: | Bonaventura, Luigi |
| Abstract: | In this paper an agent-based model (abm) will be used to study the effects of enforcement policy in Italy: d.lgs. 124/2004. Three kinds of policy will be tested in the model: control, sanction and legitimacy-regulation. The first policy is based on the number of inspectors present in the economy; the second is defined by the magnitude of punishment; the third is measured by the social legitimacy of regulation. This simulation has produced a number of results, the most important of which are: the negligible influence of control increasing to enforce irregularity; the strong influence of the level of punishment on the irregularity ratio in all Italian areas; the good political choice to increase the social legitimacy to regulation in promoting regularity. |
| Keywords: | enforcement policies; irregular sector; agent-based model |
| JEL: | C63 O17 K42 E61 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1731&r=cmp |
| By: | Boute, R.; Lambrecht, M. |
| Abstract: | An important supply chain research problem is the bullwhip effect: demand fluctuations increase as one moves up the supply chain from retailer to manufacturer. It has been recognized that demand forecasting and ordering policies are two of the key causes of the bullwhip effect. In this paper we present a spreadsheet application, which explores a series of replenishment policies and forecasting techniques under different demand patterns. It illustrates how tuning the parameters of the replenishment policy induces or reduces the bullwhip effect. Moreover, we demonstrate how bullwhip reduction (order variability dampening) may have an adverse impact on inventory holdings. Indeed, order smoothing may increase inventory fluctuations resulting in poorer customer service. As such, the spreadsheets can be used as an educational tool to gain a clear insight into the use or abuse of inventory control policies and improper forecasting in relation to the bullwhip effect and customer service. |
| Keywords: | Bullwhip effect, forecasting techniques, replenishment rules, inventory fluctuations, spreadsheet simulation |
| Date: | 2007–02–09 |
| URL: | http://d.repec.org/n?u=RePEc:vlg:vlgwps:2007-4&r=cmp |
| By: | Szilárd Benk (Magyar Nemzeti Bank); Zoltán M. Jakab (Magyar Nemzeti Bank); Mihály András Kovács (Magyar Nemzeti Bank); Balázs Párkányi (Magyar Nemzeti Bank); Zoltán Reppa (Magyar Nemzeti Bank); Gábor Vadas (Magyar Nemzeti Bank) |
| Abstract: | This document gives a detailed account of the current version of the Hungarian Quarterly Projection Model (NEM). It describes the main building blocks, presents the forecast performance of the model and, finally, it illustrates the responses to the most important shocks the Hungarian economy may face. This version of the model is used to produce the Bank’s quarterly projections, as well as to perform simulations and scenario analyses. |
| Keywords: | econometric modelling, forecasting, simulation. |
| JEL: | C50 C53 E17 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:mnb:opaper:2006/60&r=cmp |