ADAPTIVE RANKS CLONE AND k‐NEAREST NEIGHBOR LIST–BASED IMMUNE MULTI‐OBJECTIVE OPTIMIZATION

Artificial immune systems (AIS) are computational systems inspired by the principles and processes of the vertebrate immune system. The AIS‐based algorithms typically exploit the immune system's characteristics of learning and adaptability to solve some complicated problems. Although, several AIS‐based algorithms have proposed to solve multi‐objective optimization problems (MOPs), little focus have been placed on the issues that adaptively use the online discovered solutions. Here, we proposed an adaptive selection scheme and an adaptive ranks clone scheme by the online discovered solutions in different ranks. Accordingly, the dynamic information of the online antibody population is efficiently exploited, which is beneficial to the search process. Furthermore, it has been widely approved that one‐off deletion could not obtain excellent diversity in the final population; therefore, a k‐nearest neighbor list (where k is the number of objectives) is established and maintained to eliminate the solutions in the archive population. The k‐nearest neighbors of each antibody are founded and stored in a list memory. Once an antibody with minimal product of k‐nearest neighbors is deleted, the neighborhood relations of the remaining antibodies in the list memory are updated. Finally, the proposed algorithm is tested on 10 well‐known and frequently used multi‐objective problems and two many‐objective problems with 4, 6, and 8 objectives. Compared with five other state‐of‐the‐art multi‐objective algorithms, namely NSGA‐II, SPEA2, IBEA, HYPE, and NNIA, our method achieves comparable results in terms of convergence, diversity metrics, and computational time.     

Optimization of quality and operational costs through improved scheduling of harvest operations

The agriculture sector still lacks the tools and models to enhance the utilization of different resources. This paper addresses the vineyard harvesting problem in developing countries, with the objective of optimizing the wine quality and minimizing the operational costs. Heuristics were introduced to better assign the harvesting days to the different grape blocks that exist in the vineyard's field. The quality of the grapes was a key target as it can transform production from a pinnacle wine to a bulk one. We solved several numerical examples for verification and demonstrative purposes and found that our proposed approach finds solutions that significantly reduce the harvesting costs in the vineyard and considerably outperform Branch and Bound algorithm especially for large problems.     

Discussions of worker ants’ rule-based CHC dealing with changing environments

Contrary to popular belief, biologists discovered that worker ants are really not all hardworking. It has been found that in three separate 30-strong colonies of black Japanese ants (Myrmecina nipponica), about 20% of worker ants are diligent, 60% are ordinary, and 20% are lazy. That is called 20:60:20 rule. Though they are lazy, biologists suggested that lazy worker ants could be contributing something to the colony that is yet to be determined. In our last research, we used CHC (cross generational elitist selection, heterogeneous recombination, and cataclysmic mutation) with the worker ants’ rule (WACHC) aiming at solving optimization problems in changing environments. CHC is a nontraditional genetic algorithm (GA) which combines a conservative selection strategy that always preserves the best individuals found so far with a radical (highly disruptive) recombination operator. In our last research, we verified that WACHC performs better than CHC in only one case of fully changing environment. In this paper, we further discuss our proposed WACHC dealing with changing environment problems with varying degree of difficulty, compare our proposal with hypermutation GA which is also proposed for dealing with changing environment problems, and discuss the difference between our proposal and ant colony optimization algorithms.     

