### Affinity Based Search Amount Control in Decomposition Based Evolutionary Multi-Objective Optimization

- Research Article in 10th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS)
- Authors
- Hiroyuki Sato, Minami Miyakawa, Keiki Takadama
- Abstract
This work proposes a search amount control method on each search part of the Pareto front in decomposition based evolutionary multi-objective optimization. The conventional MOEA/DC decomposes the Pareto front with a set of weight vectors and pairs one solution with each weight vector to approximate…

more »This work proposes a search amount control method on each search part of the Pareto front in decomposition based evolutionary multi-objective optimization. The conventional MOEA/DC decomposes the Pareto front with a set of weight vectors and pairs one solution with each weight vector to approximate the entire Pareto front with the set of solutions. Well-matched pairs of weight vector and solution contribute to uniformly approximating the Pareto front, and mismatched pairs having a long distance between weight vector and solution in the objective space deteriorate the approximation quality and the search. To eliminate mismatched pairs and improve the search performance, this work proposes affinity based search amount control method for MOEA/DC. Experimental results using continuous WFG4 test problems with 2-5 objectives show that the proposed method improves the well-matched pair ratio in all pairs of weight vector and solution and the search performance.

### Polynomial Mean-Centric Crossover for Directed Mating in Evolutionary Constrained Multi-Objective Continuous Optimization

- Research Article in 10th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS)
- Authors
- Minami Miyakawa, Hiroyuki Sato, Yuji Sato
- Abstract
This paper proposes a mean-centric crossover to improve the effectiveness of the directed mating utilizing useful infeasible solutions in evolutionary constrained multi-objective continuous optimization. The directed mating selects a feasible solution as the first parent and a solution dominating t…

more »This paper proposes a mean-centric crossover to improve the effectiveness of the directed mating utilizing useful infeasible solutions in evolutionary constrained multi-objective continuous optimization. The directed mating selects a feasible solution as the first parent and a solution dominating the first parent in the objective space from the population involving infeasible solutions as the second parent. Since infeasible solutions having better objective values than feasible ones have useful variables, it helps to improve the search performance. So far, the commonly used simulated binary crossover (SBX) have been employed to generate offspring from two parents selected by the directed mating. However, it is not clear that the commonly used SBX is appropriate also for parents selected by the directed mating. When the Pareto front exists on the boundary between the feasible and the infeasible regions in the variable space, a mean-centric crossover generating offspring around intermediate area of two parents would be more effective than SBX which is a parent-centric crossover generating offspring around two parents. This work proposes the polynomial mean-centric crossover (PMCX) and combines it with the directed mating. The experimental results show that the proposed PMCX achieves higher search performance than SBX on several test problems.

### On Arithmetic Functions in Actin Filament Networks

- Research Article in 10th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS)
- Authors
- Andrew Schumann
- Abstract
This paper is devoted to actin filament networks as a computation medium. The point is that actin filaments are sensitive to outer cellular stimuli (attractants as well as repellents) and they appear and disappear at different places of the cell to change the cell structure, e.g. its shape. Due to …

more »This paper is devoted to actin filament networks as a computation medium. The point is that actin filaments are sensitive to outer cellular stimuli (attractants as well as repellents) and they appear and disappear at different places of the cell to change the cell structure, e.g. its shape. Due to assembling and disassembling actin filaments, Amoeba proteus can move in responses to different stimuli. As a result, Amoeba proteus can be considered a simple reversible logic gate, where outer cellular signals are its inputs and the amoeba motions are its outputs. In this way, we can implement the FREDKIN logic gate on the amoeba behaviours. The actin filament networks have the same basic properties as neural networks: lateral inhibition; lateral activation; recurrent inhibition; recurrent excitation; feedforward inhibition; feedforward excitation; convergence/divergence. These networks can embody arithmetic functions defined recursively and corecursively within p-adic valued logic. Furthermore, within these networks we can define the so-called diagonalization for deducing undecidable arithmetic functions.

### Quantitative Assessment of Ambiguities in Plasmodium Propagation in Terms of Complex Networks and Rough Sets

- Authors
- Krzysztof Pancerz
- Abstract
A Physarum machine is a biological computing device implemented in the plasmodium of Physarum polycephalum, a one-cell organism able to build large and manifold networks of protoplasmic veins for solving different computational tasks. In the paper, we propose to use complex networks as an underlyin…

more »A Physarum machine is a biological computing device implemented in the plasmodium of Physarum polycephalum, a one-cell organism able to build large and manifold networks of protoplasmic veins for solving different computational tasks. In the paper, we propose to use complex networks as an underlying model of plasmodium propagation in Physarum machines. For such models, we define a measure, derived from rough set theory, for quantitative assessment of the cohesion of plasmodium connections between distinguished regions of interest. Rough sets are an appropriate tool to deal with some ambiguities which appear in plasmodium propagation.

### Talmudic Foundations of Mathematics

- Authors
- Andrew Schumann, Alexander V. Kuznetsov
- Abstract
In this paper, we assume that the mathematicians in proving new signiﬁcant theorem, such as Fermat’s Last Theorem, deal with combining proof trees on tree forests by using the analogy as an inference metarule. In other words, the real mathematical proofs cannot be formalized as discrete sequences, …

more »In this paper, we assume that the mathematicians in proving new signiﬁcant theorem, such as Fermat’s Last Theorem, deal with combining proof trees on tree forests by using the analogy as an inference metarule. In other words, the real mathematical proofs cannot be formalized as discrete sequences, but they are concurrent and can by formalized as analog processes within a space with some topological properties. For the ﬁrst time, inference metarules in a topological space were proposed in the Talmud within a general Judaic approach to concurrent or even massive-parallel conclusions. The mathematician does not think sequentially like a logical automaton, but concurrently, also. Hence, we suppose that the proof technique of real mathematics cannot be formalized by discrete methods. It is just a hypothesis of the foundations of mathematics that we can use discrete tools so that mathematics can be reduced to logic. We show in the paper how the mathematical proof can be formalized just by analog computations, not discrete ones.