Parameter sensitivity study of the Nelder-Mead Simplex Method

This paper presents a parameter sensitivity study of the Nelder-Mead Simplex Method for unconstrained optimization. Nelder-Mead Simplex Method is very easy to implement in practice, because it does not require gradient computation; however, it is very sensitive to the choice of initial points selected. Fan-Zahara conducted a sensitivity study using a select set of test cases and suggested the best values for the parameters based on the highest percentage rate of successful minimization. Begambre-Laier used a strategy to control the Particle Swarm Optimization parameters based on the Nelder Mead Simplex Method in identifying structural damage. The main purpose of the paper is to extend their parameter sensitivity study to better understand the parameter’s behavior. The comprehensive parameter sensitivity study was conducted on seven test functions: B2, Beale, Booth, Wood, Rastrigin, Rosenbrock and Sphere Functions to search for common patterns and relationships each parameter has in producing the optimum solution. The results show important relations of the Nelder-Mead Simplex parameters: reflection, expansion, contraction, and Simplex size and how they impact the optimum solutions. This study is crucial, because better understanding of the parameters behavior can motivate current and future research using Nelder-Mead Simplex in creating an intelligent algorithm, which can be more effective, efficient, and save computational time.     

Discrete particle swarm optimization based on estimation of distribution for terminal assignment problems

Terminal assignment problem (TEAP) is to determine minimum cost links to form a network by connecting a given set of terminals to a given collection of concentrators. This paper presents a novel discrete particle swarm optimization (PSO) based on estimation of distribution (EDA), named DPSO-EDA, for TEAP. EDAs sample new solutions from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The DPSO-EDA incorporates the global statistical information collected from personal best solutions of all particles into the PSO, and therefore each particle has comprehensive learning and search ability. In the DPSO-EDA, a modified constraint handling method based on Hopfield neural network (HNN) is also introduced to fit nicely into the framework of the PSO and thus utilize the merit of the PSO. The DPSO-EDA adopts the asynchronous updating scheme. Further, the DPSO-EDA is applied to a problem directly related to TEAP, the task assignment problem (TAAP), in order to show that the DPSO-EDA can be generalized to other related combinatorial optimization problems. Simulation results on several problem instances show that the DPSO-EDA is better than previous methods.     

A new mathematical programming approach to multi-group classification problems

In this paper we introduce a goal programming formulation for the multi-group classification problem. Although a great number of mathematical programming models for two-group classification problems have been proposed in the literature, there are few mathematical programming models for multi-group classification problems. Newly proposed multi-group mathematical programming model is compared with other conventional multi-group methods by using different real data sets taken from the literature and simulation data. A comparative analysis on the real data sets and simulation data shows that our goal programming formulation may suggest efficient alternative to traditional statistical methods and mathematical programming formulations for the multi-group classification problem.     

A heuristic approach for packing identical rectangles in convex regions

In this paper we propose a heuristic approach for the problem of packing equal rectangles within a convex region. The approach is based on an Iterated Local Search scheme, in which the key step is the perturbation move. Different perturbation moves, both combinatorial and continuous ones, are proposed and compared through extensive computational experiments on a set of test instances. The overall results are quite encouraging.     

Some algebraic methods for solving multiobjective polynomial integer programs

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce.     

Shape optimization for tumor location

In non-invasive thermal diagnostics, accurate correlations between the thermal image at skin surface and interior human physiology are desired. In this work, an estimation methodology to determine unknown geometrical parameters of an embedded tumor is proposed. We define a functional that represents the mismatch between a measured experimental temperature profile, which may be obtained by infrared thermography on the skin surface, and the solution of an appropriate boundary problem. This functional is related to the geometrical parameters through the solution of the boundary problem, in such a way that finding the minimum of this functional form also means finding the unknown geometrical parameters of the embedded tumor. Sensitivity analysis techniques coupled with the adjoint method were considered to compute the shape derivative of the functional. Then, a nonmonotone spectral projected gradient method was implemented to solve the optimization problem of finding the optimal geometric parameters.     

Tabu search-based metaheuristic algorithm for software system reliability problems

This paper presents a new metaheuristic-based algorithm for complex reliability problems. The algorithm effectively uses features of the Tabu Search paradigm, with special emphasis on the exploitation of memory-based mechanisms. It balances intensification with diversification via the use of short-term and long-term memory. The algorithm has been thoroughly tested on benchmark problems from the literature as well as on a pool of random generated instances of very large scale software systems. The proposed algorithm proves to be robust with respect to its parameters and it is especially suited for very large scale instances of the reliability problem, when exact approaches are doomed to fail.